We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate 1/T_1 at 250 mK and for (ii) the phase transition to a 3D ordered phase occuring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and Luttinger liquid model tested in detail over the whole fermion band.
We apply a generalized version of the Lieb-Schultz-Mattis Theorem to fermionic ladder systems to show the existence of a low-lying excited state (except for some special fillings). This can be regarded as a non-perturbative proof for the conservation under interaction of the sum of the Fermi wave vectors of the individual channels, corresponding to a generalized version of the Luttinger Theorem to fermionic ladder systems. We conclude by noticing that the Lieb-Schultz-Mattis Theorem is not applicable in this form to show the existence of low-lying excitations in the limit that the number of le…
The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)2CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modelling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the complete phase diagram.
We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines we determine the phase boundary and the order parameter of the low-temperature (3-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1 T^(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We fin…
Magnetic excitations in the strong-leg quantum spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a…
We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S…
Using micromechanical force magnetometry, we have measured the magnetization of the strong-leg spin-1/2 ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_2$ at temperatures down to 45 mK. Low-temperature magnetic susceptibility as a function of field exhibits a maximum near the critical field H_c at which the magnon gap vanishes, as expected for a gapped one-dimensional antiferromagnet. Above H_c a clear minimum appears in the magnetization as a function of temperature as predicted by theory. In this field region, the susceptibility in conjunction with our specific heat data yields the Wilson ratio R_…
We present two methods to determine whether the interactions in a Tomonaga-Luttinger liquid (TLL) state of a spin-$1/2$ Heisenberg antiferromagnetic ladder are attractive or repulsive. The first method combines two bulk measurements, of magnetization and specific heat, to deduce the TLL parameter that distinguishes between the attraction and repulsion. The second one is based on a local-probe, NMR measurements of the spin-lattice relaxation. For the strong-leg spin ladder compound $\mathrm{(C_7H_{10}N)_2CuBr_4}$ we find that the isothermal magnetic field dependence of the relaxation rate, $T_1…
We study the Luttinger-liquid parameter $K_ρ$ of the Hubbard chain and the Hubbard ladder models by the ordinary perturbation method combined with the Luttinger-liquid relation. According to the Luttinger-liquid relation, the critical exponent $K_ρ$ is related to the charge susceptibility $χ_c$ and the Drude weight D by $ K\sbρ={1/2}(πχ_c D)^{1/2}$. By calculating these quantities with the perturbation method, we obtain $K_ρ$ at the first-order analytically and up to the second-order numerically. We compare these results with results of the Bethe ansatz for the Hubbard chain and that of the nu…
The $S=1/2$ quantum spin ladder system with the anisotropic ferromagnetic exchange interaction on the rung under magnetic field is investigated using the numerical diagonalization and the density matrix renormalization group (DMRG) analyses. It is found that the nematic-spin-correlation-dominant Tomonaga-Luttinger liquid (TLL) appears in some high magnetic field. It is included in the TLL phase where the two-magnon bound state is realized. For some suitable parameters, after the field-induced phase transition from this two-magnon-bound TLL phase to the single-magnon TLL one, the re-entrant tra…
The integrable su(4)-invariant spin-ladder model with boundary defect is studied using the Bethe ansatz method. The exact phase diagram for the ground state is given and the boundary quantum critical behavior is discussed. It consists of a gapped phase in which the rungs of the ladder form singlet states and a gapless Luttinger liquid phase. It is found that in the gapped phase the boundary bound state corresponds to an unscreened local moment, while in the Luttinger liquid phase the local moment is screened at low temperatures in analogy to the Kondo effect.
An exact solvable 'zig-zag' ladder model of degenerated spinless fermions is proposed and solved exactly by the means of the Bethe ansatz. An effective attractive hard-core interaction and direct Coulomb repulsion of fermions on the nearest-neighbor sites of different chains induce a new phase state of the ladder. We give a detailed analysis of the exact phase diagram at zero temperature, that is characterized by two phases at the filling exceeding 2/3: itinerant and 'frozen' fermions, for which two different species reside in spatially separate regions. The critical exponents describing asymp…
Magnetic insulators have proven to be usable as quantum simulators for itinerant interacting quantum systems. In particular the compound (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$ (short (Hpip)$_{2}$CuBr$_{4}$) was shown to be a remarkable realization of a Tomonaga-Luttinger liquid (TLL) and allowed to quantitatively test the TLL theory. Substitution weakly disorders this class of compounds and allows thus to use them to tackle questions pertaining to the effect of disorder in TLL as well, such as the formation of the Bose glass. As a first step in this direction we present in this paper a study of th…
Using the recently developed transfer-matrix renormalization group method, we have studied the thermodynamic properties of two-leg antiferromagnetic ladders in the magnetic field. Based on different behavior of magnetization, we found disordered spin liquid, Luttinger liquid, spin-polarized phases and a classical regime depending on magnetic field and temperature. Our calculations in Luttinger liquid regime suggest that both the divergence of the NMR relaxation rate and the anomalous specific heat behavior observed on Cu$_2$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$}are due to quasi-one-dimensional effect…
A phase diagram of the t-J three-leg ladder as a function of hole dopping is derived in the limit where the coupling parameters along the rungs, $t_{\perp}$ and $J_{\perp}$, are taken to be much larger than those along the legs, $t_{||}$ and $J_{||}$ At large exchange coupling along the rungs, $J_{\perp}/t_{\perp}> 3 / \sqrt{2}$, there is a transition from a low-dopping Luttinger liquid phase into a Luther-Emery liquid at a critical hole concentration $n_{crit}\approx 1/3$. In the opposite case, $J_{\perp}/t_{\perp}< 3 / \sqrt{2}$, there as a sequence of three Luttinger liquid phases (LLI, LLI…
We derive a Hamiltonian for a two-leg ladder which includes an arbitrary number of charge and spin interactions. To illustrate this Hamiltonian we consider two examples and use a renormalization group technique to evaluate the ground state phases. The first example is a two-leg ladder with zigzagged legs. We find that increasing the number of interactions in such a two-leg ladder may result in a richer phase diagram, particularly at half-filling where a few exotic phases are possible when the number of interactions are large and the angle of the zigzag is small. In the second example we determ…
We study the transport properties of three Luttinger liquid wires (with possibly different interaction strength), connected through a Y-junction, within the scattering state formalism. We first formulate the problem in current algebra language and focus on the case of a symmetric set-up, for which the scattering matrix and the matrix of conductances is parametrized by two variables. For these we derive coupled RG equations, first in a ladder summation up to infinite order in the interaction. The fixed point structure and the implicit solution of these equations is presented. It is shown that h…
We present experiments on the magnetic field-dependent thermal transport in the spin-1/2 ladder system (C$_5$H$_{12}$N)$_2$CuBr$_4$. The thermal conductivity $κ(B)$ is only weakly affected by the field-induced transitions between the gapless Luttinger-liquid state realized for $B_{c1}< B < B_{c2}$ and the gapped states, suggesting the absence of a direct contribution of the spin excitations to the heat transport. We observe, however, that the thermal conductivity is strongly suppressed by the magnetic field deeply within the Luttinger-liquid state. These surprising observations are discussed i…
Correlation functions and low-energy excitations are investigated in the asymmetric two-leg ladder consisting of a Hubbard chain and a noninteracting tight-binding (Fermi) chain using the density matrix renormalization group method. The behavior of charge, spin and pairing correlations is discussed for the four phases found at half filling, namely, Luttinger liquid, Kondo-Mott insulator, spin-gapped Mott insulator and correlated band insulator. Quasi-long-range antiferromagnetic spin correlations are found in the Hubbard leg in the Luttinger liquid phase only. Pair-density-wave correlations ar…
We study hard-core bosons with unfrustrated nearest-neighbor hopping $t$ and repulsive interaction $V$ on a zig-zag ladder. As a function of the boson density $ρ$ and $V/t$, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for $ρ<1/3$ (and $ρ>2/3$) at any value of $V/t$. At commensurate densities $ρ=1/3$, $1/2$, and $2/3$ insulating (crystalline) phases are stabilized for a sufficiently large interaction $V$. For intermediate densities $1/3<ρ<2/3$ and large $V/t$, the ground state shows a clear evidence of a bound state of two bos…
We study the entanglement spectrum (ES) and entropy between two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. This problem gives access to the entanglement properties of various interesting systems, such as spin ladders as well as two-dimensional topological phases. By expanding interchain interactions to quadratic order in bosonic fields, we are able to calculate the ES for both gapped and gapless systems using only methods for free theories. In certain gapless phases of coupled non-chiral TLLs, we interestingly find an ES with a dispersion relation proportional to th…
We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder (C$_{7}$H$_{10}$N)$_{2}$CuBr$_{4}$ in a magnetic field $H=9$~T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\approx1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.
In these lecture notes, the basic physics of Fermi liquids and Luttinger liquids is presented. Fermi liquids are discussed both from a phenomenological viewpoint, in relation to microscopic approaches, and as renormalization group fixed points. Luttinger liquids are introduced using the bosonization formalism, and their essential differences with Fermi liquids are pointed out. Applications to transport effects, the effect of disorder, quantum spin chains, and spin ladders, both insulating and metallic, are given.
One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depends on the so-called Jordan-Wigner string, real-space observables are similar for free-fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed, and leads to a totally different physics between free-fermion…
We demonstrate that quantum-critical spin dynamics can be probed in high magnetic fields using muon-spin relaxation ($μ^{+}$SR). Our model system is the strong-leg spin ladder bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). In the gapless Tomonaga-Luttinger liquid phase we observe finite-temperature scaling of the $μ^{+}$SR $1/T_1$ relaxation rate which allows us to determine the Luttinger parameter $K$. We discuss the benefits and limitations of local probes compared with inelastic neutron scattering.
Inelastic neutron scattering is used to measure the spin excitation spectrum of the Heisenberg $S=1/2$ ladder material (C$_7$H$_10$N)$_2$CuBr$_4$ in its entirety, both in the gapped spin-liquid and the magnetic field induced Tomonaga-Luttinger spin liquid regimes. A fundamental change of the spin dynamics is observed between these two regimes. DMRG calculations quantitatively reproduce and help understand the observed commensurate and incommensurate excitations. The results validate long-standing quantum field theoretical predictions, but also test the limits of that approach.
We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet $d_{xy}$ in the non-trivial phase and triplet $S_z=0$ in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, …
Recently, conductivity measurements were performed on the hole-doped two-leg ladder material Sr_{14-x}Ca_xCu_{24}O_{41}. In this work, we calculate the conductivity for doped two-leg ladders using a model of hole-pairs forming a strongly correlated liquid - a single component Luttinger liquid - in the presence of disorder. Quantum interference effects are handled using renormalization group methods. We find that our model can account for the low energy features of the experimental results. However, at higher energies the experiments show deviations from the predictions of this model. Using the…
The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point which unifies different competing dimerized orders and a scalar chirality phase which breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is governed by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of an exact U(1) self-duality symmetry.
Recently Lin, Balents, and Fisher have demonstrated that two-leg Hubbard ladders and armchair carbon nanotubes renormalize onto the integrable SO(8) Gross-Neveu model. We exploit this integrability to examine these systems in their doped phase. Using thermodynamic Bethe ansatz, we compute exactly both the spin and single particle gaps and the Luttinger parameter describing low energy excitations. We show both the spin and particle gap do not vanish at finite doping, while the Luttinger parameter remains close to its free fermionic value of 1. A similar set of conclusions is drawn for the undop…
The three-leg ladder has one odd-parity and two even-parity channels. At low doping these behave quite differently. Numerical calculations for a t-J model show that the initial phase upon hole doping has two components - a conducting Luttinger liquid in the odd-parity channel, coexisting with an insulating (i.e. undoped) spin liquid phase in the even-parity channels. This phase has a partially truncated Fermi surface and violates the Luttinger theorem. This coexistence of conducting fermionic and insulating paired bosonic degrees of freedom is similar to the recent proposal of Geshkenbein, Iof…
We study the magnetic phase diagram of two coupled mixed-spin $(1,{1/2})$ Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram--containing the Luttinger liquid phase, the plateau phase with a magnetization per rung $M=1/2$, and the fully polarized phase--is closely related to the generic $(J/U,μ/U)$ phase diagram of the one-dimensional boson Hubbard model.
We study a half filled ladder of spinless fermions. We show that contrarily to a single chain, the ladder becomes a Mott insulator for arbitrarily small repulsive interactions. We obtain the full phase diagram and physical quantities such as the charge gap. We show that there is only a single insulating phase for repulsive interactions, regardless of the stength of the interchain hopping and single chain Mott gap. There is thus no confinement-deconfinement transition in this system but a simple crossover. We show that upon doping the system becomes a Luttinger liquid with a universal parameter…
In this work we derive a new scheme to calculate Tomonaga-Luttinger liquid (TLL) parameters and holon (charge modes) velocities in a quasi-1D material that consists of two-leg ladders coupled through Coulomb interactions. Firstly, we obtain an analytic formula for electron-electron interaction potential along the conducting axis for a generalized charge distribution in a plane perpendicular to it. In the second step we introduce many-body screening that is present in a quasi-1D material. To this end we propose a new approximation for the charge susceptibility. Based on this we are able to find…
We measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a spinon continuum at intermediate fields characteristic of the Luttinger-liquid phase. By tuning the magnetic field, we drive the fractionalization of magnons into spinons and, in this deconfined regime, observe both commensurate and incommensurate continua.
To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $π$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomona…
A theoretical description is presented for low-temperature magnetic-field induced three-dimensional (3D) ordering transitions in strongly anisotropic quantum antiferromagnets, consisting of weakly coupled antiferromagnetic spin-1/2 chains and ladders. First, effective continuum field theories are derived for the one-dimensional subsystems. Then the Luttinger parameters, which determine the low-temperature susceptibilities of the chains and ladders, are calculated from the Bethe ansatz solution for these effective models. The 3D ordering transition line is obtained using a random phase approxim…
An interacting spinless fermion wire coupled to a three-dimensional (3D) semiconducting substrate is approximated by a narrow ladder model (NLM) with varying number of legs. We compute density distributions, gaps, charge-density-wave (CDW) order parameters, correlation functions, and the central charge using the density-matrix renormalization group method. Three ground-state phases are observed: a one-component Luttinger liquid, a quasi-one-dimensional (1D) CDW insulator, and a band insulator. We investigated the convergence of the NLM properties with increasing number of legs systematically a…
We study the spin-1/2 two-leg Heisenberg ladder with four-spin ring exchanges under a magnetic field. We introduce an exact duality transformation which is an extension of the spin-chirality duality developed previously and yields a new self-dual surface in the parameter space. We then determine the magnetic phase diagram using the numerical approaches of the density-matrix renormalization-group and exact diagonalization methods. We demonstrate the appearance of a magnetization plateau and the Tomonaga-Luttinger liquid with dominant vector-chirality quasi-long-range order for a wide parameter …
The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides usual rung-singlet and saturated ferromagnetic states we obtai…
A two-leg ladder with $n$-component fermionic fields in the chains has been considered using an analytic renormalization group method. The fixed points and possible phases have been determined for generic filling as well as for a half-filled system and for the case when one of the subbands is half filled. A weak-coupling Luttinger-liquid phase and several strong-coupling gapped phases have been found. In the Luttinger liquid phase, for the most general spin dependence of the couplings, all $2n$ modes have different velocities if the interband scattering processes are scaled out, while $n$ doub…
Neutron diffraction is used to investigate the field-induced, antiferromagnetically ordered state in the two-leg spin-ladder material (Hpip)2CuBr4. This "classical" phase, a consequence of weak interladder coupling, is nevertheless highly unconventional: its properties are influenced strongly by the spin Luttinger-liquid state of the ladder subunits. We determine directly the order parameter (transverse magnetization), the ordering temperature, the spin structure, and the critical exponents around the transition. We introduce a minimal, microscopic model for the interladder coupling and calcul…
We report low temperature electron spin resonance experimental and theoretical studies of an archetype $S=1/2$ strong-rung spin ladder material (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$. Unexpected dynamics is detected deep in the Tomonaga-Luttinger spin liquid regime. Close to the point where the system is half-magnetized (and believed to be equivalent to a gapless easy plane chain in zero field) we observed orientation-dependent spin gap and anomalous $g$-factor values. Field theoretical analysis demonstrates that the observed low-energy excitation modes in magnetized (C$_{5}$H$_{12}$N)$_{2}$CuBr$_…
We study a lattice realization of a Luttinger liquid interacting with a bath of quantum spins in terms of an antiferromagnetic S=1/2 Heisenberg chain, where each spin is also coupled to a σ=1/2 Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi one dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction J' there are two phases corresponding to an effective spin-1 Heisenberg ch…
We introduce a new Kondo ladder model by coupling the well-known Takhtajan-Babujan S=1 chain to a half-filled one-dimensional electron gas, and we solve it using quantum field theory techniques. Through the so-called underscreened Kondo effect, this gives novel insights into low-dimensional spin liquid systems. For instance, the optical conductivity reveals only a pseudogap at $k=π$ despite of the insulating state, a coherent magnon peak in the dynamical spin susceptibility coexists with an incoherent spinon background, the magnetization yields a fractional-like quantization. More generally, t…
We consider the isotropic spin-1/2 two-leg ladders with the dominant spatially modulated rung exchanges. We study the effect of a uniform magnetic field on the ground state phase diagram of the model using the perturbation theory and the numerical Lanczos method. The ground state phase diagram consists of two gapless Luttinger liquid (LL) and three gapped phases. Numerically, we calculate the concurrence between two spins and entanglement entropy between legs. Numerical experiment shows that in principle the gapless LL phases are different. In the first LL phase, only spins on rungs are entang…
We present an extensive NMR study of the spin-1/2 antiferromagnetic Heisenberg ladder Cu2(C5H12N2)2Cl4 in a magnetic field range 4.5 - 16.7 T. By measuring the proton NMR relaxation rate 1/T_1 and varying the magnetic field around the critical field H_c1 = Delta / gμ_B = 7.5 T, we have studied the transition from a gapped spin liquid ground state to a gapless magnetic regime which can be described as a Luttinger liquid. We identify an intermediate regime T > |H-H_c1|, where the spin dynamics is (possibly) only controlled by the T=0 critical point H_c1.
We study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $ν= 1/m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer $m$. In contrast for even integer $m$, the spin sector remains gapless and the resulting insu…
We analyze a model of two-leg Hubbard ladders weakly coupled by interladder tunneling. At half filling a semimetallic state with small Fermi pockets is induced beyond a threshold tunneling strength. The sign changes in the single electron Green's function relevant for the Luttinger Sum Rule now take place at surfaces with both zeroes and infinities with important consequences for the interpretation of ARPES experiments. Residual interactions between electron and hole-like quasi-particles cause a transition to long range order at low temperatures. The theory can be extended to small doping lead…
In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields Hc1 and Hc2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understan…
The strong-leg S=1/2 Heisenberg spin ladder system (C7H10N)2CuBr4 is investigated using Density Matrix Renormalization Group (DMRG) calculations, inelastic neutron scattering, and bulk magneto-thermodynamic measurements. Measurements showed qualitative differences compared to the strong-rung case. A long-lived two-triplon bound state is confirmed to persist across most of the Brillouin zone in zero field. In applied fields, in the Tomonaga-Luttinger spin liquid phase, elementary excitations are attractive, rather than repulsive. In the presence of weak inter-ladder interactions, the strong-leg…
The 2-leg t-J ladder forms a spin liquid at half-filling which evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e. rungs and legs equal) as a function of electron density n and the ratio J/t (>0). Two known limiting cases are: n<1/2 which is a single band Luttinger liquid and small hole doping for J/t close to 0 which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for 1>n>1/2. We find evidences for gapless behavior in both spin and charge channels for J/t<0…
Using a combination of neutron scattering, calorimetry, Quantum Monte Carlo (QMC) simulations and analytic results we uncover confinement effects in depleted, partially magnetized quantum spin ladders. We show that introducing non-magnetic impurities into magnetized spin ladders leads to the emergence of a new characteristic length L in the otherwise scale-free Tomonaga-Luttinger liquid (serving as the effective low-energy model). This results in universal LT scaling of staggered susceptibilities. Comparison of simulation results with experimental phase diagrams of prototypical spin ladder com…
We derive an effective low-energy theory for a ferromagnetic $(2N+1)$-leg spin-$\frac{1}{2}$ ladder with strong $XXZ$ anisotropy $\left|J_{\parallel}^z\right|\ll \left|J_{\parallel}^{xy}\right|$, subject to a kink-like non-uniform magnetic field $B_z(X)$ which induces a domain wall (DW). Using Bosonization of the quantum spin operators, we show that the quantum dynamics is dominated by a single one-dimensional mode, and is described by a sine-Gordon model. The parameters of the effective model are explored as functions of $N$, the easy-plane anisotropy $Δ=-J_{\parallel}^z/J_{\parallel}^{xy}$, …
We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. First the renormalization group (RG) equation for weak interaction is derived in the current operator language both using the operator product expansion and the equation of motion method. To access the strong coupling regime, two methods of deducing the RG equation from pertur…
We study two-leg spin ladder systems analytically by using a t-J model which includes the interchain spin exchange and the interchain hopping term. The spin part is mapped to a quantum sine-Gordon model via a bosonization method that fully accounts for the phase fluctuation. The spin gap in the Luther-Emery phase evolves to gapless Luttinger liquid phases in even-ladders at certain doping concentration. This transition occurs as doping rate increases and/or the ratio of the interchain spin exchange and hopping to the intrachain couplings decreases. We also estimate the transition temperature a…
We investigate a ladder system with two inequivalent legs, namely a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge …
Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbors interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a 'spin-locked' cluster Luttinger liquid at strong interactions alon…
