We test the analytical formula for the enhancement of the nuclear magnetic resonance rate $T_1^{-1}$ by the critical spin fluctuations, over the simple power-law dependence predicted for a purely one-dimensional spin system, recently derived in the random phase approximation [M. Dupont et al., Phys. Rev. B 98, 094403 (2018)]. This prediction is experimentally confirmed by excellent fits to the published temperature dependence of $T_1^{-1}$ data in the two representative spin compounds, (C$_7$H$_{10}$N)$_2$CuBr$_4$ (DIMPY) and BaCo$_2$V$_2$O$_8$, providing at the same time a direct and convenient experimental determination of the Tomonaga-Luttinger-liquid parameter $K$, very well in agreement with theoretical predictions.
The differential cross section for resonant Raman scattering from the collective modes in a one dimensional system of interacting electrons is calculated non-perturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behaviour in quasi-one dimensional electron systems.
It is shown that for some special values of Hamiltonian parameters the Tomonaga-Luttinger model with nonlinear dispersion is unitary equivalent to the system of noninteracting fermions. For such parameter values the density-density propagator of the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion can be found exactly. In a generic situation the exact solution can be used as a reference point around which a perturbative expansion in orders of certain irrelevant operators may be constructed.
We find a unitary operator which asymptotically diagonalizes the Tomonaga-Luttinger hamiltonian of one-dimensional spinless electrons. The operator performs a Bogoliubov rotation in the space of electron-hole pairs. If bare interaction of the physical electrons is sufficiently small this transformation maps the original Tomonaga-Luttinger system on a system of free fermionic quasiparticles. Our representation is useful when the electron dispersion deviates from linear form. For such situation we obtain non-perturbative results for the electron gas free energy and the density-density propagator…
We examine the spectral function of the single electron Green function at finite temperatures for the Tomonaga-Luttinger model which consists of the mutual interaction with only the forward scattering. The spectral weight, which is calculated as a function of the frequency with the fixed wave number, shows that several peaks originating in the excitation spectra of charge and spin fluctuations vary into a single peak by the increase of temperature.
Hidden duality and associated instabilities of the spinless Luttinger liquid on lattice are reported. The local quantum fluctuations and the long-distance chiral modes compete and as a result produce a hierarchy of exotic charge/density instabilities. Explicit bosonic quantum operators for the local density fluctuations are constructed and are used to make identification of the Luttinger liquid with the classical 2D Coulomb gas with $θ$-term and with the rich hidden duality.
The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low energy spectrum of noniteracting fermions is identical to the one of a harmonic chain. This fermion-boson transmutation allows to describe interacting fermions as a system of coupled oscillators. Tomonaga's model of interacting nonrelativistic fermions on a ring is presented and first discussed in low order perturbation theory. After introducing the concept of two independent species of right and left moving fermions the exact solution of the Tomonaga-Luttinger model is discussed…
We calculate the finite temperature single hole spectral function and the spin dynamic structure factor of spinfull one-dimensional Tomonaga-Luttinger liquid. Analytical expressions are obtained for a number of special cases. We also calculate the single hole spectral function of a spin gapped Luther-Emery liquid and obtain exact results at the free fermion point K_s=1/2. These results may be applied to the analysis of angle resolved photoemission and neutron scattering experiments on quasi-one-dimensional materials.
Arguments are presented that in the one-dimensional Kondo lattice model f-electron spins participate in filling of the Fermi sea. It is shown that in its paramagnetic phase this model belongs to the spin-1/2 Tomonaga-Luttinger liquid universality class. The ratio of the spin and charge velocities v_s/v_c and K_c are estimated to be of the order of (T_K/E_F)^{1/2}.
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.
The validity of the CFT in the Tomonaga-Luttinger liquid with the $1/r^β$ type long-range interactions is discussed. The arguments by CFT for long-range forward scatterings predict the finite size corrections which depend on the power of the long-range interactions. Especially from finite size corrections in the ground state, we find the effective central charge deviates from $c=1$. These conformal arguments are numerically tested in the one particle excitations and the ground state.
The Tomonaga-Luttinger model with impurity is studied by means of flow equations for Hamiltonians. The system is formulated within collective density fluctuations but no use of the bosonization formula is made. The truncation scheme includes operators consisting of up to four fermion operators and is valid for small electron-electron interactions. In this regime, the exact expression for the anomalous dimension is recovered. Furthermore, we verify the phase diagram of Kane and Fisher also for intermediate impurity strength. The approach can be extended to more general one-body potentials.
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.
We study a single-particle density of states (DOS) in a model of Tomonaga-Luttinger liquid with small (large) values of the Luttinger parameter $K_\rc < 0.17$, ($K_\rc > 5.82$), in the charge sector. We explain that such values of $K_\rc$ may be achieved by electron-phonon interactions without generating the spin gap. We suggest that electron-phonon interactions can be partially incorporated into the Tomonaga-Luttinger liquid scheme by introducing frequency dependent $K_\rc(ω)$. We demonstrate that when the low-frequency asymptotic value $K_\rc(0) < 0.17$ or $K_\rc(0) > 5.82$, the single-parti…
We develop a theory of spontaneously magnetized Tomonaga-Luttinger liquid (SMTLL) in geometrically frustrated quasi-one-dimensional quantum magnets by taking an $S=1/2$ ferrimagnet on a union-jack lattice as an example. We show that a strong frustration leads to a spontaneous magnetization because of the ferrimagnetic nature of lattice. Due to the ferrimagnetic order, the local magnetization has an incommensurate oscillation with the position. We show that the spontaneously magnetized TLL is smoothly connected to the existence of a Nambu-Goldstone boson in the canted ferrimagnetic phase of a t…
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…
As voltage decreases d.c. condctivity of a Tomonaga-Luttinger liquid wire collapses to a small value determined by the length of the wire and its contacts with the leads. In condition that voltage drop (V) mostly occurs across a tunnel barrier inside the wire the tunneling density of states and, hence, the differential conductivity are shown to exhibit an interference structure resulted from the transition of the Luttinger liquid quasiparticles into free electrons at the exits from the wire. The finite length correction to the scale-invariant $V^{2/g-2}$ dependence of the conductivity oscillat…
The Tomonaga-Luttinger-Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.
An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on infinite DMRG utilizing a finite system with infinite boundary conditions, which can be applied to correlation functions near an impurity. For the $S=1/2$ chain, we demonstrate that the full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with…
We investigate charge fractionalizations in artificial Tomonaga-Luttinger liquids (TLLs) composed of two capacitively coupled quantum Hall edge channels (ECs) in graphene. The interaction strength of the artificial TLLs can be controlled through distance W between the ECs. We show that the fractionalization ratio r and the TLL mode velocity v vary with W. The experimentally obtained relation between v and r follows a unique function predicted by the TLL theory. We also show that charged wavepackets are reflected back and forth multiple times at both ends of the TLL region.
Photo-induced metallic states in a Mott insulator are studied for the half-filled, one-dimensional Hubbard model with the time-dependent density matrix renormalization group. An irradiation of strong AC field is found to create a linear dispersion in the optical spectrum (current-current correlation) in the nonequilibrium steady state reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux-Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier-dopin…
In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have calculated the electron density of states (DOS) for tunneling into a repulsive Luttinger liquid close to the location of an impurity. The result of their calculation is a DOS which is enhanced with respect to the pure system, and moreover diverging for not too strong repulsion. In this Comment we intend to show that OF's calculation suffers from a subtle flaw which, being corrected, results into a DOS not only vanishing at zero frequency but in fact suppressed in comparison with the DOS of a pure Luttinger liquid.
Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional $t$-$J$ model, to study the universal property of the $c=1$ conformal field theory with U(1) symmetry near the $K\to\infty$ instability. On the analogy of the spinless fermion, we discuss that the compressibility behaves as $κ\propto (J_c-J)^{-1}$, and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite size effect from the result of the exact diagonalization.
We provide evidence for the mapping of critical spin-1 chains, in particular the SU(3) symmetric bilinear-biquadratic model with additional interactions, to free boson theories using exact diagonalization and the density matrix renormalization group algorithm. Using the correspondence with a conformal field theory with central charge c=2, we determine the analytic formulae for the scaling dimensions in terms of four Tomonaga-Luttinger liquid parameters. By matching the lowest scaling dimensions, we numerically calculate these field-theoretic parameters and track their evolution as a function o…
The von Neumann entanglement entropy is studied with the density-matrix renormalization group technique. We propose a simple approach to calculate the central charge using the entanglement entropy for one-dimensional (1D) quantum system. This approach is applied to a couple of quantum systems: (i) 1D frustrated spin model and (ii) 1D half-filled spinless fermions with nearest-neighbor repulsion; and, it is confirmed that the central charge is estimated very accurately for the both systems. Also, a new method to determine the critical point between TL-liquid and gapped (or ordered) phases from …
One-dimensional electron systems (1DESs) exhibit properties that are fundamentally different from higher-dimensional systems. For example, electron-electron interactions in 1DESs have been predicted to induce Tomonaga-Luttinger liquid behavior. Naturally-occurring grain boundaries in single-layer semiconducting transition metal dichalcogenides provide 1D conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behavior. Clear identification of the electronic ground state of this system has been hamp…
We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the Umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitat…
We study the relaxation dynamics of the one-dimensional Tomonaga-Luttinger model after an interaction quench paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical form are investigated all leading to universal Luttinger liquid physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the Luttinger liquid phenomenology. For generic regular potentials the large time decay of the momentum distribution function towards the steady-state value is characterized by a pow…
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…
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…
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_…
The magnetic response of antiferromagnetic CsO2, coming from the p-orbital S=1/2 spins of anionic O2- molecules, is followed by 133Cs nuclear magnetic resonance across the structural phase transition occuring at Ts1=61 K on cooling. Above Ts1, where spins form a square magnetic lattice, we observe a huge, nonmonotonic temperature dependence of the exchange coupling originating from thermal librations of O2- molecules. Below Ts1, where antiferromagnetic spin chains are formed as a result of p-orbital ordering, we observe a spin Tomonaga-Luttinger-liquid behavior of spin dynamics. These two inte…
The orthogonality catastrophe in a Tomonaga-Luttinger liquid with an impurity is reexamined for the case when the interaction parameter or the dimensionless conductance is g=1/2. By transforming bosons back to fermions, the Hamiltonian is reduced to a quadratic form, which allows for explicit calculation of the overlap integral and the local density of states at the defect site. The exponent of the orthogonality catastrophe due to a backward scattering center is found to be 1/8, in agreement with previous studies using different approaches. The time-dependence of the core-hole Green's function…
We use nuclear magnetic resonance to map the complete low-temperature phase diagram of the antiferromagnetic Ising-like spin-chain system BaCo2V2O8 as a function of the magnetic field applied along the chains. In contrast to the predicted crossover from the longitudinal incommensurate phase to the transverse antiferromagnetic phase, we find a sequence of three magnetically ordered phases between the critical fields 3.8 T and 22.8 T. Their origin is traced to the giant magnetic-field dependence of the total effective coupling between spin chains, extracted to vary by a factor of 24. We explain …
Properties of fluctuations in two chains of Tomonaga-Luttinger liquids coupled by the interchain hopping have been studied by calculating retarded response functions $χ^R_ρ (q_x,q_y;ω)$ for charge and $χ^R_{\p} (q_x,q_y;ω)$ for spin where $q_x$ and $q_y (=0$ or $π$) denote the longitudinal and transverse wave vector, respectively, and $ω$ is the frequency. We have found the notable fact that the repulsive intrachain interaction results in the clear enhancement of ${\rm{Im}}χ^R_\p (q_x,π;ω)$ and the suppression of ${\rm{Im}}χ^R_ρ(q_x,π;ω)$ at low energies. This result indicates the importance o…
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…
Combining inelastic neutron scattering and numerical simulations, we study the quasi-one dimensional Ising anisotropic quantum antiferromagnet \bacovo\ in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinl…
We report 13C nuclear magnetic resonance measurements on single wall carbon nanotube (SWCNT) bundles. The temperature dependence of the nuclear spin-lattice relaxation rate, 1/T1, exhibits a power-law variation, as expected for a Tomonage-Luttinger liquid (TLL). The observed exponent is smaller than that expected for the two band TLL model. A departure from the power law is observed only at low T, where thermal and electronic Zeeman energy merge. Extrapolation to zero magnetic field indicates gapless spin excitations. The wide T range on which power-law behavior is observed suggests that SWCNT…
The Tomonaga--Luttinger parameter $K_ρ$ determines the critical behavior in quasi one-dimensional correlated electron systems, e.g., the exponent $α$ for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate $K_ρ$ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine $K_ρ$ in the phase diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and c…
We discuss effects of $1/r^β$ type long-range (LR) interactions in a tight-binding model by utilizing the bosonization technique, renormalization group and conformal field theory (CFT). We obtain the low energy action known for Kibble's model which generates the mass gap in 3 dimension when $β=1$, the Coulomb force case. In one dimension, the dispersion relations predict that the system remains gapless even for $β=1$ and the existences of Tomonaga-Luttinger liquid (TLL) when $β> 1$. When $β=1$, the LR interactions break TLL in the long wavelength limits, even if the strength is very small. We …
Specific heat experiments on single crystals of the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C_9H_24N_4)(NO_2)ClO_4, alias NTENP, have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C_mag) is proportional to temperature (T) above a critical field H_c, at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C_mag/T increases as the magnetic field approaches H_c from above. The data are in g…
We establish a theoretical framework for artificial control of the power-law singularities in Tomonaga-Luttinger liquid states. The exponent governing the power-law behaviors is found to increase significantly with an increase in the amplitude of the periodic electric field modulation applied externally to the system. This field-induced shift in the exponent indicates the tunability of the transport properties of quasi-one-dimensional electron systems.
We calculate the tunneling density of states for a Tomonaga-Luttinger liquid placed under a strong bias voltage. For the tunneling through a side-coupled point contact, one can observe the power law singularities in the tunneling density of states separately for the right- and left-movers despite the point-like tunnel contact. Deviations of the nonequilibrium tunneling exponents from the equilibrium case are discussed.
Recent transport measurements [Churchill \textit{et al.} Nat. Phys. \textbf{5}, 321 (2009)] found a surprisingly large, 2-3 orders of magnitude larger than usual $^{13}$C hyperfine coupling (HFC) in $^{13}$C enriched single-wall carbon nanotubes (SWCNTs). We formulate the theory of the nuclear relaxation time in the framework of the Tomonaga-Luttinger liquid theory to enable the determination of the HFC from recent data by Ihara \textit{et al.} [Ihara \textit{et al.} EPL \textbf{90}, 17004 (2010)]. Though we find that $1/T_1$ is orders of magnitude enhanced with respect to a Fermi-liquid behav…
We study theoretically the nonlinear optical response of Tomonaga-Luttinger spin liquid in the context of terahertz (THz) two-dimensional coherent spectroscopy (2DCS). Using the gapless phase of the XXZ-type spin chain as an example, we show that its third-order nonlinear magnetic susceptibilities $χ^{(3)}_{+--+}$ and $χ^{(3)}_{-++-}$ exhibit photon echo, where $\pm$ refers to the left/right-hand circular polarization with respect to the $S^z$ axis. The photon echo arises from a ``lensing'' phenomenon in which the wave packets of fractional excitations move apart and then come back toward each…
We apply field theoretical renormalization group (RG) methods to describe the Tomonaga-Luttinger model as an important test ground to deal with spin-charge separation effects in higher spatial dimensions. We compute the anomalous dimension associated with the one-particle Green's functions $G_{(a)R}$. We calculate the RG equations for the renormalized forward couplings $g_{2R}$ and $g_{4R}$ up to two-loop order and demonstrate that they don't flow in the vicinities of the Fermi points (FPs). We solve the Callan-Symanzik equation for $G_{(a)R}$ in the neighborhood of the FPs. We calculate the r…
We study persistent currents in semiconductor ballistic rings with spin-orbit Rashba interaction. We use as a working model the multicomponent Tomonaga-Luttinger liquid which arises due to the nonparabolic dispersion relations of electrons in the rings with rather strong spin-orbit coupling. This approach predicts some new characteristic features of persistent currents, which may be observed in experimental studies of semiconductor ballistic rings.
K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is a highly one-dimensional spin-1/2 inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet dimer excitations are observed in the inelastic neutron scattering spectra, which is in excellent agreement with a theoretical prediction: a dimer-monomer composite structure, where the dimer is caused by strong antiferromagnetic (AFM) coupling and the monomer forms an almost isolated quantum AFM chain controlling low-energy excitations. Moreover, muon spin rotation/relaxation spectroscopy shows no long-range ordering down to 90~mK, which is roughly…
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…
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 present experimental results on the tunneling into the edge of a two dimensional electron gas (2DEG) obtained with GaAs/AlGaAs cleaved edge overgrown structures. The electronic properties of the edge of these systems can be described by a one-dimensional chiral Tomonaga-Luttinger liquid when the filling factor of the 2DEG is very small. Here we focus on the region where the Tomonaga-Luttinger liquid breaks down to form a standard Fermi liquid close to $ν=1$ and show that we recover a universal curve, which describes all existing data.
The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to …
We develop two novel numerical schemes to study the conductance of the two-wire junction of inequivalent Tomonaga-Luttinger Liquids. In the first scheme we use the static current-current correlation function across the junction to extract the linear conductance through a relation that is derived via the bosonization method. In the second scheme we apply a bias and evaluate the time-dependent current across the junction to obtain the current-voltage characteristic. The conductance is then extracted from the small bias result within the linear response regime. Both schemes are based on the infin…
It is well-known that, generically, the one-dimensional interacting fermions cannot be described in terms of the Fermi liquid. Instead, they present different phenomenology, that of the Tomonaga-Luttinger liquid: the Landau quasiparticles are ill-defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine-tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both the Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaki…
We give the details of the analysis for critical properties of spin-gap phases in one-dimensional lattice electron models. In the Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is shown to be equivalent to that of the level-crossing of the singlet and the triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy from the …
We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.
Effects of a single impurity potential on bulk properties of a spinful Tomonaga-Luttinger (TL) liquid is studied. A boundary bosonization technique is developed to include the impurity potential of {\it arbitrary} strength $V$. Our new bosonization formula for fermion field $ψ$ smoothly connects the two existing expressions in the strong ($V = \infty$) and the weak ($V = 0$) impurity limits. With use of the formula, we found the TL parameters determined from the long-distance correlation functions are renormalized due to the partial transmission through the impurity potential.
