The effect of disorder is studied on the field-induced quantum phase transition in the frustrated spin-ladder compound H8C4SO2Cu2(Cl[1-x]Brx)4 using bulk magnetic and thermodynamic measurements. The parent material (x=0) is a quantum spin liquid, which in applied fields is known to form a magnon condensate with long-range helimagnetic order. We show that bond randomness introduced by a chemical substitution on the non-magnetic halogene site destroys this phase transition at very low concentrations, already for x=0.01. The extreme fragility of the magnon condensate is attributed to random frustration in the incommensurate state.
Three magnon bound states in all total spin sectors of general nonintegrable exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this result a dispersion law for $m$-magnon ($m>3$) bound states is conjectured. It is suggested that (depending on correlations between coupling constants) a behavior of the gas parameter (density of rung-triplets) on the boundary of the rung-dimerized phase may either be smooth or have a leap.
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those whe…
We consider the two-chain Heisenberg ladder with antiferromagnetic interactions. Our approach is based on the description of spin excitations as triplets above a strong-coupling singlet ground state. It is shown that interaction with dynamic phonons drastically changes the dispersion of the elementary triplet excitation (magnon) and the spin structure factor. It is also shown that a new triplet excitation appears in the spectrum: the bound state of a magnon and a phonon.
An exactly solvable effective model is suggested for an asymmetric spin ladder with dimerized rungs. Magnon mode truncation originated from magnon decay (recently observed in the 1D compound ${\rm IPA-CuCl}_3$) is naturally described within this model. Using Bethe Ansatze we described a one-magnon sector and obtained relations between interaction constants of the model and experimentally observable quantities such as the gap and truncation energies, spin velocity and the truncation wave vector. It is also shown that structure factor turns to zero at the truncation point.
We consider topological order and dimer order in several frustrated spin ladder models, which are related to higher dimensional models of current interest; we also address the occurrence of fractionalized phases with deconfined spinon excitations in these models. Combining results obtained with both analytic and numerical methods, we discuss how the occurrence of dimerized or fractionalized phases are dictated by the system's geometry.
Inelastic neutron scattering is used to measure spin excitations in fully deuterated single crystal samples of the strong-leg antiferromagnetic S=1/2 spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$. Sharp resolution-limited magnons are observed across the entire one-dimensional Brillouin zone. The results validate the previously proposed {\it symmetric} spin ladder model and provide a reliable estimate of the relevant exchange interactions.
We investigate magnetic excitations and spin transport properties of a frustrated spin chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in a magnetic field by density-matrix renormalization group methods. In the field-induced quadrupole and octupole regimes, the low-energy excitation is governed by two- and three-magnon bound states, respectively, so that bound magnon clusters would contribute to the spin transport. We show that spin current correlations decrease when the system goes from the quadrupole regime into the octupole regime. Th…
We construct frustrated antiferromagnetic spin ladders with m chains for which the exact ground state can be determined in a particular parameter regime. The excitation spectrum is shown rigorously to be gapless ( with gap ) for odd ( even ) m. In a general parameter regime, the four-chain and periodic ladders are studied using a mean-field theory based on the bond operator formalism for spin $S=1/2$. The excitation spectrum and the spin-gap are calculated in both the cases. The spin-gap of the frustrated ladder system has a larger magnitude than in the case of non-frustrated ladders. For the …
We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.
Using the Density Matrix Renormalization Group method, we determined the phase diagram of a frustrated antiferromagnetic spin-$\frac 1 2$ ladder at zero temperature. Two spin-gapped phases, the Haldane phase and the singlet phase, are identified. A phase transition between the two phases occurs at any non-zero value of frustration coupling $J_{\times}$. On the phase boundary, the spin gap vanishes for sufficiently small $J_{\times}$. Crossing this non-gapped line, the transition is of second order, while of first order for larger $J_{\times}$. Striking frustration effects are predicted for lad…
The magnon thermal conductivity $κ_{\mathrm{mag}}$ of the spin ladders in $\rm Sr_{14}Cu_{24-x}Zn_xO_{41}$ has been investigated at low doping levels $x=0$, 0.125, 0.25, 0.5 and 0.75. The Zn-impurities generate nonmagnetic defects which define an upper limit for $l_{\mathrm{mag}}$ and therefore allow a clear-cut relation between $l_{\mathrm{mag}}$ and $κ_{\mathrm{mag}}$ to be established independently of any model. Over a large temperature range we observe a progressive suppression of $κ_{\mathrm{mag}}$ with increasing Zn-content and find in particular that with respect to pure $\rm Sr_{14}Cu_…
One-magnon problem for spin-ladders with exact singlet-rung ground state in arbitrary oriented constant and staggered magnetic fields is studied. For two special configurations when the both fields are parallel or perpendicular to each other the exact formulas for eigenstates and eigenvectors are presented. In the parallel case the one-magnon contribution to the ESR absorption line shape is obtained. The latter is non-Lorentzian, has finite range and a gap around resonance. For low fields both the range of the spectrum and the width of the gap are controlled by the width of the one-magnon zone…
We present a theoretical study of the magnetic phase diagram of the frustrated coupled ladder structure realized recently in several materials. This system displays a nondegenerate spin-gap state in the dimer limit and an infinitely degenerate spin-gap state in the regime of weakly-coupled zig-zag chains. Between these we demonstrate the existence of gapless, magnetically ordered regions whose order is antiferromagnetic close to the honeycomb lattice limit, and incommensurate along the chains when all three magnetic interactions compete.
Spin-waves e.g. magnons are the conventional elementary excitations of ordered magnets. However, other possibilities exist. For instance, magnon bound-states can arise due to attractive magnon-magnon interactions and drastically impact the static and dynamic properties of materials. Here, we demonstrate a zoo of distinct multi-magnon quasiparticles in the frustrated spin-1 triangular antiferromagnet FeI$_2$ using time-domain terahertz spectroscopy. The energy-magnetic field excitation spectrum contains signatures of one-, two-, four- and six-magnon bound-states, which we analyze using an exact…
For a class of frustrated spin lattices including the kagome lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagome lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classic…
A spin-1/2 frustrated two-leg ladder with four-spin exchange interaction is studied by quantized Berry phases. We found that the Berry phase successfully characterizes the Haldane phase in addition to the rung-singlet phase, and the dominant vector-chirality phase. The Hamiltonian of the Haldane phase is topologically identical to the S=1 antiferromagnetic Heisenberg chain. Decoupled models connected to the dominant vector-chirality phase revealed that the local object identified by the non-trivial ($π$) Berry phase is the direct product of two diagonal singlets.
We theoretically study a spin-spin correlation enhanced by non-magnetic impurities in a frustrated two-leg spin ladder. The frustration is introduced by the next-nearest-neighbor antiferromagnetic interaction in the leg direction in the antiferromagnetic two-leg spin ladder. The spin-spin correlation function around impurity site is calculated by the density-matrix renormalization-group method. We find that the spin-spin correlation is enhanced around impurity site with the wavenumber reflecting the frustration. As increasing the frustration, the wavenumber is shifted from commensurate to inco…
We calculate the two-magnon Raman scattering spectra in antiferromagnetic phases of several frustrated spin models defined on the honeycomb lattice. These include the Néel antiferromagnetic phase of a $J_1$-$J_2$-$J_3$ model and the stripe phase of the Heisenberg-Kitaev model. We show that both the magnetic frustration and the anisotropy of interactions may significantly affect the Raman spectra. We further discuss the implications of our results to the magnetic excitations of the iron-based compound BaFe$_2$Se$_2$O and show how the magnetic interactions can be extracted from fit to the Raman …
We investigate the resonant two-magnon Raman scattering in the two-dimensional (2D) and ladder-type Mott insulators by using a half-filled Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the model can reproduce the experimental features in the 2D that the Raman intensity is enhanced when the incoming photon energy is not near the absorption edge but well above it. In the ladder-type Mott insulators, the Raman intensity is found to resonate with absorption spectrum in contrast to the 2D system. The difference betw…
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.
We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy and linewidth of the magnon resonance in IPA-Cu(Cl$_{0.95}$Br$_{0.05}$)$_3$, a model spin-1/2 ladder antiferromagnet where Br substitution induces bond randomness. We find that the bond defects induce a blueshift, $δΔ$, and broadening, $δΓ$, of the magnon gap excitation compared to the pure compound. At temperatures exceeding the energy scale of the inter-ladder exchange interactions, $δΔ$ and $δΓ$ are temperature independent within the experimental error, in agreement with Matthiess…
We study a two-leg spin-1/2 ladder with isotropic exchanges and biquadratic interactions in the basic plaquettes. It is shown that for the extremely frustrated case, the system exhibits a self-organized phase separation. In some parameter regions, the singlet rungs form a Wigner-like lattice in the triplet-rung host. There are three types of elementary excitations in this modulation phase, i.e., the spinons in a triplet domain, the broken singlet rungs and the deformation of the Wigner-like lattice. The flux phase induced by an external magnetic field in the rung-dimerized phase is also discus…
Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings $J_1$. These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with $J^2_1$, and the systems show an incommensurate phase for $0.0<J_1<1.0$. The spin-spin…
The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange $J_2 > 0$ between first neighbors in the legs, variable isotropic AF exchange $J_1$ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when $J_1 \gg J_2$. Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions leading to multiple quantum phases: AF at small $J_1$, either F…
We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy, fine structure, and linewidth of the magnon resonance in the model spin-1/2 ladder antiferromagnet IPA-CuCl_3 at temperatures T << Delta_0 /k_B, where Delta_0 is the spin gap at T=0. In this low-temperature regime we find that the results deviate substantially from the predictions of the non-linear sigma model proposed as a description of magnon excitations in one-dimensional quantum magnets and attribute these deviations to real-space and spin-space anisotropies in the spin Hamilto…
The magnetization curve in a frustrated two-leg spin-ladder system is theoretically studied using both analytical and numerical methods. This spin system is mapped onto a hard-core boson system, which is composed of bond-operators describing the triplon excitation. By the analytical method using the mean-field theory on the bond-operators, we show that cusp singularities emerge in the magnetization curve as a function of a magnetic field due to the strong frustration. This originates from a change of number of Fermi points in the bosonic dispersion relation with the applied field. It is analog…
We suggest a family of spin-ladder models with exact singlet-rung vacuum. In addition to the terms describing interactions along legs and rungs the Hamiltonian has frustration and cyclic terms. Using coordinate Bethe ansatze all one- and two-dimensional states are constructed. The explicit formula for zero-temperature Raman scattering cross section is derived. The corresponding line-shapes are strongly asymmetric and have no more than one van-Hove singularity. The results are in good agreement with experimental data.
Frustrated spin ladders show magnetization plateaux depending on the rung-exchange interaction and frustration defined by the ratio of first and second neighbor exchange interactions in each chain. This paper is the first report on its magnetic phase diagram. Using the variational matrix-product state method, we accurately determine phase boundaries. Several kinds of magnetization plateaux are induced by the frustration and the strong correlation among quasi-particles on a lattice. The appropriate description of quasi-particles and their relevant interactions are changed by a magnetic field. W…
Phonon-assisted 2-magnon absorption is studied at T=4 K in the spin-1/2 two-leg ladders of Ca_14-x La_x Cu_24 O_41 (x=5 and 4) for polarization of the electrical field parallel to the legs and the rungs, respectively. Two peaks at about 2140 and 2800 1/cm reflect van-Hove singularities in the density of states of the strongly dispersing 2-magnon singlet bound state, and a broad peak at about 4000 1/cm is identified with the 2-magnon continuum. Two different theoretical approaches (Jordan-Wigner fermions and perturbation theory) describe the data very well for J_parallel = 1050 - 1100 1/cm and …
In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomo…
We study the excitation spectrum of the two-leg antiferromagnetic S=1/2 Heisenberg ladder. Our approach is based on the description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. We find singlet (S=0) and triplet (S=1) two-particle bound states of the elementary triplets. We argue that bound states generally exist in any dimerized quantum spin model.
We investigate magnetic excitations in the frustrated zigzag spin-1/2 chain compound $β$-TeVO$_4$ by inelastic neutron scattering. In the magnetically ordered ground state, the excitation spectrum exhibits coexisting magnon dispersion, characteristic of long-range magnetic order, and a spinon-like continuum that prevails above 2 meV, indicating the dominance of intrachain interactions. Combining linear-spin-wave-theory and pre-calculated spinon-continuum results, we reproduce the experimental spectrum. Our analysis offers a minimal exchange-network model which determines dominant intrachain in…
The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.
Three-magnon problem for exactly rung-dimerized spin ladder is brought up separately at all total spin sectors. At first a special duality transformation of the $\rm Schr\ddot odinger$ equation is found within general outlook. Then the problem is treated within Coordinate Bethe Ansatze. A straightforward approach is developed to obtain pure scattering states. At values S=0 and S=3 of total spin the $\rm Schr\ddot odinger$ equation has the form inherent in the $XXZ$ chain. For $S=1,2$ solvability holds only in five previously found {\it completely integrable} cases. Nevertheless a partial S=1 B…
We study the magnetization process of the $S=1/2$ antiferromagnetic spin ladder in the presence of the second and the third-neighbor couplings which lead to frustration with the typical nearest-neighbor coupling. We use degenerate perturbation theory and level spectroscopy analysis of the numerical diagonalization data of the Hamiltonian for finite systems. We find two kinds of plateaux at half the saturation moment in the magnetization curve. One is mainly due to the second-neighbor couplings and the other to the third-neighbor couplings. The mechanisms of these two plateaux are quite differe…
We study the magnetization plateau at 1/4 of the saturation magnetization of the S=1 antiferromagnetic spin ladder both analytically and numerically, with the aim of explaining recent experimental results on BIP-TENO by Goto et al. We propose two mechanisms for the plateau formation and clarify the plateau phase diagram on the plane of the coupling constants between spins.
Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of t…
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature o…
A model of two-leg spin-S ladder with two additional frustrating diagonal exchange couplings J_{D}, J_{D}' is studied within the framework of the nonlinear sigma model approach. The phase diagram has a rich structure and contains 2S gapless phase boundaries which split off the boundary to the fully saturated ferromagnetic phase when J_{D} and J_{D}' become different. For the S=1/2 case, the phase boundaries are identified as separating two topologically distinct Haldane-type phases discussed recently by Kim et al. (cond-mat/9910023).
The magnetic phase diagram of a plaquette dimerized antiferromagnetic system is studied by using a combination of numerical and analytical techniques. For the strongly frustrated regime, series expansions and bond operators techniques are employed to analyze zero magnetization plateau, whereas low energy effective models are used to study the complete magnetization process. The interplay between frustration and dimerization gives rise to a rich plateaus structure that is captured by effective models and corroborated by numerical density matrix renormalization group simulations, in particular t…
The weakly coupled quasi-one-dimensional spin ladder compound (CH$_3$)$_2$CHNH$_3$CuCl$_3$ is studied by neutron scattering in magnetic fields exceeding the critical field of Bose-Einstein condensation of magnons. Commensurate long-range order and the associated Goldstone mode are detected and found to be similar to those in a reference 3D quantum magnet. However, for the upper two massive magnon branches the observed behavior is totally different, culminating in a drastic collapse of excitation bandwidth beyond the transition point.
This talk was about the frustration-induced criticality in the antiferromagnetic Heisenberg model on the two-leg ladder with exchange interactions along the chains, rungs, and diagonals, and also about the effect of thermal fluctuations on this criticlity. The method used is the bond mean-field theory, which is based on the Jordan-Wigner transformation in dimensions higher than one. In this paper, we will summarize the main results presented in this talk, and report on new results about the couplings and temperature dependences of the spin susceptibility.
The quasi-spin correlations in a frustrated quantum spin ladder with one-half magnetization are theoretically studied by using the density-matrix renormalization-group method and the quasi-spin transformation. In this model, the frustration induces a gapless-to-gapful phase transition with a strong rung coupling. The gapful state is observed as the one-half magnetization plateau in the magnetization curve. In the magnetization-plateau state, we find that the quasi-spin dimer has a large expectation value with long-ranged correlations. This result does not only comes in useful to clarify the ma…
We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. In the doped case, we find that static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. This polarization induces short range …
Magnetization plateaux emerging in quantum spin systems due to spontaneously breaking of translational symmetry have been reported both theoretically and experimentally. The broken symmetry can induce reconstruction of elementary excitations such as Goldstone and Higgs modes, whereas its microscopic mechanism and reconstructed quasi-particle in magnetization-plateau phases have remained unclear so far. Here we theoretically study magnetic excitations in the magnetization-plateau phases of a frustrated spin ladder by using dynamical density-matrix renormalization-group method. Additionally, ana…
We study geometrical responses of magnons driven by a temperature gradient in frustrated spin systems. While Dzyaloshinskii-Moriya (DM) interactions are usually incorporated to obtain geometrically nontrivial magnon bands, here we investigate thermal Hall responses of magnons that do no rely on the DM interactions. Specifically, we focus on frustrated spin systems with sublattice degrees of freedom and show that a nonzero Berry curvature requires breaking of an effective $PT$ symmetry. According to this symmetry consideration, we study the $J_1$-$J_2$-$J_2^\prime$ Heisenberg models on a honeyc…
We show that spin-S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an inter…
Recent developments concerning localized-magnon eigenstates in strongly frustrated spin lattices and their effect on the low-temperature physics of these systems in high magnetic fields are reviewed. After illustrating the construction and the properties of localized-magnon states we describe the plateau and the jump in the magnetization process caused by these states. Considering appropriate lattice deformations fitting to the localized magnons we discuss a spin-Peierls instability in high magnetic fields related to these states. Last but not least we consider the degeneracy of the localized-…
The magnon thermal conductivity $κ_{\mathrm{mag}}$ of the hole doped spin ladders in $\rm Sr_{14-x}Ca_xCu_{24}O_{41}$ has been investigated at low doping levels $x$. The analysis of $κ_{\mathrm{mag}}$ reveals a strong doping and temperature dependence of the magnon mean free path $l_{\mathrm{mag}}$ which is a local probe for the interaction of magnons with the doped holes in the ladders. In particular, this novel approach to studying charge degrees of freedom via spin excitations shows that charge ordering of the holes in the ladders leads to a freezing out of magnon-hole scattering processes.
Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly t…
To establish the microscopic model of the compound BiCu$_2$PO$_6$ is a challenging task. Inelastic neutron scattering experiments showed that the dispersion of this material is non-degenerate suggesting the existence of anisotropic interactions. Here we present a quantitative description of the excitation spectrum for BiCu$_2$PO$_6$ on the one-particle level. The solution of the isotropic frustrated spin ladder by continuous unitary transformations is the starting point of our approach. Further couplings such as isotropic interladder couplings and anisotropic interactions are included on the m…
We study, at T=0, the anomalies in the magnetization curve of the S=1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the $M=\Ms/2$ plateau, where $\Ms$ is the saturation magnetization. We use analytical methods (degenerate perturbation theory and non-Abelian bosonization) as well as numerical methods (level spectroscopy and density matrix renormalization group), which lead to the consistent conclusion with each other. We also touch on the $M=\Ms/4$ and $M=(3/4)\Ms$ plateaux and cusps.
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.
