We add a Heisenberg interaction term $\proptoλ$ in the one-dimensional SU(2)$\otimes$XY spin-orbital model introduced by B. Kumar. At $λ=0$ the spin and orbital degrees of freedom can be separated by a unitary transformation leading to an exact solution of the model. We show that a finite $λ>0$ leads to spontaneous dimerization of the system which in the thermodynamic limit becomes a smooth phase transition at $λ\to 0$, whereas it remains discontinuous within the first order perturbation approach. We present the behavior of the entanglement entropy, energy gap and dimerization order parameter in the limit of $λ\to 0$ confirming the critical behavior. Finally, we show the evidence of another phase transition in the Heisenberg limit, $λ\to\infty$, and give a qualitative analytical explanation of the observed dimerized states both in the limit of small and large $λ$.
Because the three-leg ladder behaves like a renormalized single Heisenberg chain we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase not the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets explains why the columnar configuration is favored. No quantum criticality (g…
As a simple model for spin-Peierls systems we study a frustrated Heisenberg chain coupled to optical phonons. In view of the anorganic spin-Peierls compound CuGeO3 we consider two different mechanisms of spin-phonon coupling. Combining variational concepts in the adiabatic regime and perturbation theory in the anti-adiabatic regime we derive effective spin Hamiltonians which cover the dynamical effect of phonons in an approximate way. Ground-state phase diagrams of these models are determined, and the effect of frustration is discussed. Comparing the properties of the ground state and of low-l…
We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond-phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling alpha exceeds a critical value alpha_c. Using sum rules, we show that the phonon spectral function has divergent (for infinite N) weight extending to zero frequency for alpha < alpha_c. The equal-time phonon-phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0 < alpha < alpha_c and the q=pi phonon does not soften (to z…
The spin-Peierls transition in the ground state of a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a spin-gapped Peierls state is explored in the parameter space spanned by the spatial anisotropy and the strength of spin-lattice coupling. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state occurs only when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D mo…
We consider the frustrated antiferromagnetic s=1 Heisenberg quantum spin chain with regard to the Marshall-Peierls sign rule (MPSR). By using exact diagonalization data we investigate the breakdown of the MPSR in dependence on frustration and compare our findings with data for s=1/2. We calculate a critical value of frustration J_2(crit) where the MPSR is violated. The extrapolation of this value to the infinite chain limit holds J_2(crit) approx. 0.016, lower than in the case of s=1/2 (J_2(crit) approx. 0.027). This points to a stronger influence of frustration in the case of s=1. Nevertheles…
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is investigated using the Stochastic Series Expansion (SSE) Quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless Neel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, inter-chain coupling strength and spin-lattice coupling strength. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupli…
We compute the magnetic profile of spin Peierls solitons in a simple Heisenberg model with magneto elastic couplings, using independently the DMRG method and the Hartree Fock approximation. Our results agree qualitatively with published NMR data provided we average over the spin profiles. We conclude that he dynamics of the spin plus lattice system must be included in a more detailed theory of the spin Peierls transition in CuGeO.
We use the density matrix renormalization group method to investigate the role of longitudinal quantized phonons on the Peierls transition in the spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show that the staggered phonon order parameter scales as $\sqrtλ$ (and the dimerized bond order scales as $λ$) as $λ\to 0$ (where $λ$ is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at $λ=0$ in these models. Moreover, for the XY spin-Peierls model we show that the quantum predictions…
We report on the magnetic susceptibility and electron spin resonance measurements on polycrystalline samples of the vanadium oxide VOSb$_{2}$O$_{4}$, a quasi-one dimensional S=1/2 Heisenberg system. We show that the susceptibility vanishes at zero temperature, as in a gapped system, and we argue that this is due to a spin-Peierls transition with strong structural fluctuations.
The present understanding of the electronic and magnetic properties of $α'$-NaV$_2$O$_5$ is based on the hypothesis of strong charge disproportionation into V$^{4+}$ and V$^{5+}$, which is assumed to lead to a spin-1/2 Heisenberg chain system. A recent structure analysis shows, however, that the V-ions are in a mixed valence state and indistiguishable. We propose an explanation for the insulating state, which is not based on charge modulation, and show that strong correlations together with the Heitler-London character of the relevant intermediate states naturally lead to antiferromagnetic Hei…
We explore the ground-state phase diagram of a Heisenberg spin chain coupled locally to optical phonons (bond coupling), using large-scale density matrix renormalization group calculations and an extended perturbative analysis. For the quantum phase transition from the spin liquid to the dimerized phase, we find deviations from previous quantum Monte Carlo and flow equation results.
We show that the introduction of frustration into the spin-1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for ${\rm Li_2VOSiO_4}$, the first realization of that model, will be discussed.
Within the random phase approximation to the spin-Peierls transition two parameter regimes of phonon softening and hardening are present. Magneto-elastic excitations are discussed in detail for phonons coupled to the exactly solvable model of XY spin chains for both regimes, leading to a modified interpretation of the 30 cm$^{-1}$ mode in CuGeO$_3$. Frustrated Heisenberg chains coupled to phonons satisfactory describe the pre-transitional quasi-elastic scattering in CuGeO$_3$. A real space interpretation of the quasi-elastic scattering is given justifying effective Ising model approaches.
We have calculated the magnetic excitation spectrum in frustrated and dimerized spin 1/2 Heisenberg chains for model parameters which describe the thermodynamics and low frequency spin dynamics in the spin--Peierls system $CuGeO_{3}$. As a test the chosen model is found to reproduce the lowest Raman excitation energy near $30 cm^{-1}$ in the dimerized phase. We establish the elementary triplet and singlet excitation branches below the continuum and estimate the interchain coupling effects on the dimerization parameter.
The role of dynamical magneto-elastic coupling in spin-Peierls chains is investigated by numerical and analytical techniques. We show that a Heisenberg spin chain coupled to dynamical optical phonons exhibits a transition towards a spontaneously dimerized state in a wide range of parameter space. The low energy excitations are characterized as solitons. No binding between solitons occurs in the isolated spin-phonon chain and the dynamical spin structure factor shows a broad magnon dispersion. However, elastic interchain coupling can lead to the formation of bound states.
We study spin dynamics of a spin-Peierls chain with nearest-neighbor and next-nearest-neighbor Heisenberg spin exchange interactions together with a gapped and dispersionless phonon. The dynamical spin correlation function and phonon excitation spectrum are calculated at zero temperature by using dynamical density-matrix renormalization-group method. We find a new spin excitation assisted by non-softening phonon. The excitation is located above phonon in energy and shows a dispersive feature with strong intensity near the momentum $π$. The phonon excitation spectrum is also influenced by the s…
We study the magnetic properties of a frustrated Heisenberg spin chain with a dynamic spin-phonon interaction. By Lanczos diagonalization, preserving the full lattice dynamics, we explore the non-adiabatic regime with phonon frequencies comparable to the exchange coupling energy which is e.g. the relevant limit for the spin-Peierls compound $CuGeO_3$. When compared to the static limit of an alternating spin chain the magnetic properties are strongly renormalized due to the coupled dynamics of spin and lattice degrees of freedom. The magnitude of the spin triplet excitation gap changes from a s…
A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including pho…
We investigate elastic deformations of spin $S=1/2$ antiferromagnetic $J_1-J_2$ Heisenberg chains, at $M=1/3$ magnetization, coupled to phonons in the adiabatic approximation. Using a bosonization approach we predict the existence of non-homogeneous trimerized magnetoelastic phases. A rich ground state phase diagram is found, including classical and quantum plateau states for the magnetic sector as well as inequivalent lattice deformations within each magnetic phase. The analytical results are supported by exact diagonalization of small clusters.
Interactions between elementary excitations in quasi-one dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wavefunctions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (non integrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasi-particle excitations are bound states of topological solit…
We study TiOCl as an example of an S=1/2 layered Mott insulator. From our analysis of new susceptibility data, combined with LDA and LDA+U band structure calculations, we conclude that orbital ordering produces quasi-one-dimensional spin chains and that TiOCl is a new example of Heisenberg-chains which undergo a spin-Peierls transition. The energy scale is an order of magnitude larger than that of previously known examples. The effects of non-magnetic Sc impurities are explained using a model of broken finite chains.
Electronic structure calculations are presented for the well-known CuGeO3 and the recently discovered isostructural CuSiO3 compounds. The magnitude of the dispersion in chain direction is considerably smaller for CuSiO3, whereas the main interchain couplings are rather similar in both compounds. Starting from extended one-band tight-binding models fitted to the bandstructures, the exchange integrals were estimated for both compounds in terms of a spatially anisotropic Heisenberg model. Remarkable frustrating second neighbor couplings are found both for intra- and inter-chain interactions. A ma…
We study numerically the dimerized Heisenberg model with frustration appropriate for the quasi-1D spin-Peierls compound CuGeO$_3$. We present evidence for a bound state in the dynamical structure factor for any finite dimerization $δ$ and estimate the respective spectral weight. For the homogeneous case ($δ=0$) we show that the spin-wave velocity $v_s$ is renormalized by the n.n.n. frustration term $α$ as $v_s=π/2 J(1-bα)$ with $b\approx1.12$
Three-dimensional (3D) variants of the Kitaev model can harbor gapless spin liquids with a Majorana Fermi surface on certain tricoordinated lattice structures such as the recently introduced hyperoctagon lattice. Here we investigate Fermi surface instabilities arising from additional spin exchange terms (such as a Heisenberg coupling) which introduce interactions between the emergent Majorana fermion degrees of freedom. We show that independent of the sign and structure of the interactions, the Majorana surface is always unstable. Generically the system spontaneously doubles its unit cell at e…
Dynamical properties of the novel inorganic spin-Peierls compound α'--NaV2O5 are investigated using a one-dimensional dimerized Heisenberg model. By exact diagonalizations of chains with up to 28 sites, supplemented by a finite-size scaling analysis, the dimerization parameter δis determined by requiring that the model reproduces the experimentally observed spin gap Δ. The dynamical and static spin structure factors are calculated. As for CuGeO3, the existence of a low energy magnon branch separated from the continuum is predicted. The present calculations also suggest that a large magnetic Ra…
We study three-leg antiferromagnetic Heisenberg model with the periodic boundary conditions in the rung direction. Since the rungs form regular triangles, spin frustration is induced. We use the density-matrix renormalization group method to investigate the ground state. We find that the spin excitations are always gapped to remove the spin frustration as long as the rung coupling is nonzero. We also visibly confirm spin-Peierls dimerization order in the leg direction. Both the spin gap and the dimerization order are basically enhanced as the rung coupling increases.
We report an ultrasonic study of the magneto-elastic coupling of the hydrogenated and deuterated (TMTTF)$_2$PF$_6$ organic salts. For both salts the temperature dependence of the longitudinal velocity along the c* axis displays a monotonic stiffening of the $C_{33}$ compressibility modulus upon cooling. Below the characteristic temperature scale 40 K the modulus stiffening becomes markedly enhanced, in concomitance with the reduction of spin degrees of freedom previously seen in magnetic measurements as low dimensional precursors of the spin-Peierls transition. The magneto-elastic coupling app…
We study weakly coupled antiferromagnetic spin chains in their ordered phase by combinining an exact solution of the single-chain problem with an RPA analysis of the interchain interaction. A single chain is described by a quantum Sine-Gordon model and dynamical staggered susceptibilities are determined by employing the formfactor approach to quantum correlation functions. We consider both antiferromagnetic order encountered in quasi-1D materials like $KCuF_3$ and spin-Peierls order as found in $CuGeO_3$.
The density matrix renormalization group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite size scaling analysis, bond order auto-correlation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of …
The site- and bond-dilution effects of the nonmagnetic ground state of a two-dimensional $S=1/2$ antiferromagnetic Heisenberg model, coupled with the lattice distortions on a square lattice, are investigated by performing quantum Monte Carlo simulations. In the nondiluted system, a phase diagram parameterized by the interchain interaction and the elastic constant is obtained, and the values of the lattice distortions in the dimerized phase are evaluated precisely. In the diluted system, we compare two ground-state energies assuming two patterns of lattice distortions with magnetic moments (eff…
The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T=0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized pha…
Effects of disorder and external field on the competing spin-Peierls and antiferromagnetic states are studied theoretically in terms of the numerical transfer matrix method applied to a quasi one-dimensional spin 1/2 Heisenberg model coupled to the lattice degree of freedom. We show that, at temperatures above the impurity-induced antiferromagnetic phase, inhomogeneous spin-Peierls lattice distortions remain to exist showing a re-entrant behavior. This feature can be drastically altered by very weak perturbations, e.g., the staggered magnetic field or the change in interchain exchange coupling…
We study a model of a Spin-Peierls material consisting of a set of antiferromagnetic Heisenberg chains coupled with phonons and interacting among them via an inter-chain elastic coupling. The excitation spectrum is analyzed by bosonization techniques and the self-harmonic approximation. The elementary excitation is the creation of a localized domain structure where the dimerized order is the opposite to the one of the surroundings. It is a triplet excitation whose formation energy is smaller than the magnon gap. Magnetic internal excitations of the domain are possible and give the further exci…
Motivated by the global phase diagram of antiferromagnetic heavy-fermion metals, we study the Kondo effect from the perspective of a nonlinear sigma model in the one dimensional Kondo-Heisenberg model. We focus on the effects of the instanton configurations of the sigma-model field and the associated Berry phase. Guided by the results derived using bosonization methods, we demonstrate that the Kondo singlet formation is accompanied by an emergent Berry phase. This Berry phase also captures the competition between the Kondo-singlet formation and spin Peierls correlations. Related effects are li…
We present a detailed numerical analysis of the low energy excitation spectrum of a frustrated and dimerized spin $S=1/2$ Heisenberg chain. In particular, we show that in the commensurate spin--Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory . We discuss the relevance of our data in connection with recen…
The purpose of this paper is to investigate the ground-state properties of two-dimensional Heisenberg models on a square lattice with a given dimerization. Our aim is threefold: First, we want to investigate the dimensional transition from two to one dimension for three models consisting of weakly coupled chains for large dimerizations. Simple scaling arguments show that the interchain coupling is always relevant. The ground states of two of these models therefore have one-dimensional nature only at the decoupling point. The third considered model is more complicated, because it contains addit…
We extend previous analytical studies of the ground-state phase diagram of a one-dimensional Heisenberg spin chain coupled to optical phonons, which for increasing spin-lattice coupling undergoes a quantum phase transition from a gap-less to a gaped phase with finite lattice dimerisation. We check the analytical results against established four-block and new two-block density matrix renormalisation group (DMRG) calculations. Different finite-size scaling behaviour of the spin excitation gaps is found in the adiabatic and anti-adiabatic regimes.
We present the results of an exact diagonalization study of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low energy spectra for systems of up to 24 spins, we find that all clusters studied have non-degenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of non-magnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short-r…
Ferromagnetic, in contrast to antiferromagnetic, Heisenberg chains can undergo a Spin-Peierls dimerization only at finite temperatures. They show reentrant behavior as a function of temperature, which might play a role for systems with small effective elastic constants as, for example, monatomic chains on surfaces. We investigate the physical properties of the dimerized ferromagnetic Heisenberg chain using a modified spin-wave theory. We calculate the exponentially decaying spin and dimer correlation functions, analyze the temperature dependence of the corresponding coherence lengths, the susc…
Magnetic Raman scattering from a frustrated spin-1/2 Heisenberg-chain is considered with a focus on the uniform phase of the spin-Peierls compound CuGeO_3. The Raman intensity is analyzed in terms of a Loudon-Fleury scattering process using a spinless-fermion mean-field theory developed for the frustrated spin-chain. A comparison to experimental data is presented and the frustration and temperature dependence is studied. In good agreement with observed spectra a broad inelastic four-spinon continuum is found at low temperatures above the spin-Peierls transition. At high temperatures the intens…
We investigate the ground-state properties of the spin-half $J_1{-}J_2$ Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen, we find that for small frustration ($J_2/J_1$) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhan…
We report results from a systematic strong-coupling expansion of a spin-1/2 Heisenberg chain coupled to Einstein phonons. In the non-adiabatic regime this model is used to describe zero temperature properties of CuGeO3. The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. In particular, the spin gap and the dispersion of the elementary triplet excitation are calculated up to 10th order in a dimer expansion. The magnetic structure factor of the ground state is eval…
The bulk properties and impurity effect in the one-dimensional S=1/2 Heisenberg model with dimerization and next-nearest-neighbor exchange are studied by the density matrix renormalization group (DMRG) and exact diagonalization methods. This model widely covers the S=1 Heisenberg model, two-leg ladders, bond-alternating chains and the S=1/2 Heisenberg model. Almost the whole parameter space belongs to the Haldane phase. In the non-dimerizing limit a transition to a kind of spin liquid takes place, characterized by the delocalized spin polarization. This transition causes the distinct impurity …
Spin dynamics as well as static properties of the one-dimensional J-J' model (S=1/2, J>0 and 0\le α=J'/J\le 0.5) are studied by the exact diagonalization and the recursion method of finite systems up to 26 sites. Especially, the dynamical structure factor S(q,ω) is investigated carefully for various values of α. As αincreases beyond the gapless-gapful critical value α_c=0.2411, there appear features definitely different from the Heisenberg model but the same with the Majumdar-Ghosh model. Some of these features depend only on the value of αand not on δ: a parameter introduced for the coupling …
We perform an exact diagonalization study of the spin-$1/2$ XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization $m = \frac{2}{3}$ with an emphasis on the XY point ($J_z = 0$), and in the presence of a small chiral term. Recent analytic work by Kumar, Sun and Fradkin [Phys. Rev. B 90, 174409 (2014)] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of $σ_{xy} = \frac{1}{2}$. Such a state is topological in nature, has a groun…
The spin-lattice coupling plays an important role in strongly frustrated magnets. In ZnCr$_2$O$_4$, an excellent realization of the Heisenberg antiferromagnet on the ``pyrochlore'' network, a lattice distortion relieves the geometrical frustration through a spin-Peierls-like phase transition at $T_c = 12.5$ K. Conversely, spin correlations strongly influence the elastic properties of a frustrated magnet. By using infrared spectroscopy and published data on magnetic specific heat, we demonstrate that the frequency of an optical phonon triplet in ZnCr$_2$O$_4$ tracks the nearest-neighbor spin co…
We consider the quantum spin-$s$ $XXZ$ Heisenberg antiferromagnet on the two- and three-dimensional pyrochlore lattices and examine a spin-Peierls mechanism of lowering the total energy by a lattice distortion in a high magnetic field. For the exact eigenstates consisting of several independent localized magnons in a ferromagnetic environment we show the existence of a spin-Peierls instability by rigorous analytical calculations. In addition we report on exact diagonalization data for finite two-dimensional pyrochlore lattices up to N=64 sites. We discuss a scenario of the field-tuned changes …
Heavy fermion systems represent a prototypical setting to study magnetic quantum phase transitions. A particular focus has been on the physics of Kondo destruction, which captures quantum criticality beyond the Landau framework of order-parameter fluctuations. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum non-linear sigma model, and show that the skyrmion defects of the…
We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba$_4$Ir$_3$O$_{10}$. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong run…
We investigate a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field. Using field theoretic methods complemented by extensive Density Matrix Renormalisation Group techniques generalized to include self-consistent lattice distortions, we show that magnetization plateaux at non-trivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.
We analyse the antiferromagnetic spin-$1/2$ XXZ model on the kagome lattice at finite external magnetic field with the help of a nonperturbative zero-temperature renormalization group (RG) technique. Following the work of Kumar \emph{et al} (Phys. Rev. B {\bf 90}, 174409 (2014)), we use a Jordan-Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbour interactions. While the work of Kumar \emph{et al} was confined mostly to the plateau at $1/3$-filling (magnetisation per site) in the XY regime…
Correlation functions of dimer operators, the product operators of spins on two adjacent sites, are studied in the spin-$\frac{1}{2}$ XXZ chain in the critical regime. The amplitudes of the leading oscillating terms in the dimer correlation functions are determined with high accuracy as functions of the exchange anisotropy parameter and the external magnetic field, through the combined use of bosonization and density-matrix renormalization group methods. In particular, for the antiferromagnetic Heisenberg model with SU(2) symmetry, logarithmic corrections to the dimer correlations due to the m…
Properties of low-dimensional spin-Peierls systems are described by using a one dimensional S=1/2 antiferromagnetic Heisenberg chain linearly coupled to a single phonon mode of wave vector pi (whose contribution is expected to be dominant). By exact diagonalizations of small rings with up to 24 sites supplemented by a finite size scaling analysis, static and dynamical properties are investigated. Numerical evidences are given for a spontaneous discrete symmetry breaking towards a spin gapped phase with a frozen lattice dimerization. Special emphasis is put on the comparative study of the two i…
Due to the interaction between topological defects of an order parameter and underlying fermions, the defects can possess induced fermion numbers, leading to several exotic phenomena of fundamental importance to both condensed matter and high energy physics. One of the intriguing outcome of induced fermion number is the presence of fluctuating competing orders inside the core of topological defect. In this regard, the interaction between fermions and skyrmion excitations of antiferromagnetic phase can have important consequence for understanding the global phase diagrams of many condensed matt…
The effect of dimerization on the random antiferomagnetic Heisenberg chain with spin 1/2 is studied by the density matrix renormalization group method. The ground state energy, the energy gap distribution and the string order parameter are calculated. Using the finite size scaling analysis, the dimerization dependence of the these quantities are obtained. The ground state energy gain due to dimerization behaves as $u^a$ with $a > 2$ where $u$ denotes the degree of dimerization, suggesting the absence of spin-Peierls instability. It is explicitly shown that the string long range order survives …
