© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Physics A Mathematical and General

Quantum Monte Carlo study on commensurate–incommensurate transition in the spin-1/2 XXZ chain at finite temperatures

Masamichi Nishino, Kazumitsu Sakai, Masahiro Shiroishi, Seiji Miyashita

Published May 6, 2004• 1 citation

Abstract

A crossover phenomenon of the longitudinal spin–spin correlation function is investigated on the spin-1/2 XXZ chain in a magnetic field at finite temperatures. A commensurate–incommensurate transition of the correlation function in the asymptotic behaviour has been pointed out by Klumper et al in the framework of the quantum transfer matrix method. We show the field dependence and the anisotropy-constant dependence of the critical temperature by the quantum transfer matrix method. Using a quantum Monte Carlo method with the continuous time loop algorithm, we directly observe the commensurate–incommensurate transition. Detailed quantum Monte Carlo analyses for the longitudinal spin–spin correlation in both the high and low temperature regions are presented. Especially in the low temperature region, evaluating the precise distance dependence of the correlation function, we prove that the incommensurate oscillation has detectable amplitude, which has not been estimated before. We also estimate the phase factor of the incommensurate oscillation, which accurately coincides with the one from the quantum transfer matrix method.

DOI: 10.1088/0305-4470/37/20/003

Related papers

Exotic incommensurate order of weakly coupled S=1/2 XXZ antiferromagnetic chains

Takafumi Suzuki, Naoki Kawashima, Kouichi Okunishi

We study the ordered state of the quasi-one dimensional S = 1/2 XXZ spin model in magnetic fields by using quantum Monte Carlo simulations based on the directed-loop algorithm. The H-T phase diagram is illustrated and we find that an incommensurate long-range-ordered state is stable in a certain low-magnetized region. The result of the finite-size scaling analysis indicates that the finite temperature transition to the incommensurate order is of the first order.

Journal of Physics Conference Series•Mar 1, 2009•1 citation

Exotic Finite-Temperature Phase Diagram for Weakly CoupledS= 1/2 XXZ Chain in a Magnetic Field

Takafumi Suzuki, Naoki Kawashima, Kohichi Okunishi

We investigate the ordered state in S = 1/2 XXZ spin chains with weak interchain couplings in a magnetic field by using quantum Monte Carlo simulations based on the directed-loop algorithm. The H – T phase diagram is illustrated for a square lattice and we find that an exotic spin-liquid state with quasi long-range incommensurate correlations in both the spin-chain and interchain directions may appear in the low-magnetization region without a finite-temperature transition. We also show that the incommensurate long-range-ordered state is stable for a cubic lattice.

Journal of the Physical Society of Japan•Nov 26, 2007•10 citations

Dynamical correlations of S=1/2 quantum spin chains

Rodrigo G. Pereira

Spin-1/2 chains demonstrate some of the striking effects of interactions and quantum fluctuations in one-dimensional systems. The XXZ model has been used to study the unusual properties of anisotropic spin chains in an external magnetic field. The zero temperature phase diagram for this model exhibits a critical or quasi-long-range-ordered phase which is a realization of a Luttinger liquid. While many static properties of spin-1/2 chains have been explained by combinations of analytical techniques such as bosonization and Bethe ansatz, the standard approach fails in the calculation of some time-dependent correlation functions. I present a study of the longitudinal dynamical structure factor for the XXZ model in the critical regime. I show that an approximation for the line shape of the dynamical structure factor in the limit of small momentum transfer can be obtained by going beyond the Luttinger model and treating irrelevant operators associated with band curvature effects. This approach is able to describe the width of the on-shell peak and the high-frequency tail at finite magnetic field. Integrability is shown to affect the low-energy effective model at zero field, with consequences for the line shape. The power-law singularities at the thresholds of the particle-hole continuum are investigated using an analogy with the X-ray edge problem. Using methods of Bethe ansatz and conformal field theory, I compute the exact exponents for the edge singularities of the dynamical structure factor. The same methods are used to study the long-time asymptotic behavior of the spin self-correlation function, which is shown to be dominated by a high-energy excitation.

•Jan 1, 2008•0 citations

Temperature-Dependent Spatial Oscillations in the Correlations of the XXZ Spin Chain

K. Fabricius, Andreas Klümper, Barry M. McCoy

We study the correlation $〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉$ for the $\mathrm{XXZ}$ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.

arXiv:cond-mat/9812012•Physical Review Letters•Jun 28, 1999•13 citations

Spin dynamics of the antiferromagnetic spin- 12 chain at finite magnetic fields and intermediate temperatures

Simon Grossjohann, W. Brenig

We present a study of the dynamic structure factor of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain at finite temperatures and finite magnetic fields. Using quantum Monte Carlo based on the stochastic series expansion and maximum entropy methods, we evaluate the longitudinal and the transverse dynamic structure factors from vanishing magnetic fields up to and above the threshold ${B}_{c}$ for ferromagnetic saturation, as well as for high and for intermediate temperatures. We study the field-induced redistribution of spectral weight contrasting longitudinal versus transverse excitations. At finite fields below saturation incommensurate low-energy modes are found consistent with zero-temperature Bethe ansatz. The crossover between the field-induced ferromagnet above ${B}_{c}$ and the Luttinger liquid below ${B}_{c}$ is analyzed in terms of the transverse spin dynamics. Evaluating sum rules we assess the quality of the analytic continuation and demonstrate excellent consistency of the maximum entropy results.

arXiv:0811.1956•Physical Review B•Mar 10, 2009•25 citations

Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-1/2 XXZ Chain at Finite Temperature

K. Fabricius, Andreas Klümper, Barry M. McCoy

An analytical study is presented of the crossover in the gapless attractive XXZ chain from antiferromagnetic to ferromagnetic behaviour at low to high temperature, respectively. In particular, an analytic formula for the crossover in the long distance asymptotics and explicit results for the nearest-neighbour longitudinal correlation are obtained. We also provide results for the specific heat and magnetic susceptibility for various anisotropies.

arXiv:cond-mat/9810278•Oct 21, 1998•3 citations

A crossover phenomenon of the longitudinal spin–spin correlation function is investigated on the spin-1/2 XXZ chain in a magnetic field at finite temperatures. A commensurate–incommensurate transition of the correlation function in the asymptotic behaviour has been pointed out by Klumper et al in the framework of the quantum transfer matrix method. We show the field dependence and the anisotropy-constant dependence of the critical temperature by the quantum transfer matrix method. Using a quantum Monte Carlo method with the continuous time loop algorithm, we directly observe the commensurate–incommensurate transition. Detailed quantum Monte Carlo analyses for the longitudinal spin–spin correlation in both the high and low temperature regions are presented. Especially in the low temperature region, evaluating the precise distance dependence of the correlation function, we prove that the incommensurate oscillation has detectable amplitude, which has not been estimated before. We also estimate the phase factor of the incommensurate oscillation, which accurately coincides with the one from the quantum transfer matrix method.

We investigate the ordered state in S = 1/2 XXZ spin chains with weak interchain couplings in a magnetic field by using quantum Monte Carlo simulations based on the directed-loop algorithm. The H – T phase diagram is illustrated for a square lattice and we find that an exotic spin-liquid state with quasi long-range incommensurate correlations in both the spin-chain and interchain directions may appear in the low-magnetization region without a finite-temperature transition. We also show that the incommensurate long-range-ordered state is stable for a cubic lattice.

Spin-1/2 chains demonstrate some of the striking effects of interactions and quantum fluctuations in one-dimensional systems. The XXZ model has been used to study the unusual properties of anisotropic spin chains in an external magnetic field. The zero temperature phase diagram for this model exhibits a critical or quasi-long-range-ordered phase which is a realization of a Luttinger liquid. While many static properties of spin-1/2 chains have been explained by combinations of analytical techniques such as bosonization and Bethe ansatz, the standard approach fails in the calculation of some time-dependent correlation functions. I present a study of the longitudinal dynamical structure factor for the XXZ model in the critical regime. I show that an approximation for the line shape of the dynamical structure factor in the limit of small momentum transfer can be obtained by going beyond the Luttinger model and treating irrelevant operators associated with band curvature effects. This approach is able to describe the width of the on-shell peak and the high-frequency tail at finite magnetic field. Integrability is shown to affect the low-energy effective model at zero field, with consequences for the line shape. The power-law singularities at the thresholds of the particle-hole continuum are investigated using an analogy with the X-ray edge problem. Using methods of Bethe ansatz and conformal field theory, I compute the exact exponents for the edge singularities of the dynamical structure factor. The same methods are used to study the long-time asymptotic behavior of the spin self-correlation function, which is shown to be dominated by a high-energy excitation.

We study the correlation $〈{\ensuremath{\sigma}}_{0}^{z}{\ensuremath{\sigma}}_{n}^{z}〉$ for the

\mathrm{XXZ}

chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.

We present a study of the dynamic structure factor of the antiferromagnetic spin-

\frac{1}{2}

Heisenberg chain at finite temperatures and finite magnetic fields. Using quantum Monte Carlo based on the stochastic series expansion and maximum entropy methods, we evaluate the longitudinal and the transverse dynamic structure factors from vanishing magnetic fields up to and above the threshold

{B}_{c}

for ferromagnetic saturation, as well as for high and for intermediate temperatures. We study the field-induced redistribution of spectral weight contrasting longitudinal versus transverse excitations. At finite fields below saturation incommensurate low-energy modes are found consistent with zero-temperature Bethe ansatz. The crossover between the field-induced ferromagnet above

{B}_{c}

and the Luttinger liquid below

{B}_{c}

is analyzed in terms of the transverse spin dynamics. Evaluating sum rules we assess the quality of the analytic continuation and demonstrate excellent consistency of the maximum entropy results.