Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Le Journal de Physique Colloques

DISORDER LINE IN A QUANTUM SPIN CHAIN WITH COMPETING INTERACTIONS

I. Harada, Tsukasa Kimura, Takashi Tonegawa

Published Dec 1, 1988• 0 citations
Publisher

Abstract

The spin-1/2 Heisenberg chain with antiferromagnetic first- and second-neighbor interactions is studied by the cluster transfer-matrix method. It is found that this quantum model exhibits a disorder temperature above which the spin correlation function decays with an incommensurate oscillation while below which it decays antiferromagnetically.

DOI
10.1051/jphyscol:19888647

Related papers

Thermodynamic Properties of the One-Dimensional Spin-1/2 Heisenberg Antiferromagnet with Competing Interactions

Isao Harada, Tetsuji Kimura, Takashi Tonegawa

Thermodynamic properties are studied for the one-dimensional spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions. The internal energy, the specific heat, and the two-spin correlation function are calculated by means of the cluster transfer matrix method based on the Suzuki-Trotter equivalence theorem. Special attention is paid to the asymptotic behavior of the two-spin correlation function in the long-distarace limit. It is found that for a certain range of values of the interaction constants and of the temperature, the two-spin correlation function decays with an incommensurate or a higher-order commensurate oscillation as a function of the distance between two spins. We also find that there exists a quantum analog of the disorder line, on which the two-spin correlation function changes its character.

Journal of the Physical Society of Japan•Aug 15, 1988•16 citations

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

Masamichi Nishino, Kazumitsu Sakai, Masahiro Shiroishi +1 more

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.

Journal of Physics A Mathematical and General•May 6, 2004•1 citation

Spin pair correlation of the ANNNI chain in a field

Nelson A. Alves, Carlos S. O. Yokoi

We study the spin pair correlation function of the one-dimensional Ising model with competing nearest and next-nearest neighbor interactions, or ANNNI chain, in the presence of an external field. Of particular interest are the disorder lines where exponential decay of the spin pair correlation changes from monotonic to oscillatory. We extend previous studies for higher field values and obtain asymptotic expressions for disorder lines at low temperatures. We also observe reentrant disorder lines.

Brazilian Journal of Physics•Dec 1, 2000•4 citations

Finite-size study of a spin-1/2 Heisenberg chain with competing interactions: Phase diagram and critical behavior

K. Hallberg, Eduardo R. Gagliano, C. A. Balseiro

We study the ground-state properties of the one-dimensional anisotropic spin-1/2 antiferromagnetic Heisenberg model with competing antiferromagnetic second-neighbor Ising interaction. Using the modified Lanczos method, we obtain the phase diagram in parameter space and different correlation functions, which we use to characterize the different phases. For small next-nearest-neighbor parameters we evaluate the critical exponent \ensuremath{\eta} of the spin-spin correlation function. We find good agreement between the numerical results and those obtained using the Luther and Peschel approach.

Physical review. B, Condensed matter•May 1, 1990•23 citations

Comparison between disordered quantum spin- 12 chains

Carlos Alberto Lamas, D. C. Cabra, Marcelo D. Grynberg +1 more

We study the magnetic properties of two types of one-dimensional $XX$ spin-$\frac{1}{2}$ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.

arXiv:cond-mat/0607387•Physical Review B•Dec 27, 2006•12 citations

Monte Carlo calculations of the correlation functions for Heisenberg spin chains atT=0

Shoudan Liang

We compute the ground-state spin-spin correlation function for the one-dimensional antiferromagnetic Heisenberg model of spin 1/2, 1, and 3/2. The spin-1 chain has a disordered ground state with a correlation length of 6.2 lattice spacings whereas the spin-1/2 and the spin-3/2 chains both have (ln(r)${)}^{\mathrm{\ensuremath{\sigma}}}$/r decaying correlation functions. The logarithmic corrections are different for the spin-1/2 and the spin-3/2 chains. Finite-size scaling is used to analyze the data for chains of up to 128 spins.

Physical Review Letters•Mar 26, 1990•101 citations
The spin-1/2 Heisenberg chain with antiferromagnetic first- and second-neighbor interactions is studied by the cluster transfer-matrix method. It is found that this quantum model exhibits a disorder temperature above which the spin correlation function decays with an incommensurate oscillation while below which it decays antiferromagnetically.
Thermodynamic properties are studied for the one-dimensional spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions. The internal energy, the specific heat, and the two-spin correlation function are calculated by means of the cluster transfer matrix method based on the Suzuki-Trotter equivalence theorem. Special attention is paid to the asymptotic behavior of the two-spin correlation function in the long-distarace limit. It is found that for a certain range of values of the interaction constants and of the temperature, the two-spin correlation function decays with an incommensurate or a higher-order commensurate oscillation as a function of the distance between two spins. We also find that there exists a quantum analog of the disorder line, on which the two-spin correlation function changes its character.
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 study the ground-state properties of the one-dimensional anisotropic spin-1/2 antiferromagnetic Heisenberg model with competing antiferromagnetic second-neighbor Ising interaction. Using the modified Lanczos method, we obtain the phase diagram in parameter space and different correlation functions, which we use to characterize the different phases. For small next-nearest-neighbor parameters we evaluate the critical exponent \ensuremath{\eta} of the spin-spin correlation function. We find good agreement between the numerical results and those obtained using the Luther and Peschel approach.
We study the magnetic properties of two types of one-dimensional XXXXXX spin-12\frac{1}{2}21​ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.
We compute the ground-state spin-spin correlation function for the one-dimensional antiferromagnetic Heisenberg model of spin 1/2, 1, and 3/2. The spin-1 chain has a disordered ground state with a correlation length of 6.2 lattice spacings whereas the spin-1/2 and the spin-3/2 chains both have (ln(r)${)}^{\mathrm{\ensuremath{\sigma}}}$/r decaying correlation functions. The logarithmic corrections are different for the spin-1/2 and the spin-3/2 chains. Finite-size scaling is used to analyze the data for chains of up to 128 spins.