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

Journal of Guangxi University

Quantum Monte Carlo simulation of tow-dimensional antiferromagnetic Heisenberg model

Jinbin Li

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The Antiferromagnetic Heisenberg Model with spin 1/2 on a square lattice was simulated by using the Stochastic Series Expansion(SSE) Quantum Monte Carlo Method.The temperature dependence of the internal energy,specific heat and uniform susceptibility was observed.The results showed that specific heat has a maximum at kT/J=0.6 and uniform susceptibility saturates at kT/J=1 for the isotropy case.And the size of lattice also affects the temperature dependence of these thermodynamic quantities.For the anisotropy case,energy decreases with anisotropic parameter g increasing.Susceptibility changes slowly with temperature for g1 and exponentially decay for g1 in the low temperature region and its behaviors approach consistent for different g in the high temperature region.

Related papers

Investigating the stochastic series expansion method for one-dimensional spin-1/2 antiferromagnetic Heisenberg model

Ali Akbar Hasan, Mohammad G. Merdan, Hayder M. Abdualjalil

We investigate the Stochastic Series Expansion (SSE) technique, guided by Sandvik's algorithm of the quantum Monte Carlo simulation for spin-1/2 antiferromagnetic Heisenberg linear chain. The impact of the Monte Carlo steps, lattice sizes, and various temperatures on the variability and fidelity of simulation outcomes are studied. The findings show that the Monte Carlo steps where measurements are made (Msteps), and lattice size are crucial for stabilizing the results. Our results show that for larger lattice sizes, such as L=1024, achieving reliable outcomes necessitates extensive Monte Carlo simulations, specifically. The convergence in the properties is achieved with a high number of Monte Carlo steps starting from 7×10^4. Strong fluctuations are calculated between the results for each magnetic property and the existence of negative and positive in the specific heat at low temperatures.

AIP conference proceedings•Jan 1, 2026•0 citations

QMC simulations of Heisenberg ferromagnet

L. Bogacz, Wolfhard Janke E

We use the Quantum Monte Carlo Stochastic Series Expansion (SSE) algorithm to investigate the properties of the one-dimensional Heisenberg ferromagnet.We consider the model for two spin values s = 1 2 and s = 1 and study the dependence of the specific heat, magnetisation, magnetic susceptibility and correlation functions on temperature and magnetic field.Obtained results are compared to those derived by analytical methods (Bethe ansatz, Green's function, Random Phase Approximation).In particular, the surprising prediction of a double-peak structure in the specific heat at low temperatures and small magnetic fields can be confirmed.

Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005)•Dec 14, 2005•0 citations

Thermodynamic properties ofS=2 antiferromagnetic Heisenberg chains

Shoji Yamamoto

Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Feb 1, 1996•36 citations

Monte Carlo studies of two dimensional quantum spin systems

M. S. Makivić

Spin-1/2 nearest neighbor Heisenberg antiferromagnet and XY model on a square lattice are studied via large scale quantum Monte Carlo simulations using a fast and efficient multispin coding algorithm on the Caltech/JPL MarkIIIfp parallel supercomputer, based on the Suzuki-Trotter transformation. We performed simulations with very good statistics on lattices as large as 128x128 spins, in the temperature range from 0.1 to 2.5 in units of the effective exchange coupling J. We calculated energy, specific heat, magnetic susceptibilities and also spin correlation functions from which we deduce the correlation lengths. For the Heisenberg model, at temperatures higher than J the results are in excellent agreement with high-temperature series expansion. At low temperatures the long wavelength behavior is essentially classical. Our data show that the correlation length and staggered susceptibility are quantitatively well described by the renormalized classical picture at the 2-loop level of approximation. From the divergence of the correlation length, we deduce the value of the quantum renormalized spin stiffness, [rho][subscript s]/J = 0.199(2). We give evidence that the correlation function is of the Ornstein-Zernicke type. By comparing the largest measured correlation lengths with neutron scattering experiments on La2CuO4, we deduce the value of effective exchange coupling J = 1450±30 K. By measuring the imaginary time-dependent correlation functions, we show that the dynamics of the model can be well understood within a Bose liquid-type picture. The spin waves are rather sharp throughout most of the Brillouin zone and the damping is weakly dependent on the wave vector. In the case of the XY model, convincing numerical evidence is obtained on square lattices as large as 96x96 that the spin-1/2 XY model undergoes a Kosterlitz-Thouless (KT) phase transition at kTc/J = 0.350(4). The correlation length and in-plane susceptibility diverge at Tc precisely according to the form predicted by Kosterlitz and Thouless for the classical XY model. The specific heat increases very rapidly on heating near Tc and exhibits a peak around kT/J = 0.45. We also measure the spin stiffness and the correlation function exponent below the transition temperature. Within the statistical accuracy of the measurements, the results are well described by the square root singularity (with a nonuniversal amplitude) below Tc, and they have the universal values in agreement with KT theory at Tc.

•Jul 20, 2007•0 citations

Thermodynamic properties of disordered quantum spin ladders

Erol Vatansever, Georgi Georgiev Grahovski, Nikolaos G. Fytas

Abstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( $$r=0$$ r = 0 ) case up to the diluted ( $$r \rightarrow 1$$ r → 1 ) limit, and for selected choices of number of legs $$L_y$$ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $$L_y$$ L y . Graphical Abstract

arXiv:2312.12834•The European Physical Journal B•Mar 1, 2024•1 citation

Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder

Beat Ammon, Manfred Sigrist

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as $Sr_3 CuPt_{1-x} Ir_x O_6$. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of $Sr_3 CuPt_{1-x} Ir_x O_6$ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.

arXiv:cond-mat/9902252•Journal of the Physical Society of Japan•Mar 15, 1999•6 citations
The Antiferromagnetic Heisenberg Model with spin 1/2 on a square lattice was simulated by using the Stochastic Series Expansion(SSE) Quantum Monte Carlo Method.The temperature dependence of the internal energy,specific heat and uniform susceptibility was observed.The results showed that specific heat has a maximum at kT/J=0.6 and uniform susceptibility saturates at kT/J=1 for the isotropy case.And the size of lattice also affects the temperature dependence of these thermodynamic quantities.For the anisotropy case,energy decreases with anisotropic parameter g increasing.Susceptibility changes slowly with temperature for g1 and exponentially decay for g1 in the low temperature region and its behaviors approach consistent for different g in the high temperature region.
We investigate the Stochastic Series Expansion (SSE) technique, guided by Sandvik's algorithm of the quantum Monte Carlo simulation for spin-1/2 antiferromagnetic Heisenberg linear chain. The impact of the Monte Carlo steps, lattice sizes, and various temperatures on the variability and fidelity of simulation outcomes are studied. The findings show that the Monte Carlo steps where measurements are made (Msteps), and lattice size are crucial for stabilizing the results. Our results show that for larger lattice sizes, such as L=1024, achieving reliable outcomes necessitates extensive Monte Carlo simulations, specifically. The convergence in the properties is achieved with a high number of Monte Carlo steps starting from 7×10^4. Strong fluctuations are calculated between the results for each magnetic property and the existence of negative and positive in the specific heat at low temperatures.
We use the Quantum Monte Carlo Stochastic Series Expansion (SSE) algorithm to investigate the properties of the one-dimensional Heisenberg ferromagnet.We consider the model for two spin values s = 1 2 and s = 1 and study the dependence of the specific heat, magnetisation, magnetic susceptibility and correlation functions on temperature and magnetic field.Obtained results are compared to those derived by analytical methods (Bethe ansatz, Green's function, Random Phase Approximation).In particular, the surprising prediction of a double-peak structure in the specific heat at low temperatures and small magnetic fields can be confirmed.
Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. \textcopyright{} 1996 The American Physical Society.
Spin-1/2 nearest neighbor Heisenberg antiferromagnet and XY model on a square lattice are studied via large scale quantum Monte Carlo simulations using a fast and efficient multispin coding algorithm on the Caltech/JPL MarkIIIfp parallel supercomputer, based on the Suzuki-Trotter transformation. We performed simulations with very good statistics on lattices as large as 128x128 spins, in the temperature range from 0.1 to 2.5 in units of the effective exchange coupling J. We calculated energy, specific heat, magnetic susceptibilities and also spin correlation functions from which we deduce the correlation lengths. For the Heisenberg model, at temperatures higher than J the results are in excellent agreement with high-temperature series expansion. At low temperatures the long wavelength behavior is essentially classical. Our data show that the correlation length and staggered susceptibility are quantitatively well described by the renormalized classical picture at the 2-loop level of approximation. From the divergence of the correlation length, we deduce the value of the quantum renormalized spin stiffness, [rho][subscript s]/J = 0.199(2). We give evidence that the correlation function is of the Ornstein-Zernicke type. By comparing the largest measured correlation lengths with neutron scattering experiments on La2CuO4, we deduce the value of effective exchange coupling J = 1450±30 K. By measuring the imaginary time-dependent correlation functions, we show that the dynamics of the model can be well understood within a Bose liquid-type picture. The spin waves are rather sharp throughout most of the Brillouin zone and the damping is weakly dependent on the wave vector. In the case of the XY model, convincing numerical evidence is obtained on square lattices as large as 96x96 that the spin-1/2 XY model undergoes a Kosterlitz-Thouless (KT) phase transition at kTc/J = 0.350(4). The correlation length and in-plane susceptibility diverge at Tc precisely according to the form predicted by Kosterlitz and Thouless for the classical XY model. The specific heat increases very rapidly on heating near Tc and exhibits a peak around kT/J = 0.45. We also measure the spin stiffness and the correlation function exponent below the transition temperature. Within the statistical accuracy of the measurements, the results are well described by the square root singularity (with a nonuniversal amplitude) below Tc, and they have the universal values in agreement with KT theory at Tc.
Abstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( r=0r=0r=0 r = 0 ) case up to the diluted ( r→1r \rightarrow 1r→1 r → 1 ) limit, and for selected choices of number of legs LyL_yLy​ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing LyL_yLy​ L y . Graphical Abstract
One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as Sr3CuPt1−xIrxO6Sr_3 CuPt_{1-x} Ir_x O_6Sr3​CuPt1−x​Irx​O6​. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of Sr3CuPt1−xIrxO6Sr_3 CuPt_{1-x} Ir_x O_6Sr3​CuPt1−x​Irx​O6​ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.