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

arXiv:2009.07942 · Physical review. E

Thermal properties of rung-disordered two-leg quantum spin ladders: Quantum Monte Carlo study

Ulvi Kanbur, Hamza Polat, Erol Vatansever

Published Oct 6, 2020• 6 citations
arXivHTMLPDF

Abstract

A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.

DOI
10.1103/physreve.102.042104

Related papers

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

Bond disorder in even-leg Heisenberg ladders

Kien Trinh, Stephan Haas

Random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders is investigated using the stochastic series expansion quantum Monte Carlo method. We find that the effects of individual bond impurities vary strongly, depending on their positions on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes (${h}^{\ensuremath{'}}<h\ensuremath{\lesssim}{h}_{c1}$ and ${h}^{\ensuremath{'}\ensuremath{'}}<h<{h}_{c2}$) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.

arXiv:1211.7078•Physical Review B•Feb 22, 2013•4 citations

Quantum Monte Carlo Calculation for Spin Systems in Two-Leg Ladders with Alternating Heisenberg-Bond Chains

Takafumi Momose, Toshihiko Suzuki, Yuhei Natsume

Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.

Journal of the Physical Society of Japan•Jun 15, 1997•0 citations

Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder

Stefan Weßel, Bruce Normand, Frédéric Mila +1 more

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 where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L = 200 L = 200 rungs (400 spins 1/2) and down to very low temperatures.

arXiv:1704.01973•SciPost Physics•Jul 18, 2017•43 citations

Low-energy properties of antiferromagnetic spin-1/2 Heisenberg ladders with an odd number of legs

Beat Frischmuth, Stephan Haas, Germán Sierra +1 more

An effective low-energy description for multileg spin- Heisenberg ladders with an odd number of legs is proposed. Using a recently developed Monte Carlo loop algorithm and exact-diagonalization techniques, the uniform and staggered magnetic susceptibility and the entropy are calculated for ladders with one, three, and five legs. These systems show a low-temperature scaling behavior similar to spin- chains with longer ranged unfrustrated exchange interactions. The spinon velocity does not change as the number of legs increases, but the energy scale parameter decreases markedly.

arXiv:cond-mat/9606183•Physical review. B, Condensed matter•Feb 1, 1997•29 citations

Quantum Monte Carlo simulation of tow-dimensional antiferromagnetic Heisenberg model

Jinbin Li

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.

Journal of Guangxi University•Jan 1, 2011•0 citations
A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.
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
Random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders is investigated using the stochastic series expansion quantum Monte Carlo method. We find that the effects of individual bond impurities vary strongly, depending on their positions on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes (${h}^{\ensuremath{'}}<h\ensuremath{\lesssim}{h}_{c1}$ and ${h}^{\ensuremath{'}\ensuremath{'}}<h<{h}_{c2}$) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.
Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.
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 where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L = 200 L = 200 rungs (400 spins 1/2) and down to very low temperatures.
An effective low-energy description for multileg spin- Heisenberg ladders with an odd number of legs is proposed. Using a recently developed Monte Carlo loop algorithm and exact-diagonalization techniques, the uniform and staggered magnetic susceptibility and the entropy are calculated for ladders with one, three, and five legs. These systems show a low-temperature scaling behavior similar to spin- chains with longer ranged unfrustrated exchange interactions. The spinon velocity does not change as the number of legs increases, but the energy scale parameter decreases markedly.
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.