Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

Alet, Fabien; Damle, Kedar; Pujari, Sumiran

doi:10.1103/physrevlett.117.197203

Cited by 49 publications

(64 citation statements)

References 64 publications

(77 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Closing this section with a brief technical summary, we perform stochastic series expansion [44] QMC simulations in the dimer basis [29,30] with directed loop updates [45,46] to compute the thermodynamic properties of the Shastry-Sutherland model (1) and to characterize the sign problem in the extended model (2). These simulations perform an unrestricted sampling of the configuration space, meaning one not constrained to any subset of the Hilbert space defined by the S z and D z operators of the total system.…”

Section: The Modelsmentioning

confidence: 99%

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

et al. 2018

View full text Add to dashboard Cite

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S = 1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter-and intra-dimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding "sign-problem-free" model, obtained by changing the signs of all positive off-diagonal matrix elements in the dimer basis. By exploiting this insight, we map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to zero temperature. For larger coupling ratios, our QMC results assist us in benchmarking the evolution of the thermodynamic properties by systematic comparison with exact diagonalization calculations and interpolated high-temperature series expansions. arXiv:1808.02043v2 [cond-mat.str-el] FIG. 1. Schematic representations of the extended Shastry-Sutherland model [Eq. (2)] in (a) single-plane and (b) bilayer format.

show abstract

Section: The Modelsmentioning

confidence: 99%

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

et al. 2018

View full text Add to dashboard Cite

show abstract

“…1, frustrated quantum spin models have been identified where the sign problem can indeed be overcome, and their number continues to grow. Leading methods for tackling the sign problem to date include meron and nested cluster algorithms [27,28,30] and a suitable choice of simulation basis [25,26,29,[31][32][33][34][35]68]. For the frustrated ladder, we follow the latter approach, taking the rung basis as a natural choice for the rewritten Hamiltonian (4).…”

Section: 1 Sign Problemmentioning

confidence: 99%

“…For the example of a frustrated ladder, the clusters correspond to the ladder rungs. In the present manuscript, we will go away from the case of perfect frustration, where the sign problem can be eliminated completely [33,34]. We will show that, although a sign problem remains present, it is so mild that the cluster basis allows efficient QMC simulations at all points in the phase diagram of the frustrated antiferromagnetic spin-1/2 ladder.The structure of this article is as follows.…”

mentioning

confidence: 94%

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

et al. 2017

View full text Add to dashboard Cite

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 rungs (400 spins 1/2) and down to very low temperatures.

show abstract

“…The "negative sign problem," or simply the "sign problem," is the single most important unresolved challenge in quantum manybody simulations, preventing physicists, chemists, and material scientists alike from a true understanding of many of the most profound macroscopic quantum physical phenomena of Nature-in areas as diverse as material design and high temperature superconductivity through the physics of neutron stars to lattice quantum chromodynamics, and more. [1][2][3][4] The sign problem slows down quantum Monte Carlo (QMC) algorithms, [5][6][7] which are in many cases the only tool available to us for studying large quantum many-body systems, to the point where these schemes become practically useless. QMC algorithms allow us to evaluate thermal averages of physical observables by sampling the configuration space of the model in question via the decomposition of the partition function into a sum of efficiently computable terms, which are in turn interpreted as probabilities in a Markov process.…”

Section: Introductionmentioning

confidence: 99%

Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem

Gupta

Hen

2019

Adv Quantum Tech

View full text Add to dashboard Cite

The sign problem is a key challenge in computational physics, encapsulating the inability to properly understand many important quantum many‐body phenomena in physics, chemistry, and the material sciences. Despite its centrality, the circumstances under which the problem arises or can be resolved as well as its interplay with the related notion of “non‐stoquasticity” are often not very well understood. In this study, an attempt is made to elucidate the circumstances under which the sign problem emerges and to clear up some of the confusion surrounding this intricate computational phenomenon. To that aim, the recently introduced off‐diagonal series expansion quantum Monte Carlo scheme is used to analyze in detail a number of examples that capture the essence of the results.

show abstract

Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

Cited by 49 publications

References 64 publications

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

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

Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem

Contact Info

Product

Resources

About