SciPost Physics

SciPost Phys. 3, 005 (2017) · published 18 July 2017

• doi: 10.21468/SciPostPhys.3.1.005
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

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.

• Mondaini et al., Quantum critical points and the sign problem
  Science 375, 418 (2022) [Crossref]
• Xu et al., Accurate Prediction of the Magnetic Ordering Temperature of Ultralow-Temperature Magnetic Refrigerants
  ACS Appl. Mater. Interfaces 16, 32394 (2024) [Crossref]
• Ma et al., Defining a universal sign to strictly probe a phase transition
  Phys. Rev. B 110, 125141 (2024) [Crossref]
• Sousa-Júnior et al., Half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations
  Phys. Rev. B 109, 165102 (2024) [Crossref]
• Zad et al., The specific heat and magnetic properties of two species of spin-1/2 ladders with butterfly-shaped unit blocks
  J. Phys.: Condens. Matter 31, 445802 (2019) [Crossref]
• De Nicola, Disentanglement approach to quantum spin ground states: field theory and stochastic simulation
  J. Stat. Mech. 2021, 013101 (2021) [Crossref]
• Luo et al., Intrinsic jump character of first-order quantum phase transitions
  Phys. Rev. B 100, 121111 (2019) [Crossref]
• Strečka et al., Frustrated magnetism of spin- 12 Heisenberg diamond and octahedral chains as a statistical mechanical monomer-dimer problem
  Phys. Rev. B 105, 064420 (2022) [Crossref]
• Weber et al., Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets
  SciPost Phys. 12, 054 (2022) [Crossref]
• Torlai et al., Wave-function positivization via automatic differentiation
  Phys. Rev. Research 2, 032060 (2020) [Crossref]
• Hen, Determining quantum Monte Carlo simulability with geometric phases
  Phys. Rev. Research 3, 023080 (2021) [Crossref]
• Jiang, Coupled cluster study of the coupled spin ladders with frustration
  Physica A: Statistical Mechanics and its Applications 540, 123131 123131 (2020) [Crossref]
• Almeida et al., Quantum bicritical point and phase separation in a frustrated Heisenberg ladder
  Phys. Rev. B 108, 224433 (2023) [Crossref]
• Ding et al., Thermodynamics of correlated electrons in a magnetic field
  Commun Phys 5, 204 (2022) [Crossref]
• Stapmanns et al., Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet
  Phys. Rev. Lett. 121, 127201 (2018) [Crossref]
• Wessel et al., Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations
  Phys. Rev. B 98, 174432 (2018) [Crossref]
• D'Emidio et al., Reduction of the sign problem near T=0 in quantum Monte Carlo simulations
  Phys. Rev. B 102, 064420 (2020) [Crossref]
• Hangleiter et al., Easing the Monte Carlo sign problem
  Sci. Adv. 6, eabb8341 (2020) [Crossref]
• Yi et al., Hamming distance and the onset of quantum criticality
  Phys. Rev. B 106, 205113 (2022) [Crossref]
• Chang et al., Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models
  Front. Phys. 19, 63202 (2024) [Crossref]
• Pan et al.,
  , 879 (2024) [Crossref]
• Rahaman et al., Interplay of alternation and further neighbor interaction in S=12 spin chains: A case study of Cs2CuAl4O8
  Phys. Rev. B 98, 144412 (2018) [Crossref]
• Ghimire et al., Frustrated plane-polarized dipoles in one dimension
  Phys. Rev. B 100, 115110 (2019) [Crossref]
• Ahmadi et al., Frustrated mixed-spin ladders: Evidence for a bond-order wave phase between rung-singlet and Haldane phases
  Phys. Rev. B 106, 174419 (2022) [Crossref]
• Mondaini et al., Universality and critical exponents of the fermion sign problem
  Phys. Rev. B 107, 245144 (2023) [Crossref]
• Lotshaw et al., Simulations of frustrated Ising Hamiltonians using quantum approximate optimization
  Phil. Trans. R. Soc. A. 381, 20210414 (2023) [Crossref]
• Slavin et al., Quantum Phase Transitions and Finite Size Effects in Frustrated Two-Leg Spin Ladders
  J Low Temp Phys 206, 182 (2022) [Crossref]
• Honecker et al., Quantum Monte Carlo simulations of highly frustrated magnets in a cluster basis: The two-dimensional Shastry-Sutherland model
  J. Phys.: Conf. Ser. 2207, 012032 (2022) [Crossref]