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

Fabien Alet, Kedar Damle, and Sumiran Pujari
Phys. Rev. Lett. 117, 197203 – Published 4 November 2016
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    Abstract

    We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.

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    • Received 21 January 2016

    DOI:https://doi.org/10.1103/PhysRevLett.117.197203

    © 2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Frustrated magnetism
    1. Techniques
    Monte Carlo methods
    Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

    Authors & Affiliations

    Fabien Alet1, Kedar Damle2, and Sumiran Pujari3

    • 1Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, 31062 Toulouse, France
    • 2Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005, India
    • 3Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055, USA

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    Vol. 117, Iss. 19 — 4 November 2016

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    Images

    • Figure 1
      Figure 1

      Vertices that appear in the SSE operator string for Hbilayer, with corresponding weights in the canonical cluster basis. All other valid vertices are obtained by symmetry operations that exchange left and right, or upper and lower, legs (keeping the weight fixed). The constant C in the function f(lA,lB,mA,mB)=C−JzmAmB−ζ(Δz−Δ⊥)(mA2+mB2)−ζΔ⊥[lA(lA+1)+lB(lB+1)] is chosen to ensure that f≥0. Bottom right: Lattice structure and exchange couplings of Hbilayer. Vertices and lattice structure for Hmixed are detailed in Supplemental Material [56].

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    • Figure 2
      Figure 2

      Temperature (T) dependence of the susceptibility and specific heat of Hbilayer with Dz=D⊥=1, J⊥=K⊥=1, Jz=1+Kz, and Kz=1−Kz. Symbols display data for a sample with L=64 unit cells, plotted for a variety of values of Kz. The inset shows the perfect agreement between QMC data (symbols) and exact diagonalization results (lines) for L=6.

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    • Figure 3
      Figure 3

      QMC results (symbols) for Hbilayer in a field on the square lattice, with Jz=Kz=1, Dz=D⊥=5, J⊥=1+K⊥, K⊥=1−K⊥, and h=7. Left panel: Specific heat Cv for K⊥=0 (inset zooms into the critical range). Right panels: Binder cumulant U=⟨ms4⟩/⟨ms2⟩2 of the staggered magnetization ms=∑r(−)r(SIrz+SIIrz). The critical temperature Tc, estimated by the crossing point of U, decreases with K⊥. U at the estimated Tc tends to the 2d Ising critical value U*=1.16793 [62] at large L for all K⊥ displayed. The solid lines in the K⊥>0 panels are guides to the eye. At K⊥=0, they denote results for the 2d classical Ising model at TIsing=4T.

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    • Figure 4
      Figure 4

      This operator string for a single plaquette of the Bravais lattice of the bilayer system illustrates the origin of the sign problem faced when simulating the general bilayer Hamiltonian Hbilayer: Its weight is negative, independent of the signs of the nonzero couplings J⊥, Kz, and K⊥.

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