A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm

Abstract

Quantum Monte-Carlo (QMC) simulations involving fermions have the notorious sign problem. Some well-known exceptions of the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC algorithm [1] has been found in which the fermion determinant may not necessarily factorizable, but can instead be expressed as a product of complex conjugate pairs of eigenvalues, thus eliminating the sign problem for a much wider class of models. In this paper, we present general conditions for the applicability of this algorithm and point out that it is deeply related to the time reversal symmetry of the fermion matrix. We apply this method to various models of strongly correlated systems at all doping levels and lattice geometries, and show that many novel phases can be simulated without the sign problem.

arXiv comment14 pages, 7 figures, to appear in Phys. Rev. B

References in corpus (21)

• Hidden Order in the Cuprates
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Exact SO(5) Symmetry in spin 3/2 fermionic system
• SO(5) Theory of Antiferromagnetism and Superconductivity
• SU(4) Theory for Spin Systems with Orbital Degeneracy
• Density Wave States of Non-Zero Angular Momentum
• Meron-Cluster Solution of Fermion Sign Problems
• Exact SO(8) Symmetry in the Weakly-Interacting Two-Leg Ladder
• Numerical Study of Dense Adjoint Matter in Two Color QCD
• Dynamic generation of spin orbit coupling
• Pairing of Fermions with Arbitrary Spin
• Path-Integral Renormalization Group Method for Numerical Study on Ground States of Strongly Correlated Electronic Systems
• An SO(5) Symmetric Ladder
• Path-Integral Renormalization Group Method for Numerical Study of Strongly Correlated Electron Systems
• Competing Orders in Coupled Luttinger Liquids
• Generalized two-leg Hubbard ladder at half-filling: Phase diagram and quantum criticalities
• A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models
• Thermodynamical properties of a mean-field plus pairing model and applications for the Fe nuclei
• Current Carrying Ground State in a Bi-layer Model
• Electronic Ladders with SO(5) Symmetry: Phase Diagrams and Correlations at half-filling
• Spin and charge dynamics of stripes in doped Mott insulators

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