Applying the tempered Lefschetz thimble method to the Hubbard model away from half-filling

Abstract

The tempered Lefschetz thimble method is a parallel-tempering algorithm towards solving the numerical sign problem. It uses the flow time of the gradient flow as a tempering parameter and is expected to tame both the sign and multimodal problems simultaneously. In this paper, we further develop the algorithm so that the expectation values can be estimated precisely with a criterion ensuring global equilibrium and the sufficiency of the sample size. To demonstrate that this algorithm works well, we apply it to the quantum Monte Carlo simulation of the Hubbard model away from half-filling on a two-dimensional lattice of small size, and show that the numerical results agree nicely with exact values.

arXiv comment12 pages, 9 figures. v2: some discussions clarified, references added. To appear in Physical Review D

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Cited by in corpus (27)

• Quantum Critical Points and the Sign Problem
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Path integral contour deformations for observables in $SU(N)$ gauge theory
• Path integral contour deformations for noisy observables
• Worldvolume approach to the tempered Lefschetz thimble method
• Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
• Implementation of the HMC algorithm on the tempered Lefschetz thimble method
• Sign Problem in Quantum Monte Carlo Simulation
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• Deconvolving the components of the sign problem
• Simulating Yang-Mills theories with a complex coupling
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Improving efficiency of the path optimization method for a gauge theory
• On the Infinite Variance Problem in Fermion Models
• Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm
• Instanton gas approach to the Hubbard model
• Application of the path optimization method to a discrete spin system
• Single Particle Spectrum of Doped ${\mathrm{C}}_{20}{\mathrm{H}}_{12}$-Perylene
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Tensor network approach to 2D Yang-Mills theories
• Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions
• Distance between configurations in MCMC simulations and the geometrical optimization of the tempering algorithms
• Emergent quantum geometry from stochastic random matrices
• Evading the model sign problem in the PNJL model with repulsive vector-type interaction via path optimization
• Tempered Lefschetz thimble method and its application to the Hubbard model away from half filling