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Related papers: A Generic Solution of Fermion Sign Problem

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We tutorially review the determinantal Quantum Monte Carlo method for fermionic systems, using the Hubbard model as a case study. Starting with the basic ingredients of Monte Carlo simulations for classical systems, we introduce aspects…

Strongly Correlated Electrons · Physics 2007-05-23 Raimundo R. dos Santos

We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of "ring-polymers" and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to…

Condensed Matter · Physics 2010-07-27 J. Shumway , D. M. Ceperley

The sign problem is a key challenge in computational physics, encapsulating our inability to properly understand many important quantum many-body phenomena in physics, chemistry and the material sciences. Despite its centrality, the…

Quantum Physics · Physics 2019-10-31 Lalit Gupta , Itay Hen

The calculation of the ground state and thermodynamics of mass-imbalanced Fermi systems is a challenging many-body problem. Even in one spatial dimension, analytic solutions are limited to special configurations and numerical progress with…

Quantum Gases · Physics 2018-07-20 Lukas Rammelmüller , William J. Porter , Joaquín E. Drut , Jens Braun

The mystery of the infamous sign problem in quantum Monte Carlo simulations mightily restricts applications of the method in fermionic and frustrated systems. A recent work [Science 375, 418 (2022)] made a remarkable breakthrough in the…

Statistical Mechanics · Physics 2024-09-27 Nvsen Ma , Jun-Song Sun , Gaopei Pan , Chen Cheng , Zheng Yan

A kink-based expression for the canonical partition function is developed using Feynman's path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on…

Statistical Mechanics · Physics 2009-11-07 Randall W. Hall

We investigate the positivity of the Euclidean path integral measure for low-energy modes in dense fermionic matter. We show that the sign problem usually associated with fermions is absent if one considers only low-energy degrees of…

High Energy Physics - Phenomenology · Physics 2017-08-23 D. K. Hong , S. D. H. Hsu

We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…

Computational Physics · Physics 2026-01-27 Arman Babakhani , Lev Barash , Itay Hen

We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo…

High Energy Physics - Lattice · Physics 2013-11-15 Marco Cristoforetti , Francesco Di Renzo , Abhishek Mukherjee , Luigi Scorzato

At nonzero quark chemical potential dynamical lattice simulations of QCD are hindered by the sign problem caused by the complex fermion determinant. The severity of the sign problem can be assessed by the average phase of the fermion…

High Energy Physics - Lattice · Physics 2011-05-27 Jacques Bloch , Tilo Wettig

Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong…

Computational Physics · Physics 2020-10-28 A. Yilmaz , K. Hunger , T. Dornheim , S. Groth , M. Bonitz

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a…

Condensed Matter · Physics 2009-10-28 Shiwei Zhang , J. Carlson , J. E. Gubernatis

We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although…

Strongly Correlated Electrons · Physics 2016-08-24 Ettore Vitali , Hao Shi , Mingpu Qin , Shiwei Zhang

The Feynman checkerboard problem is an interesting path integral approach to the Dirac equation in `1+1' dimensions. I compare two approaches reported in the literature and show how they may be reconciled. Some physical insights may be…

Mathematical Physics · Physics 2011-02-08 Keith A. Earle

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…

Statistical Mechanics · Physics 2022-08-31 Leticia F. Cugliandolo , Vivien Lecomte , Frédéric Van Wijland

We apply constant imaginary offsets to the path integral for a reduction of the sign problem in the Hubbard model. These simple transformations enhance the quality of results from HMC calculations without compromising the speed of the…

Strongly Correlated Electrons · Physics 2024-07-11 Christoph Gäntgen , Evan Berkowitz , Thomas Luu , Johann Ostmeyer , Marcel Rodekamp

The usual path integral formulation for scalar particles at finite density involves a sign problem, making numerical simulation impractical. We present alternative methods free of this difficulty. We apply these approaches to phi^4 theory…

High Energy Physics - Lattice · Physics 2008-11-26 Michael G. Endres

We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces…

Strongly Correlated Electrons · Physics 2026-01-21 Tu Hong , Kun Chen , Xiao Yan Xu

Quantum Monte Carlo (QMC) methods are powerful tools for simulating quantum many-body systems, yet their applicability is limited by the infamous sign problem. We approach this challenge through the lens of Vanishing Geometric Phases (VGP)…

Quantum Physics · Physics 2025-12-11 Arman Babakhani , Armen Karakashian

We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost…

High Energy Physics - Lattice · Physics 2017-12-13 Yuto Mori , Kouji Kashiwa , Akira Ohnishi