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We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than that…

Statistical Mechanics · Physics 2009-11-13 Nikolay Prokof'ev , Boris Svistunov

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is…

General Physics · Physics 2023-05-23 David H. Wei

The fermion sign problem constitutes one of the most fundamental obstacles in quantum many-body theory. Recently, it has been suggested to circumvent the sign problem by carrying out path integral simulations with a fictitious quantum…

Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…

Quantum Physics · Physics 2022-01-06 Yongdan Yang , Bing-Nan Lu , Ying Li

Ab-initio studies of strongly interacting bosonic and fermionic systems is greatly facilitated by efficient Monte Carlo algorithms. This article emphasizes this requirement, and outlines the ideas behind the construction of the cluster…

High Energy Physics - Lattice · Physics 2021-06-29 Debasish Banerjee

We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a $2D$ harmonic trap. We…

Computational Physics · Physics 2021-09-01 Tobias Dornheim

Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…

Quantum Physics · Physics 2020-08-19 Dominik Hangleiter , Ingo Roth , Daniel Nagaj , Jens Eisert

The fermion sign problem remains the primary obstacle in simulating the thermodynamic properties of various fermionic systems. In this work, we present a sign-blocking method to mitigate the numerical instability inherent in the sign…

Computational Physics · Physics 2026-04-14 Yunuo Xiong , Hongwei Xiong

Determinant quantum Monte Carlo (DQMC), formulated in complex-fermion representation, has played a key role in studying strongly-correlated fermion systems. However, its applicability is limited due to the requirement of particle-number…

Strongly Correlated Electrons · Physics 2024-08-21 Ze-Yao Han , Zhou-Quan Wan , Hong Yao

A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter…

Statistical Mechanics · Physics 2009-10-31 C. H. Mak , R. Egger , H. Weber-Gottschick

We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to…

Strongly Correlated Electrons · Physics 2019-09-11 Fedor Simkovic IV. , Evgeny Kozik

Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time $\beta$ and system size. The sign problem…

Strongly Correlated Electrons · Physics 2021-06-02 Ryan Levy , Bryan K. Clark

To account for the interference effects of the Coulomb and exchange interactions of electrons a new path integral representation of the density matrix has been developed in the canonical ensemble at finite temperatures. The developed…

Plasma Physics · Physics 2022-01-05 Vladimir Filinov , Pavel Levashov , Alexander Larkin

Computing the ground-state energy of interacting electron (fermion) problems has recently been shown to be hard for QMA, a quantum analogue of the complexity class NP. Fermionic problems are usually hard, a phenomenon widely attributed to…

Quantum Physics · Physics 2010-02-03 Tzu-Chieh Wei , Michele Mosca , Ashwin Nayak

We present a new Monte Carlo algorithm for simulating quantum spin systems which is able to suppress the negative sign problem. This algorithm has only a linear complexity in the lattice size used for the simulation. A general description…

High Energy Physics - Lattice · Physics 2007-05-23 A. Galli

Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…

Nuclear Theory · Physics 2026-01-06 Zhong-Wang Niu , Bing-Nan Lu

Quantum simulations are a powerful tool for exploring strongly correlated many-body phenomena. Yet, their reach is limited by the fermion sign problem, which causes configuration weights to become negative, compromising statistical…

Strongly Correlated Electrons · Physics 2025-12-04 Ryan Larson , Rubem Mondaini , Richard T. Scalettar

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo…

Strongly Correlated Electrons · Physics 2015-12-23 Lei Wang , Ye-Hua Liu , Mauro Iazzi , Matthias Troyer , Gergely Harcos

Ab-initio Monte Carlo simulations of strongly-interacting fermionic systems are plagued by the fermion sign problem, making the non-perturbative study of many interesting regimes of dense quantum matter, or of theories of odd numbers of…

High Energy Physics - Lattice · Physics 2024-03-05 Debasish Banerjee , Emilie Huffman

The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two…

Strongly Correlated Electrons · Physics 2018-01-19 Z. C. Wei , Congjun Wu , Yi Li , Shiwei Zhang , T. Xiang