Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Monte Carlo Methods applied to strongly correlated and highly inhomogeneous many-Fermion systems

Lucia Dandrea

Published Jan 1, 2009• 0 citations
Publisher

Abstract

Quantum Monte Carlo Methods applied to strongly correlated and highly inhomogeneous many-Fermion systems
DOI
10.15168/11572_369209

Related papers

Quantum Monte Carlo (QMC) Methods for strongly correlated Bose and Fermi Systems

Nandini Trivedi

Bulletin of the American Physical Society•Jun 7, 2007•0 citations

High-order Path Integral Monte Carlo methods for solving strongly correlated fermion problems

Siu A. Chin

Bulletin of the American Physical Society•Mar 2, 2015•0 citations

Quantum Monte Carlo Methods for Strongly Correlated Electron Systems

Shiwei Zhang

Springer eBooks•May 8, 2006•9 citations

Elective-momentum ultrasize quantum Monte Carlo method

Zi Hong Liu, Xiao Yan Xu, Yang Qi +2 more

One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions, the best methodology at hand still scales with $\ensuremath{\beta}{N}^{3}$ where $\ensuremath{\beta}$ is the inverse temperature and $N$ is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated electron models at (2+1)D, let alone (3+1)D. To reduce the computational complexity, we develop a new QMC method with inhomogeneous momentum-space mesh, dubbed elective-momentum ultrasize quantum Monte Carlo (EQMC) method. Instead of treating all fermionic excitations on an equal footing as in conventional QMC methods, by converting the fermion determinant into the momentum space, our method focuses on fermion modes that are directly associated with low-energy (IR) physics in the vicinity of the so-called hot spots, while other fermion modes irrelevant for universal properties are ignored. As shown in the paper, for any cutoff-independent quantities, e.g., scaling exponents, this method can achieve the same level of accuracy with orders of magnitude increase in computational efficiency. We demonstrate this method with a model of antiferromagnetic itinerant quantum critical point, realized via coupling itinerant fermions with a frustrated transverse-field Ising model on a triangle lattice. The system size of $48\ifmmode\times\else\texttimes\fi{}48\ifmmode\times\else\texttimes\fi{}32$ ($L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}\ensuremath{\beta}$, almost 3 times of previous investigations) are comfortably accessed with EQMC. With much larger system sizes, the scaling exponents are unveiled with unprecedentedly high accuracy, and this result sheds new light on the open debate about the nature and the universality class of itinerant quantum critical points.

arXiv:1801.00127•Physical review. B./Physical review. B•Feb 11, 2019•19 citations

Quantum Monte Carlo Studies of Strongly Interacting Fermionic Systems

Lucas Madeira

•Jan 1, 2018•0 citations

Computation of dynamical correlation functions for many-fermion systems with auxiliary-field quantum Monte Carlo

Ettore Vitali, Hao Shi, Mingpu Qin +1 more

Quantum Monte Carlo simulations provide a powerful tool to compute static properties of quantum many-particles models and realistic systems. A vast array of ground-state energies and properties defined by equal-time correlation functions can be computed with high accuracy. On the other hand, the extensions needed to study time-displaced correlation functions, which provide access to excited states, have been challenging, especially for fermionic strongly correlated systems. The authors present a methodology that allows a high-accuracy calculation of the dynamical Green functions of many-fermions systems in the framework of the auxiliary-field quantum Monte Carlo method. They extract the the charge gap of the repulsive two-dimensional Hubbard model at half-filling as a function of the interaction strength and propose strategies for applying their methodology to more realistic systems.

arXiv:1606.04785•Physical review. B./Physical review. B•Aug 23, 2016•56 citations
One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions, the best methodology at hand still scales with $\ensuremath{\beta}{N}^{3}$ where $\ensuremath{\beta}$ is the inverse temperature and NNN is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated electron models at (2+1)D, let alone (3+1)D. To reduce the computational complexity, we develop a new QMC method with inhomogeneous momentum-space mesh, dubbed elective-momentum ultrasize quantum Monte Carlo (EQMC) method. Instead of treating all fermionic excitations on an equal footing as in conventional QMC methods, by converting the fermion determinant into the momentum space, our method focuses on fermion modes that are directly associated with low-energy (IR) physics in the vicinity of the so-called hot spots, while other fermion modes irrelevant for universal properties are ignored. As shown in the paper, for any cutoff-independent quantities, e.g., scaling exponents, this method can achieve the same level of accuracy with orders of magnitude increase in computational efficiency. We demonstrate this method with a model of antiferromagnetic itinerant quantum critical point, realized via coupling itinerant fermions with a frustrated transverse-field Ising model on a triangle lattice. The system size of $48\ifmmode\times\else\texttimes\fi{}48\ifmmode\times\else\texttimes\fi{}32$ ($L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}\ensuremath{\beta}$, almost 3 times of previous investigations) are comfortably accessed with EQMC. With much larger system sizes, the scaling exponents are unveiled with unprecedentedly high accuracy, and this result sheds new light on the open debate about the nature and the universality class of itinerant quantum critical points.
Quantum Monte Carlo simulations provide a powerful tool to compute static properties of quantum many-particles models and realistic systems. A vast array of ground-state energies and properties defined by equal-time correlation functions can be computed with high accuracy. On the other hand, the extensions needed to study time-displaced correlation functions, which provide access to excited states, have been challenging, especially for fermionic strongly correlated systems. The authors present a methodology that allows a high-accuracy calculation of the dynamical Green functions of many-fermions systems in the framework of the auxiliary-field quantum Monte Carlo method. They extract the the charge gap of the repulsive two-dimensional Hubbard model at half-filling as a function of the interaction strength and propose strategies for applying their methodology to more realistic systems.