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

Modern Physics Letters B

QUANTUM MONTE CARLO ALGORITHM FOR CONSTRAINED FERMIONS

X. Y. Zhang

Published Aug 20, 1991• 2 citations
Publisher

Abstract

Using path integral quantization in the subspace that forbids double occupancy, we introduce a quantum Monte Carlo algorithm for simulation of fermion models with constraint. The algorithm can be applied to a class of lattice fermion models, including the infinite-U Hubbard model and the t - J model.
DOI
10.1142/s0217984991001532

Related papers

Quantum Monte Carlo algorithm for constrained fermions: Application to the infinite-UHubbard model

X. Y. Zhang, Elihu Abrahams, Gabriel Kotliar

By constructing a complete set of coherent states that forbids double occupancy, we introduce a quantum Monte Carlo algorithm for simulation of fermion models with constraint, including the infinite-U Hubbard model and the t-J model. Application to the infinite-U Hubbard model on 4\ifmmode\times\else\texttimes\fi{}4 and 6\ifmmode\times\else\texttimes\fi{}6 lattices provides new physical results on the thermodynamics of the model, especially the temperature and doping dependence of the Nagaoka state.

Physical Review Letters•Mar 4, 1991•43 citations

Infinite variance in fermion quantum Monte Carlo calculations

Hao Shi, Shiwei Zhang

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

arXiv:1511.04084•Physical review. E•Mar 7, 2016•59 citations

Quantum Path-integral Method for Fictitious Particle Hubbard Model

Zhijie Fan, Tianning Xiao, Youjin Deng

We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a continuous parameter $ξ$ in the partition function that interpolates between bosonic ($ξ= 1$) and fermionic ($ξ= -1$) statistics. We generalize this approach to discrete lattice models and apply it to the two-dimensional Hubbard model of fictitious particles, including the Bose- and Fermi-Hubbard models as special cases. By combining reweighting and $ξ$-extrapolation techniques, we access both half-filled and doped regimes. In particular, we demonstrate that the method remains effective even in strongly correlated, doped systems where the fermion sign problem hinders conventional quantum Monte Carlo approaches. Our results validate the applicability of the fictitious particle framework on lattice models and establish it as a promising tool for sign-problem mitigation in strongly interacting fermionic systems.

arXiv:2508.01760•Aug 3, 2025•1 citation

Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models

Mauro Iazzi, Matthias Troyer

Efficient continuous-time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state of the art for most discrete quantum models. They have not been widely used yet for fermionic quantum lattice models, such as the Hubbard model, nor other fermionic lattice systems due to a suboptimal scaling of $O({\ensuremath{\beta}}^{3})$ with inverse temperature $\ensuremath{\beta}$, compared to the linear scaling of discrete-time algorithms. Here we present a CT-QMC algorithm for fermionic lattice systems that matches the scaling of discrete-time methods but is more efficient and free of time discretization errors. This provides an efficient simulation scheme that is free from the systematic errors opening an avenue to more precise studies of large systems at low and zero temperature.

arXiv:1411.0683•Physical Review B•Jun 30, 2015•32 citations

QUANTUM MONTE-CARLO SIMULATIONS - ALGORITHMS, LIMITATIONS AND APPLICATIONS

Hans A. De Raedt

A survey is given of Quantum Monte Carlo methods currently used to simulate quantum lattice models. The formalisms employed to construct the simulation algorithms are sketched. The origin of fundamental (minus sign) problems which limit the applicability of the Quantum Monte Carlo approach is shown to be a generic feature of the formalisms used to devise the simulation algorithms. A brief overview of recent new developments is given.

Helvetica Physica Acta (Switzerland)•Jan 1, 1992•0 citations

PROJECTOR APPROXIMATION AND QUANTUM MONTE CARLO

Richard M. Fye

We derive a general approximation for performing quantum Monte Carlo simulations within a desired subspace of the full Hilbert space. We analytically determine the form of the resulting systematic error, allowing controlled extrapolation to exact results. We discuss some numerical applications, including fermion impurity and lattice models with infinite on-site Colulomb repulsion U and quantum spin systems. We demonstrate the use of the approximation in simulations with a test model.

International Journal of Modern Physics C•Jun 1, 1994•0 citations
By constructing a complete set of coherent states that forbids double occupancy, we introduce a quantum Monte Carlo algorithm for simulation of fermion models with constraint, including the infinite-U Hubbard model and the t-J model. Application to the infinite-U Hubbard model on 4\ifmmode\times\else\texttimes\fi{}4 and 6\ifmmode\times\else\texttimes\fi{}6 lattices provides new physical results on the thermodynamics of the model, especially the temperature and doping dependence of the Nagaoka state.
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a continuous parameter ξξξ in the partition function that interpolates between bosonic (ξ=1ξ= 1ξ=1) and fermionic (ξ=−1ξ= -1ξ=−1) statistics. We generalize this approach to discrete lattice models and apply it to the two-dimensional Hubbard model of fictitious particles, including the Bose- and Fermi-Hubbard models as special cases. By combining reweighting and ξξξ-extrapolation techniques, we access both half-filled and doped regimes. In particular, we demonstrate that the method remains effective even in strongly correlated, doped systems where the fermion sign problem hinders conventional quantum Monte Carlo approaches. Our results validate the applicability of the fictitious particle framework on lattice models and establish it as a promising tool for sign-problem mitigation in strongly interacting fermionic systems.
Efficient continuous-time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state of the art for most discrete quantum models. They have not been widely used yet for fermionic quantum lattice models, such as the Hubbard model, nor other fermionic lattice systems due to a suboptimal scaling of $O({\ensuremath{\beta}}^{3})$ with inverse temperature $\ensuremath{\beta}$, compared to the linear scaling of discrete-time algorithms. Here we present a CT-QMC algorithm for fermionic lattice systems that matches the scaling of discrete-time methods but is more efficient and free of time discretization errors. This provides an efficient simulation scheme that is free from the systematic errors opening an avenue to more precise studies of large systems at low and zero temperature.