In this Letter we present a novel quantum Monte Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}\stackrel{^}{H})$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.In this Letter we present a novel quantum Monte Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}\stackrel{^}{H})$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.

arXiv:cond-mat/9805255Physical Review LettersMay 24, 199983 citations

Quantum Monte Carlo for Lattice Fermions

Alejandro Muramatsu

Springer eBooksJan 1, 19997 citations

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.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:1411.0683Physical Review BJun 30, 201532 citations

Continuous-Time Quantum Monte Carlo Algorithms for Fermions

Emanuel Gull

Jan 1, 200822 citations

QUANTUM MONTE CARLO METHODS FOR FERMIONIC SYSTEMS: BEYOND THE FIXED-NODE APPROXIMATION

Nazım Dugan

Jan 1, 20100 citations

Perturbative solution of fermionic sign problem in quantum Monte Carlo computations

Sergei Iskakov, Mikhail I. Katsnelson, Alexander I. Lichtenstein

Abstract We have developed a strong-coupling perturbation scheme for a general doped Hubbard model around a particle-hole-symmetric reference system, which is free from the fermionic sign problem. Our approach is based on the lattice determinantal Quantum Monte Carlo (QMC) method in both continuous and discrete time versions for large periodic clusters in a fermionic bath. By considering the first-order perturbation in the shift of the chemical potential and the second-neighbor hopping, we are able to obtain an accurate electronic spectral function for a range of parameters that correspond to optimally doped cuprate systems at temperatures of up to T = 0.1 t , which are challenging to access using straightforward lattice QMC calculations. We also discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system with the interaction parameter U equal to the bandwidth and the optimal value of the next-nearest-neighbor hopping parameter ${t}^{{\prime} }$ t ′ for high-temperature superconducting cuprates.Abstract We have developed a strong-coupling perturbation scheme for a general doped Hubbard model around a particle-hole-symmetric reference system, which is free from the fermionic sign problem. Our approach is based on the lattice determinantal Quantum Monte Carlo (QMC) method in both continuous and discrete time versions for large periodic clusters in a fermionic bath. By considering the first-order perturbation in the shift of the chemical potential and the second-neighbor hopping, we are able to obtain an accurate electronic spectral function for a range of parameters that correspond to optimally doped cuprate systems at temperatures of up to T = 0.1 t , which are challenging to access using straightforward lattice QMC calculations. We also discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system with the interaction parameter U equal to the bandwidth and the optimal value of the next-nearest-neighbor hopping parameter $${t}^{{\prime} }$$ t ′ for high-temperature superconducting cuprates.

arXiv:2303.01607npj Computational MaterialsFeb 15, 20246 citations

{t}^{{\prime} }

t ′ for high-temperature superconducting cuprates.