Hybrid Quantum Monte Carlo for Condensed Matter Models

Beyl, Stefan

doi:10.25972/opus-19122

Cited by 4 publications

(3 citation statements)

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“…• The biggest drawback of the above decomposition is that the imaginary-time propagation is not Hermitian. This can lead to acausal features in imaginary-time correlation functions [121]. To be more precise, the eigenvalues of H Approx = − 1 β log U Approx need not be real and thus imaginary-time displaced correlation functions may oscillate as a function of imaginary time.…”

Section: Asymmetric Trotter Decompositionmentioning

confidence: 99%

The ALF (Algorithms for Lattice Fermions) project release 2.3. Documentation for the auxiliary-field quantum Monte Carlo code

Collaboration¹,

Assaad²,

Bercx³

et al. 2020

Preprint

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The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z 2 unconstrained lattice gauge theories coupled to fermionic and Z 2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.

show abstract

Section: Asymmetric Trotter Decompositionmentioning

confidence: 99%

The ALF (Algorithms for Lattice Fermions) project release 2.3. Documentation for the auxiliary-field quantum Monte Carlo code

Collaboration¹,

Assaad²,

Bercx³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In order to mitigate concerns regarding the accuracy of the checkerboard approximation, a symmeterized form Γ † σ ( ∆τ 2 )• Γσ ( ∆τ 2 ) can be used instead. This form results in a Hermitian checkerboard matrix and significantly improves the overall accuracy of the checkerboard approximation [121]. In a DQMC simulation, this corresponds to using the checkerboard approximation in conjunction with the symmetric definition for the propagator matrices B σ,l , as defined by Eq.…”

Section: End If End If End Formentioning

confidence: 99%

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

Cohen-Stead,

Costa,

Neuhaus

et al. 2024

SciPost Phys. Codebases

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We introduce the SmoQyDQMC.jl package, a Julia implementation of the determinant quantum Monte Carlo algorithm. SmoQyDQMC.jl supports generalized tight-binding Hamiltonians with on-site Hubbard and generalized electron-phonon (ee-ph) interactions, including non-linear ee-ph coupling and anharmonic lattice potentials. Our implementation uses hybrid Monte Carlo methods with exact forces for sampling the phonon fields, enabling efficient simulation of low-energy phonon branches, including acoustic phonons. The SmoQyDQMC.jl package also uses a flexible scripting interface, allowing users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our document page at https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

show abstract

“…• The biggest drawback of the above decomposition is that the imaginary-time propagation is not Hermitian. This can lead to acausal features in imaginary-time correlation functions [126]. To be more precise, the eigenvalues of H Approx = − 1 β log U Approx need not be real and thus imaginary-time displaced correlation functions may oscillate as a function of imaginary time.…”

Section: The Trotter Error and Checkerboard Decomposition 231 Asymmet...mentioning

confidence: 99%

The ALF (Algorithms for Lattice Fermions) project release 2.0. Documentation for the auxiliary-field quantum Monte Carlo code

Assaad

Bercx

Goth

et al. 2022

SciPost Phys. Codebases

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The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five predefined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as Z_2Z2 unconstrained lattice gauge theories coupled to fermionic and Z_2Z2 matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.

show abstract

Hybrid Quantum Monte Carlo for Condensed Matter Models

Cited by 4 publications

References 0 publications

The ALF (Algorithms for Lattice Fermions) project release 2.3. Documentation for the auxiliary-field quantum Monte Carlo code

The ALF (Algorithms for Lattice Fermions) project release 2.3. Documentation for the auxiliary-field quantum Monte Carlo code

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

The ALF (Algorithms for Lattice Fermions) project release 2.0. Documentation for the auxiliary-field quantum Monte Carlo code

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