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

Assaad, Fakher F.; Bercx, Martin; Goth, Florian; Götz, Anika; Hofmann, Johannes S.; Huffman, Emilie; Liu, Z.; Toldin, Francesco Parisen; Portela, Jefferson S. E.; Schwab, Jonas

doi:10.21468/scipostphyscodeb.1

Cited by 41 publications

(6 citation statements)

References 149 publications

(154 reference statements)

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“…The squared operators in the second line of ( 14) are Hermitian, and thus AFQMC as implemented in [17] is applicable. The projector we use is the half-filled solution to the model when g 0 = g 1 = 0, where the Ising spins are polarized by the transverse field term h c † m σ x τ 0 c m .…”

Section: Qmc Simulationsmentioning

confidence: 99%

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

Hofmann,

Goth,

Zhu

et al. 2024

SciPost Phys. Core

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We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional SU(2) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

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Section: Qmc Simulationsmentioning

confidence: 99%

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

Hofmann,

Goth,

Zhu

et al. 2024

SciPost Phys. Core

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“…Several open-source implementations of the DQMC algorithm have been developed over the years with support for different classes of Hamiltonians. Perhaps the most popular and well-known are the Algorithms for Lattice Fermions (ALF) [5] and QUantum Electron Simulation Toolbox (QUEST) [4] projects. The QUEST package supports single-and multi-orbital Hubbard Hamiltonians defined on arbitrary lattice geometries.…”

Section: Background and Motivationmentioning

confidence: 99%

“…[116]. Our package also stores intermediate matrix products to improve the algorithm's efficiency [5,117,118], an approach described in greater detail below. To outline this procedure, we first introduce the L DR matrix factorization, which represents products of propagator matrices B σ,l and is based on the column-pivoted QR factorization.…”

Section: Numerically Stable Framework For Dqmc Simulationsmentioning

confidence: 99%

“…Hamiltonians can be defined on arbitrary lattice geometries and a wide variety of measurements can be performed for these simulations, including density-density, spin-spin, currentcurrent correlation functions and pairing for different symmetries. The code has been designed with a scripting interface inspired by packages like ITensor.jl [3], rather than a configuration file-based workflow commonly found in open-source implementations of DQMC [4,5]. This design allows users to easily incorporate SmoQyDQMC.jl into complex workflows and directly interface it with the Julia programming language's rich ecosystem of scientific computing and machine learning packages.…”

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confidence: 99%

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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/.

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“…Note that after computing the square one will explicitly see that the Hamiltonian is α-independent. For any value of α, we can use the ALF [19] implementation of the finite temperature auxiliary field QMC algorithm [20][21][22][23]. In fact, Eq.…”

Section: Quantum Monte Carlo Simulationsmentioning

confidence: 99%

On the validity of SLAC fermions for the 1+1D helical Luttinger liquid

Wang¹,

Assaad²,

Ulybyshev³

2022

Preprint

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The Nielson-Ninomiya theorem states that a chirally invariant free fermion lattice action, which is local, translation invariant, and real necessarily has fermion doubling. The SLAC approach gives up on locality and long range hopping leads to a linear dispersion with singularity at the zone boundary. We introduce a SLAC Hamiltonian formulation of the U(1) helical Luttinger liquid and compare our results to bosonization. We argue that non-locality and concomitant singularity at the zone edge has important implications. Large momentum transfers yield spurious features already in the noninteracting case. Upon switching interactions non-locality invalidates the Mermin-Wagner theorem and allows for long ranged magnetic ordering such that a single particle gap opens at the Dirac point. Nonetheless, since non-locality allows for charge fluctuations at any length scale, the ground state remains metallic. Hence, SLAC and bosonization results show marked differences already at intermediate coupling strengths.

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

Cited by 41 publications

References 149 publications

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

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

On the validity of SLAC fermions for the 1+1D helical Luttinger liquid

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