Publications

Order by: publication date number of citations

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

  Benjamin Cohen-Stead, Sohan Malkaruge Costa, James Neuhaus, Andy Tanjaroon Ly, Yutan Zhang, Richard Scalettar, Kipton Barros, Steven Johnston

  SciPost Phys. Codebases 29 (2024) · published 28 May 2024 | Toggle abstract · pdf

  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 ($e$-ph) interactions, including non-linear $e$-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/.

  3 citations

• Pfaffian invariant identifies magnetic obstructed atomic insulators

  Isidora Araya Day, Anastasiia Varentcova, Daniel Varjas, Anton R. Akhmerov

  SciPost Phys. 15, 114 (2023) · published 25 September 2023 | Toggle abstract · pdf

  We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four $C_4 \mathcal{T}$-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a $C_4 \mathcal{T}$-symmetric model that interpolates between them. The phase diagram shows that $C_4 \mathcal{T}$ insulators allow $\pm 1$ and $2$ changes of the invariant, where the latter is overlooked by symmetry indicators.

  3 citations

• Quantum annealing for neural network optimization problems: A new approach via tensor network simulations

  Guglielmo Lami, Pietro Torta, Giuseppe E. Santoro, Mario Collura

  SciPost Phys. 14, 117 (2023) · published 17 May 2023 | Toggle abstract · pdf

  Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

  3 citations

• Structural classification of boron nitride twisted bilayers and ab initio investigation of their stacking-dependent electronic structure

  Sylvain Latil, Hakim Amara, Lorenzo Sponza

  SciPost Phys. 14, 053 (2023) · published 29 March 2023 | Toggle abstract · pdf

  Since the discovery of superconductive twisted bilayer graphene which initiated the field of twistronics, moiré systems have not ceased to exhibit fascinating properties. We demonstrate that in boron nitride twisted bilayers, for a given moiré periodicity, there are five different stackings which preserve the monolayer hexagonal symmetry (i.e. the invariance upon rotations of 120°) and not only two as always discussed in literature. We introduce some definitions and a nomenclature that identify unambiguously the twist angle and the stacking sequence of any hexagonal bilayer with order-3 rotation symmetry. Moreover, we employ density functional theory to study the evolution of the band structure as a function of the twist angle for each of the five stacking sequences of boron nitride bilayers. We show that the gap is indirect at any angle and in any stacking, and identify features that are conserved within the same stacking sequence irrespective of the angle of twist.

  3 citations

• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation

  Miguel Alvarado, Alfredo Levy Yeyati

  SciPost Phys. 13, 009 (2022) · published 25 July 2022 | Toggle abstract · pdf

  Since the breakthrough of twistronics a plethora of topological phenomena in correlated systems has appeared. These devices can be typically analyzed in terms of lattice models using Green's function techniques. In this work we introduce a general method to obtain the boundary Green's function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. We illustrate our formalism analyzing the edge features of a Chern insulator, the Kitaev square lattice model for a topological superconductor and the Checkerboard lattice hosting topological flat bands. The efficiency and accuracy of the method is demonstrated by comparison to standard recursive Green's function calculations and direct diagonalizations.

  3 citations

• Collective Monte Carlo updates through tensor network renormalization

  Miguel Frías-Pérez, Michael Mariën, David Pérez García, Mari Carmen Bañuls, Sofyan Iblisdir

  SciPost Phys. 14, 123 (2023) · published 22 May 2023 | Toggle abstract · pdf

  We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present benchmark computations for a wide variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass instances, and we show that, with modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points. In each of the situations we have considered, the Markov chain compares well with other Monte Carlo schemes such as the Metropolis or Wolff's algorithm: equilibration times appear to be reduced by a factor that varies between $40$ and $2000$, depending on the model and the observable being monitored. We also present an extension to three spatial dimensions, and demonstrate that it exhibits fast equilibration for finite ferro- and antiferromagnetic instances. Additionally, and although it is originally designed for a square lattice of finite degrees of freedom with open boundary conditions, the proposed scheme can be used as such, or with slight modifications, to study triangular lattices, systems with continuous degrees of freedom, matrix models, a confined gas of hard spheres, or to deal with arbitrary boundary conditions.

  3 citations

• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

  Natalia Chepiga

  SciPost Phys. Core 5, 031 (2022) · published 30 May 2022 | Toggle abstract · pdf

  By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we verify that in the quantum three-state Potts model the "new" boundary conditions dual to the mixed ones can be realized by polarizing edge spins along the transverse field.

  3 citations

• Efficient flow equations for dissipative systems

  Gary Schmiedinghoff, Götz S. Uhrig

  SciPost Phys. 13, 122 (2022) · published 13 December 2022 | Toggle abstract · pdf

  Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

  2 citations

• Codebase release 1.0 for SpinParser

  Finn Lasse Buessen

  SciPost Phys. Codebases 5-r1.0 (2022) · published 24 August 2022 | Toggle abstract · src

  We present the SpinParser open-source software [ https://github.com/fbuessen/SpinParser ]. The software is designed to perform pseudofermion functional renormalization group (pf-FRG) calculations for frustrated quantum magnets in two and three spatial dimensions. It aims to make such calculations readily accessible without the need to write specialized program code; instead, custom lattice graphs and microscopic spin models can be defined as plain-text input files. Underlying symmetries of the model are automatically analyzed and exploited by the numerical core written in C++ in order to optimize the performance across large-scale shared memory and/or distributed memory computing platforms.

  2 citations

• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

  Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch

  SciPost Phys. 14, 052 (2023) · published 28 March 2023 | Toggle abstract · pdf

  The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spin-spin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>-\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

  2 citations