Publications

Order by: publication date number of citations

• Fast and stable determinant quantum Monte Carlo

  Carsten Bauer

  SciPost Phys. Core 2, 011 (2020) · published 29 June 2020 | Toggle abstract · pdf

  We assess numerical stabilization methods employed in fermion many-body quantum Monte Carlo simulations. In particular, we empirically compare various matrix decomposition and inversion schemes to gain control over numerical instabilities arising in the computation of equal-time and time-displaced Green's functions within the determinant quantum Monte Carlo (DQMC) framework. Based on this comparison, we identify a procedure based on pivoted QR decompositions which is both efficient and accurate to machine precision. The Julia programming language is used for the assessment and implementations of all discussed algorithms are provided in the open-source software library StableDQMC.jl [http://github.com/crstnbr/StableDQMC.jl].

  7 citations

• Nonequilibrium quasiparticle distribution in superconducting resonators: Effect of pair-breaking photons

  Paul B. Fischer, Gianluigi Catelani

  SciPost Phys. 17, 070 (2024) · published 2 September 2024 | Toggle abstract · pdf

  Many superconducting devices rely on the finite gap in the excitation spectrum of a superconductor: thanks to this gap, at temperatures much smaller than the critical one the number of excitations (quasiparticles) that can impact the device's behavior is exponentially small. Nevertheless, experiments at low temperature usually find a finite, non-negligible density of quasiparticles whose origin has been attributed to various non-equilibrium phenomena. Here, we investigate the role of photons with energy exceeding the pair-breaking threshold $2\Delta$ as a possible source for these quasiparticles in superconducting resonators. Modeling the interacting system of quasiparticles, phonons, sub-gap and pair-breaking photons using a kinetic equation approach, we find analytical expressions for the quasiparticles' density and their energy distribution. Applying our theory to measurements of quality factor as function of temperature and for various readout powers, we find they could be explained by assuming a small number of photons above the pair-breaking threshold. We also show that frequency shift data can give evidence of quasiparticle heating.

  7 citations

• Relaxation and entropy generation after quenching quantum spin chains

  Máté Lencses, Octavio Pomponio, Gabor Takacs

  SciPost Phys. 9, 011 (2020) · published 22 July 2020 | Toggle abstract · pdf

  This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving R\'enyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.

  7 citations

• (Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

  Andreas Schellenberger, Kai Phillip Schmidt

  SciPost Phys. Core 7, 038 (2024) · published 2 July 2024 | Toggle abstract · pdf

  We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst$^{++}$ [Phys. Rev. A 108, 013323 (2023)]

  7 citations

• Scalable imaginary time evolution with neural network quantum states

  Eimantas Ledinauskas, Egidijus Anisimovas

  SciPost Phys. 15, 229 (2023) · published 6 December 2023 | Toggle abstract · pdf

  The representation of a quantum wave function as a neural network quantum state (NQS) provides a powerful variational ansatz for finding the ground states of many-body quantum systems. Nevertheless, due to the complex variational landscape, traditional methods often employ the computation of quantum geometric tensor, consequently complicating optimization techniques. Contributing to efforts aiming to formulate alternative methods, we introduce an approach that bypasses the computation of the metric tensor and instead relies exclusively on first-order gradient descent with Euclidean metric. This allows for the application of larger neural networks and the use of more standard optimization methods from other machine learning domains. Our approach leverages the principle of imaginary time evolution by constructing a target wave function derived from the Schrödinger equation, and then training the neural network to approximate this target. We make this method adaptive and stable by determining the optimal time step and keeping the target fixed until the energy of the NQS decreases. We demonstrate the benefits of our scheme via numerical experiments with 2D $J_1-J_2$, Heisenberg model, which showcase enhanced stability and energy accuracy in comparison to direct energy loss minimization. Importantly, our approach displays competitiveness with the well-established density matrix renormalization group method and NQS optimization with stochastic reconfiguration.

  7 citations

• Quantum local random networks and the statistical robustness of quantum scars

  Federica Maria Surace, Marcello Dalmonte, Alessandro Silva

  SciPost Phys. 14, 174 (2023) · published 29 June 2023 | Toggle abstract · pdf

  We investigate the emergence of quantum scars in a general ensemble of random Hamiltonians (of which the PXP is a particular realization), that we refer to as quantum local random networks. We find a class of scars, that we call "statistical", and we identify specific signatures of the localized nature of these eigenstates by analyzing a combination of indicators of quantum ergodicity and properties related to the network structure of the model. Within this parallelism, we associate the emergence of statistical scars to the presence of "motifs" in the network, that reflects how these are associated to links with anomalously small connectivity. Most remarkably, statistical scars appear at well-defined values of energy, predicted solely on the base of network theory. We study the scaling of the number of statistical scars with system size: by continuously changing the connectivity of the system we find that there is a transition from a regime where the constraints are too weak for scars to exist for large systems to a regime where constraints are stronger and the number of statistical scars increases with system size. This allows to define the concept of "statistical robustness" of quantum scars.

  7 citations

• Suppression of the superfluid Kelvin-Helmholtz instability due to massive vortex cores, friction and confinement

  Matteo Caldara, Andrea Richaud, Massimo Capone, Pietro Massignan

  SciPost Phys. 17, 076 (2024) · published 10 September 2024 | Toggle abstract · pdf

  We characterize the dynamical instability responsible for the breakdown of regular rows and necklaces of quantized vortices that appear at the interface between two superfluids in relative motion. Making use of a generalized point-vortex model, we identify several mechanisms leading to the suppression of this instability. They include a non-zero mass of the vortex cores, dissipative processes resulting from the interaction between the vortices and the excitations of the superfluid, and the proximity of the vortex array to the sample boundaries. We show that massive vortex cores not only have a mitigating effect on the dynamical instability, but also change the associated scaling law and affect the direction along which it develops. The predictions of our massive and dissipative point-vortex model are eventually compared against recent experimental measurements of the maximum instability growth rate relevant to vortex necklaces in a cold-atom platform.

  7 citations

• Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

  Pavel A. Nosov, Ivan M. Khaymovich, Andrey Kudlis, Vladimir E. Kravtsov

  SciPost Phys. 12, 048 (2022) · published 1 February 2022 | Toggle abstract · pdf

  The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

  7 citations

• Parent Hamiltonians of Jastrow wavefunctions

  Mathieu Beau, Adolfo del Campo

  SciPost Phys. Core 4, 030 (2021) · published 18 November 2021 | Toggle abstract · pdf

  We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.

  7 citations

• Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra

  T. Scoquart, J. J. Seaward, S. G. Jackson, M. Olshanii

  SciPost Phys. 1, 005 (2016) · published 23 October 2016 | Toggle abstract · pdf

  The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line, related to the symmetry of a regular icosahedron: in two distinct limiting cases the system is constrained to a half-line. We repeat the program for a 600-cell, a four-dimensional generalization of the regular three-dimensional icosahedron.

  7 citations