Research

23 pages, 8102 KiB

Open AccessArticle

A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities

by Sergi De María-García, Albert Ferrando, J. Alberto Conejero, Pedro Fernández De Córdoba and Miguel Ángel García-March

Condens. Matter 2023, 8(1), 12; https://doi.org/10.3390/condmat8010012 - 17 Jan 2023

Cited by 1 | Viewed by 1567

Abstract

We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstein condensate in a homogeneous medium and [...] Read more.

We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstein condensate in a homogeneous medium and in a parabolic trap, for the ideal non-interacting case. Secondly, the method allows one to obtain algebraic equations for the trajectories of the position of phase singularities present in the initial condensate along with time (the vortex lines). With these equations, one can predict quantities of interest, such as the time at which a vortex and an antivortex contained in the initial condensate will merge. For the homogeneous case, this method was introduced in the context of photonics. Here, we adapt it to the context of Bose-Einstein condensates, and we extend it to the trapped case for the first time. Also, we offer numerical simulations in the non-linear case, for repulsive and attractive interactions. We use a numerical split-step simulation of the non-linear Gross-Pitaevskii equation to determine how these trajectories and quantities of interest are changed by the interactions. We illustrate the method with several simple cases of interest, both in the homogeneous and parabolically trapped systems. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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15 pages, 4399 KiB

Open AccessArticle

Neural Annealing and Visualization of Autoregressive Neural Networks in the Newman–Moore Model

by Estelle M. Inack, Stewart Morawetz and Roger G. Melko

Condens. Matter 2022, 7(2), 38; https://doi.org/10.3390/condmat7020038 - 27 May 2022

Cited by 4 | Viewed by 2127

Abstract

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, for some notably hard systems, such as those exhibiting glassiness and frustration, they have mainly achieved unsatisfactory results, despite their representational power and entanglement content, thus suggesting [...] Read more.

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, for some notably hard systems, such as those exhibiting glassiness and frustration, they have mainly achieved unsatisfactory results, despite their representational power and entanglement content, thus suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman–Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground-state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman–Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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18 pages, 6158 KiB

Open AccessArticle

Mixtures of Dipolar Gases in Two Dimensions: A Quantum Monte Carlo Study

by Sergi Pradas and Jordi Boronat

Condens. Matter 2022, 7(2), 32; https://doi.org/10.3390/condmat7020032 - 01 Apr 2022

Cited by 1 | Viewed by 2155

Abstract

We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed of a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are all considered [...] Read more.

We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed of a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are all considered to be perpendicular to the plane, turning the dipolar potential in a purely repulsive and isotropic model. Our analysis is carried out by using the diffusion Monte Carlo method, which allows for an exact solution to the many-body problem within some statistical noise. Our results show that the miscibility between the two species is rather constrained as a function of the relative dipolar moments and masses of the two components. A narrow regime is predicted where both species mix and we introduce an adimensional parameter whose value quite accurately predicts the miscibility of the two dipolar gases. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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21 pages, 533 KiB

Open AccessArticle

Path-Integral Monte Carlo Worm Algorithm for Bose Systems with Periodic Boundary Conditions

by Gabriele Spada, Stefano Giorgini and Sebastiano Pilati

Condens. Matter 2022, 7(2), 30; https://doi.org/10.3390/condmat7020030 - 29 Mar 2022

Cited by 5 | Viewed by 2526

Abstract

We provide a detailed description of the path-integral Monte Carlo worm algorithm used to exactly calculate the thermodynamics of Bose systems in the canonical ensemble. The algorithm is fully consistent with periodic boundary conditions, which are applied to simulate homogeneous phases of bulk [...] Read more.

We provide a detailed description of the path-integral Monte Carlo worm algorithm used to exactly calculate the thermodynamics of Bose systems in the canonical ensemble. The algorithm is fully consistent with periodic boundary conditions, which are applied to simulate homogeneous phases of bulk systems, and it does not require any limitation in the length of the Monte Carlo moves realizing the sampling of the probability distribution function in the space of path configurations. The result is achieved by adopting a representation of the path coordinates where only the initial point of each path is inside the simulation box, the remaining ones being free to span the entire space. Detailed balance can thereby be ensured for any update of the path configurations without the ambiguity of the selection of the periodic image of the particles involved. We benchmark the algorithm using the non-interacting Bose gas model for which exact results for the partition function at finite number of particles can be derived. Convergence issues and the approach to the thermodynamic limit are also addressed for interacting systems of hard spheres in the regime of high density. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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13 pages, 9562 KiB

Open AccessArticle

Topological Phases of an Interacting Majorana Benalcazar–Bernevig–Hughes Model

by Alfonso Maiellaro, Fabrizio Illuminati and Roberta Citro

Condens. Matter 2022, 7(1), 26; https://doi.org/10.3390/condmat7010026 - 04 Mar 2022

Cited by 7 | Viewed by 2385

Abstract

We study the effects of Coulomb repulsive interactions on a Majorana Benalcazar–Bernevig–Huges (MBBH) model. The MBBH model belongs to the class of second-order topological superconductors (

H O T S C_{2}

), featuring robust Majorana corner modes. We consider an interacting strip [...] Read more.

We study the effects of Coulomb repulsive interactions on a Majorana Benalcazar–Bernevig–Huges (MBBH) model. The MBBH model belongs to the class of second-order topological superconductors (

H O T S C_{2}

), featuring robust Majorana corner modes. We consider an interacting strip of four chains of length L and perform a density matrix renormalization group (DMRG) numerical simulation based on a tensor-network approach. Study of the non-local fermionic correlations and the degenerate entanglement spectrum indicates that the topological phases are robust in the presence of interactions, even in the strongly interacting regime. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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16 pages, 412 KiB

Open AccessArticle

The ¹S₀ Pairing Gap in Neutron Matter

by Stefano Gandolfi, Georgios Palkanoglou, Joseph Carlson, Alexandros Gezerlis and Kevin E. Schmidt

Condens. Matter 2022, 7(1), 19; https://doi.org/10.3390/condmat7010019 - 01 Feb 2022

Cited by 9 | Viewed by 2385

Abstract

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground [...] Read more.

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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9 pages, 931 KiB

Open AccessArticle

Quantum Reservoir Computing for Speckle Disorder Potentials

by Pere Mujal

Condens. Matter 2022, 7(1), 17; https://doi.org/10.3390/condmat7010017 - 28 Jan 2022

Cited by 5 | Viewed by 2741

Abstract

Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and [...] Read more.

Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it is shown to be enhanced when two-qubit correlations are employed. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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21 pages, 4233 KiB

Open AccessArticle

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

by Mingrui Yang, Matija Čufar, Elke Pahl and Joachim Brand

Condens. Matter 2022, 7(1), 15; https://doi.org/10.3390/condmat7010015 - 26 Jan 2022

Cited by 5 | Viewed by 2607

Abstract

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension of exact diagonalization, it is well suited for the [...] Read more.

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension of exact diagonalization, it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second-order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity’s motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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24 pages, 554 KiB

Open AccessArticle

Toward an Automated-Algebra Framework for High Orders in the Virial Expansion of Quantum Matter

by Aleks J. Czejdo, Joaquin E. Drut, Yaqi Hou and Kaitlyn J. Morrell

Condens. Matter 2022, 7(1), 13; https://doi.org/10.3390/condmat7010013 - 24 Jan 2022

Cited by 3 | Viewed by 2533

Abstract

The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order n requires analyzing (if not solving) the quantum n-body problem. In this [...] Read more.

The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order n requires analyzing (if not solving) the quantum n-body problem. In this work, we present a comprehensive review of automated algebra methods, which we developed to calculate high-order virial coefficients. The methods are computational but non-stochastic, thus avoiding statistical effects; they are also for the most part analytic, not numerical, and amenable to massively parallel computer architectures. We show formalism and results for coefficients characterizing the thermodynamics (pressure, density, energy, static susceptibilities) of homogeneous and harmonically trapped systems and explain how to generalize them to other observables such as the momentum distribution, Tan contact, and the structure factor. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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25 pages, 694 KiB

Open AccessArticle

Weakly-Interacting Bose–Bose Mixtures from the Functional Renormalisation Group

by Felipe Isaule and Ivan Morera

Condens. Matter 2022, 7(1), 9; https://doi.org/10.3390/condmat7010009 - 20 Jan 2022

Cited by 3 | Viewed by 2451

Abstract

We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose–Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose–Bose gases at zero and finite temperatures and [...] Read more.

We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose–Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose–Bose gases at zero and finite temperatures and find a good agreement with related works. We also study ground-state energies of repulsive Bose polarons by examining mixtures in the limit of infinite population imbalance. Finally, we discuss future applications of the FRG to novel problems in Bose–Bose mixtures and related systems. Full article

(This article belongs to the Special Issue Computational Methods for Quantum Matter)

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