A variational method for integrability-breaking Richardson-Gaudin models

Abstract

We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. The method is shown to return exact results for integrable models and improve substantially on perturbation theory for models close to integrability. For large integrability-breaking interactions, it is shown how (avoided) level crossings necessitate the use of excited states of integrable Hamiltonians in order to accurately describe the ground states of general non-integrable models.

References in corpus (74)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• The ODE/IM Correspondence
• Remarks on the notion of quantum integrability
• Wave function optimization in the variational Monte Carlo method
• Constructing the generalized Gibbs ensemble after a quantum quench
• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• Non-integrable aspects of the multi-frequency Sine-Gordon model
• Integrability of the pairing hamiltonian
• Seniority-based coupled cluster theory
• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Efficient description of strongly correlated electrons with mean-field cost
• Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Integrable model for interacting electrons in metallic grains
• Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid
• Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz
• Crossover from Poisson to Wigner-Dyson Level Statistics in Spin Chains with Integrability Breaking
• Large N limit of the exactly solvable BCS model: analytics versus numerics
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Exactly solvable pairing model for superconductors with a p+ip-wave symmetry
• The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
• Decay of particles above threshold in the Ising field theory with magnetic field
• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models
• On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
• Exactly-solvable models for atom-molecule hamiltonians
• Spin decoherence due to a randomly fluctuating spin bath
• Pumping approximately integrable systems
• Solving the Richardson equations for Fermions
• Algebraic Bethe Ansatz for a discrete-state BCS pairing model
• Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
• Exact mesoscopic correlation functions of the pairing model
• Exact solution of the p+ip pairing Hamiltonian and a hierarchy of integrable models
• Scattering particles in quantum spin chains
• Fully Self-consistent RPA description of the many level pairing model
• Exactly solvable pairing Hamiltonian for heavy nuclei
• Integrable models for confined fermions: applications to metallic grains
• Exact correlation functions of the BCS model in the canonical ensemble
• Exact solution of the $p_x+i{p}_y$ pairing Hamiltonian by deforming the pairing algebra
• Richardson-Gaudin integrability in the contraction limit of the quasispin
• Energy Level Distribution of Perturbed Conformal Field Theories
• Characterization of resonances using finite size effects
• Solving the Richardson equations close to the critical points
• Exact solution of the pairing problem for spherical and deformed systems
• The Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems
• On the determinant representations of Gaudin models' scalar products and form factors
• Read-Green resonances in a topological superconductor coupled to a bath
• What is a particle-conserving Topological Superfluid?
• Inner products in integrable Richardson-Gaudin models
• Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians
• Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode
• Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
• Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models
• Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
• Competing interactions in semiconductor quantum dots
• Different types of integrability and their relation to decoherence in central spin models
• Treatment of like-particle pairing with quartets
• Spins coupled to a Spin Bath: From Integrability to Chaos
• Mass Generation in Perturbed Massless Integrable Models
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime
• Attenuated Coupled Cluster: A Heuristic Polynomial Similarity Transformation Incorporating Spin Symmetry Projection Into Traditional Coupled Cluster Theory
• BEC-BCS crossover in a p+ip-wave pairing Hamiltonian coupled to bosonic molecular pairs
• Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange
• Order parameter, correlation functions and fidelity susceptibility for the BCS model in the thermodynamic limit
• Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin
• Probing pairing correlations in Sn isotopes using Richardson-Gaudin integrability

Cited by in corpus (6)

• Density Matrices of Seniority-Zero Geminal Wavefunctions
• Variational Bethe Ansatz approach for dipolar one-dimensional bosons
• Separable and entangled states in the high-spin XX central spin model
• Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models
• Variational theory combining number-projected BCS and coupled-cluster doubles
• Transition density matrices of Richardson-Gaudin states