Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models

Abstract

In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only reduce the number of relevant states in the Hilbert space by a non negligible fraction, they also allow to write the relevant equations in the form of sparse matrix equations. Moreover, we introduce a new inversion method based on a basis of barycentric polynomials which leads to a more stable and efficient root extraction which most importantly avoids the necessity of working with arbitrary precision. As an example we show the results of our procedure applied to the Richardson model on a square lattice.

10 pages, 3 figures, published version

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Cited by in corpus (35)

• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• Spin decoherence due to a randomly fluctuating spin bath
• Exceptional and regular spectra of a generalized Rabi model
• Exact solution of the $p_x+i{p}_y$ pairing Hamiltonian by deforming the pairing algebra
• Spin polarization through Floquet resonances in a driven central spin model
• Richardson-Gaudin integrability in the contraction limit of the quasispin
• Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem
• Exact solution of the pairing problem for spherical and deformed systems
• On the determinant representations of Gaudin models' scalar products and form factors
• Read-Green resonances in a topological superconductor coupled to a bath
• Inner products in integrable Richardson-Gaudin models
• Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model
• Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field
• Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode
• Density Matrices of Seniority-Zero Geminal Wavefunctions
• Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
• Reduced Density Matrices / Static Correlation Functions of Richardson-Gaudin States Without Rapidities
• Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models
• Separable and entangled states in the high-spin XX central spin model
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case
• A variational method for integrability-breaking Richardson-Gaudin models
• Ground-state Bethe root densities and quantum phase transitions
• On symmetries of Hamiltonians describing systems with arbitrary spins
• Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin
• Order parameter, correlation functions and fidelity susceptibility for the BCS model in the thermodynamic limit
• Exact Entanglement dynamics in Three Interacting Qubits
• Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics
• Quantum dynamics of Gaudin magnets
• Few-to-many-particle crossover of pair excitations in a superfluid
• Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models
• Transition density matrices of Richardson-Gaudin states