Guide to Exact Diagonalization Study of Quantum Thermalization

Abstract

Exact diagonalization is a powerful numerical method to study isolated quantum many-body systems. This paper provides a review of numerical algorithms to diagonalize the Hamiltonian matrix. Symmetry and the conservation law help us perform the numerical study efficiently. We explain the method to block-diagonalize the Hamiltonian matrix by using particle number conservation, translational symmetry, particle-hole symmetry, and spatial reflection symmetry in the context of the spin-1/2 XXZ model or the hard-core boson model in a one-dimensional lattice. We also explain the method to study the unitary time evolution governed by the Schrödinger equation and to calculate thermodynamic quantities such as the entanglement entropy. As an application, we demonstrate numerical results that support that the eigenstate thermalization hypothesis holds in the XXZ model.

14 pages (typo in the metadata corrected)

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Cited by in corpus (18)

• Many-Body Localization in the Age of Classical Computing
• Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
• Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Proposal for simulating quantum spin models with the Dzyaloshinskii-Moriya interaction using Rydberg atoms and the construction of asymptotic quantum many-body scar states
• Symmetry-projected cluster mean-field theory applied to spin systems
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Using a Feedback-Based Quantum Algorithm to Analyze the Critical Properties of the ANNNI Model Without Classical Optimization
• Giant rectification in strongly-interacting driven tilted systems
• Linear combinations of cluster mean-field states applied to spin systems
• Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system
• Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
• Persistent-current states originating from the Hilbert space fragmentation in momentum space
• Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential
• Exact and mean-field analysis of the role of Hubbard interactions on flux driven circular current in a quantum ring