Probing thermalization through spectral analysis with matrix product operators

Abstract

We combine matrix product operator techniques with Chebyshev polynomial expansions and present a method that is able to explore spectral properties of quantum many-body Hamiltonians. In particular, we show how this method can be used to probe thermalization of large spin chains without explicitly simulating their time evolution, as well as to compute full and local densities of states. The performance is illustrated with the examples of the Ising and PXP spin chains. For the non-integrable Ising chain, our findings corroborate the presence of thermalization for several initial states, well beyond what direct time-dependent simulations have been able to achieve so far.

References in corpus (45)

• The density-matrix renormalization group in the age of matrix product states
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Area laws for the entanglement entropy - a review
• Probing many-body dynamics on a 51-atom quantum simulator
• 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
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• An Area Law for One Dimensional Quantum Systems
• The Kernel Polynomial Method
• Quantum many-body scars
• Matrix product states represent ground states faithfully
• Generalized Gibbs ensemble in integrable lattice models
• The approach to thermal equilibrium in quantized chaotic systems
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Strong and weak thermalization of infinite non-integrable quantum systems
• Real time confinement following a quantum quench to a non-integrable model
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• Solving Gapped Hamiltonians Locally
• Matrix Product States for dynamical simulation of infinite chains
• Nonthermal states arising from confinement in one and two dimensions
• Dynamics at the Many-Body Localization Transition
• Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Thouless and relaxation time scales in many-body quantum systems
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Chebyshev matrix product state approach for spectral functions
• Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy
• Density Matrix Renormalization Group in the Heisenberg Picture
• Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
• Spectra and eigenstates of spin chain Hamiltonians
• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Spectral functions and time evolution from the Chebyshev recursion
• Connecting Entanglement in Time and Space: Improving the Folding Algorithm
• Computations in Quantum Tensor Networks
• Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization
• Slowest local operators in quantum spin chains
• Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
• Entanglement scaling of excited states in large one-dimensional many-body localized systems
• Spectral densities and partition functions of modular quantum systems as derived from a central limit theorem
• Chebyshev matrix product state approach for time evolution
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• Density-of-states of many-body quantum systems from tensor networks

Cited by in corpus (23)

• Filtering variational quantum algorithms for combinatorial optimization
• Algorithms for quantum simulation at finite energies
• Quantum many-body scars in transverse field Ising ladders and beyond
• Interacting bosons in a triple well: Preface of many-body quantum chaos
• How much entanglement is needed to reduce the energy variance?
• Taking the temperature of a pure quantum state
• Spectral density reconstruction with Chebyshev polynomials
• Classical algorithms for many-body quantum systems at finite energies
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions
• How many particles make up a chaotic many-body quantum system?
• Approximating the long time average of the density operator: Diagonal ensemble
• Quantum information scrambling in the presence of weak and strong thermalization
• Disorder enhanced quantum many-body scars in Hilbert crystals
• Entropy and Temperature in finite isolated quantum systems
• Calculating the many-body density of states on a digital quantum computer
• Density of States of the lattice Schwinger model
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Many Body Density of States of a system of non interacting spinless fermions
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
• Pauli weight requirement of the matrix elements in time-evolved local operators: dependence beyond the equilibration temperature