Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization

Abstract

Thermalization play a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter. Here, it is argued that **bipartite** entanglement measures provide key information on out-of-equilibrium states and might therefore offer stringent thermalization criteria. This is illustrated by considering a global quench in an (extended) XXZ spin-1/2 chain across its (zero-temperature) quantum critical point. A non-local **bipartition** of the chain **preserving translation symmetry** is proposed. The time-evolution after the quench of the **reduced** density matrix of the half-system is computed and its associated (time-dependent) entanglement spectrum is analyzed. Generically, the corresponding entanglement entropy quickly reaches a "plateau" after a short transient regime. However, in the case of the integrable XXZ chain, the low-energy entanglement spectrum still reveals strong time-fluctuations. In addition, its infinite-time average shows strong deviations from the spectrum of a Boltzmann thermal density matrix. In contrast, when the integrability of the model is broken (by small next-nearest neighbor couplings), the entanglement spectra of the time-average and thermal density matrices become remarkably similar.

extended version: 15 pages, 9 figures

References in corpus (14)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Thermalization and its mechanism for generic isolated quantum systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• Entanglement spectrum in one-dimensional systems
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Quantum chaos and thermalization in gapped systems
• Entanglement spectra of quantum Heisenberg ladders
• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
• Non-equilibrium electronic transport in a one-dimensional Mott insulator
• Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
• Time-dependent DMRG Study on Quantum Dot under a Finite Bias Voltage
• Dynamics of thermalisation in small Hubbard-model systems

Cited by in corpus (7)

• Trace Index and Spectral Flow in the Entanglement Spectrum
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Thermalisation of Local Observables in Small Hubbard Lattices
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Discarded weight and entanglement spectra in the Numerical Renormalization Group
• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• Entanglement-assisted local operations and classical communications conversion in the quantum critical systems