Short-time vs. long-time dynamics of entanglement in quantum lattice models

Abstract

We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as $1-(t/\tau {)}^2$, i.e. quadratically in time, with a characteristic time scale $\tau$ that is inversly proportional to the boundary size of the subsystem, i.e., as an area-law. For larger times an exponential lower bound is derived corresponding to the well-known linear-in-time bound of the entanglement entropy. The validity of the derived lower bound is illustrated by comparison to the exact dynamics of a 1D spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.

some minor additions, 6 pages, 3 figures

References in corpus (14)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Entropy scaling and simulability by Matrix Product States
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Atomic three-body loss as a dynamical three-body interaction
• General entanglement scaling laws from time evolution
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Dissipation induced Tonks-Girardeau gas in an optical lattice
• Lieb-Liniger model of a dissipation-induced Tonks-Girardeau gas
• An atomic colour superfluid via three-body loss
• Stabilization of the p-wave superfluid state in an optical lattice

Cited by in corpus (4)

• Quantum trajectories and open many-body quantum systems
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC
• Generalized Clausius inequalities and entanglement production in holographic two-dimensional CFTs