Global and short-range entanglement properties in excited, many-body localized spin chains

Abstract

We explore the use of short-range entanglement measures, such as concurrence and negativity, and global entanglement measures such as geometric entanglement, as indicators of many-body localization (MBL) in the spectra of disordered spin systems. From the perspective of entanglement monogamy, the two types of entanglement behave oppositely in the thermalized and MBL phases. In a recent work, the concurrence of subsystems, a measure of local entanglement, was used in a study of many-body localization in a one-dimensional spin-$1/2$ system (Bera and Lakshminarayan, 2016). We show numerically that the negativity displays notably similar behavior for this system, with the advantage that it can also be extended to systems of higher local dimension. We then demonstrate this extension in practice by using it to predict the existence of an MBL phase in a disordered a spin-1 system. In terms of global entanglement, the geometric entanglement of both spin-$1/2$ and spin-1 systems is also shown to behave as a complementary indicator of the MBL phenomenon.

19 pages, 15 figures

References in corpus (16)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• General Monogamy Inequality for Bipartite Qubit Entanglement
• From density-matrix renormalization group to matrix product states
• Many-Body Localization in a Quasiperiodic System
• Constructing local integrals of motion in the many-body localized phase
• Many-body localisation implies that eigenvectors are matrix-product states
• Infinite size density matrix renormalization group, revisited
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• The Miscible-Immiscible Quantum Phase Transition in Coupled Two-Component Bose-Einstein Condensates in 1D Optical Lattices
• Schur Forms of Matrix Product Operators in the Infinite Limit