Area laws in a many-body localized state and its implications for topological order

By Bela Bauer, C. Nayak. 2013

393 citations recorded by the source corpus.

The question whether Anderson insulators can persist to finite-strength interactions—a scenario dubbed many-body localization—has recently received a great deal of interest. The origin of such a many-body localized phase has been described as localization in Fock space, a picture we examine numerically. We then formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator. We call such a state a many-body localized state and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Our results are consistent with an area law and, by implication, many-body localization for almost all states and almost all regions for weak enough interactions and strong disorder. However, there are rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/1467db2196595917def8eeb13ae9332ea1bdb53a

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In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. D. Abanin
3. Tomaz Prosen
4. Maksym Serbyn
5. D. Huse
6. I. Bloch
7. J. Imbrie
8. J. Moore

Citations in the corpus

• Integrals of motion in the many-body localized phase (2014, background): “In that case, numerical approaches such as [17, 45] would not capture this divergence.”
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, background): “One of the key features of MBL systems is that excited-eigenstates satisfy a area-law scaling of the entanglement entropy [1, 63] ( ∼ S const in 1D), so that they clearly violate ETH.”
• Classification of Interacting Topological Floquet Phases in One Dimension (2016, methodology): “[22,25,27,28], we begin by formulating a sharp criterion for many-body localizability in terms of”
• Ergodicity breaking transition in finite disordered spin chains (2020, background): “[37] B.”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, background): “Bauer and Nayak (2013) and Huse et al. (2013) argued that MBL can protect the Z2 topological order in d = 2 at finite energy density.”
• Constructing local integrals of motion in the many-body localized phase (2014, background): “First, all MBL eigenstates, except for an exponentially small fraction, have an area-law entanglement entropy, typical of ground states in gapped systems; this is supported by numerical simulations of spin chains [8, 14].”
• Observation of many-body localization of interacting fermions in a quasirandom optical lattice (2015, background): “Further theoretical studies have established the many-body localized state as a distinct dynamical phase of matter that exhibits novel universal behavior [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].”
• On Many-Body Localization for Quantum Spin Chains (2014, background): “The idea that quasi-local unitary transformations may be used to isolate local variables or conserved quantities in a many-body localized system appears in [34, 45, 7, 42].”
• Criterion for Many-Body Localization-Delocalization Phase Transition (2015, neutral): “In contrast, the eigenstates of MBL systems can be obtained from product states by quasilocal unitary transformations and have low entanglement that obeys the “area law” [9,14].”