Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling

  • Pramod Padmanabhan
  • Soo-Jong Rey
  • Daniel Teixeira
  • Diego Trancanelli
Open Access
Regular Article - Theoretical Physics

Abstract

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.

Keywords

Discrete Symmetries Extended Supersymmetry Lattice Integrable Models Random Systems 

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Pramod Padmanabhan
    • 1
  • Soo-Jong Rey
    • 1
    • 2
    • 3
  • Daniel Teixeira
    • 4
  • Diego Trancanelli
    • 4
  1. 1.Fields, Gravity & Strings, CTPU, Institute for Basic ScienceDaejeonKorea
  2. 2.School of Physics and Astronomy & Center for Theoretical PhysicsSeoul National UniversitySeoulKorea
  3. 3.Department of Basic SciencesUniversity of Science and TechnologyDaejeonKorea
  4. 4.Institute of PhysicsUniversity of São PauloSão PauloBrazil

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