Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling

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 Renyi entropy to the OTOC on a thermal state in terms of partial symmetries.

45 pages, 7 figures; v2: 50 pages, Sec. 4 expanded and improved, published version

References in corpus (6)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Phenomenology of fully many-body-localized systems
• Many-Body Localization in a Quasiperiodic System
• Slow scrambling in disordered quantum systems
• Spin chains with dynamical lattice supersymmetry

Cited by in corpus (5)

• Area Law Violations and Quantum Phase Transitions in Modified Motzkin Walk Spin Chains
• Ground states of Nicolai and ${\mathbb{Z}}_2$ Nicolai models
• Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
• Topological Quantum Computation on Supersymmetric Spin Chains
• Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain