Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model

Abstract

Supersymmetry is a powerful concept in quantum many-body physics. It helps to illuminate ground state properties of complex quantum systems and gives relations between correlation functions. In this work, we show that the Sachdev-Ye-Kitaev model, in its simplest form of Majorana fermions with random four-body interactions, is supersymmetric. In contrast to existing explicitly supersymmetric extensions of the model, the supersymmetry we find requires no relations between couplings. The type of supersymmetry and the structure of the supercharges are entirely set by the number of interacting Majorana modes, and are thus fundamentally linked to the model's Altland-Zirnbauer classification. The supersymmetry we uncover has a natural interpretation in terms of a one-dimensional topological phase supporting Sachdev-Ye-Kitaev boundary physics, and has consequences away from the ground state, including in $q$-body dynamical correlation functions.

9 pages, 4 figures

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• A Generalization of Sachdev-Ye-Kitaev
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• Strange metal from local quantum chaos
• Non-ergodic extended states in the SYK model
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Quantum criticality of granular SYK matter
• Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion
• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
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• Ground-state properties of a supersymmetric fermion chain

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• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• 1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires
• Boundary supersymmetry of 1+1 d fermionic SPT phases
• Elementary derivation of the stacking rules of invertible fermionic topological phases in one dimension
• Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
• Supersymmetric boundaries of one-dimensional phases of fermions beyond symmetry-protected topological states
• Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit
• Sachdev-Ye-Kitaev type physics in the strained Kitaev honeycomb model
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• C-P-T Fractionalization
• Instanton-Induced Supersymmetry Breaking in Topological Semimetals
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics