Supersymmetry in the Standard Sachdev-Ye-Kitaev Model

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Theory
• High Energy Physics

Background:

• Supersymmetry (SUSY) is a theoretical framework in physics that relates bosons and fermions.
• It simplifies the analysis of complex quantum systems and their properties.
• The Sachdev-Ye-Kitaev (SYK) model is a solvable model of interacting fermions with applications in quantum gravity and condensed matter.

Purpose of the Study:

• To investigate the presence and nature of supersymmetry in the simplest form of the Sachdev-Ye-Kitaev model.
• To explore the implications of this supersymmetry for understanding the model's properties.
• To connect the model's supersymmetry to its classification within the Altland-Zirnbauer framework.

Main Methods:

• Analysis of Majorana fermions with random four-body interactions.
• Identification of the structure of supercharges based on the number of Majorana modes.
• Relating the findings to the Altland-Zirnbauer classification of random matrices.

Main Results:

• The simplest Sachdev-Ye-Kitaev model, with Majorana fermions and random four-body interactions, is inherently supersymmetric.
• This intrinsic supersymmetry does not require any relations between coupling constants.
• The type of supersymmetry and supercharge structure are determined by the number of Majorana modes, linking to the Altland-Zirnbauer classification.

Conclusions:

• The discovered supersymmetry offers a new perspective on the Sachdev-Ye-Kitaev model.
• It provides a natural interpretation as a one-dimensional topological phase with boundary physics.
• The findings have implications beyond the ground state, affecting dynamical correlation functions.