Solvable Quantum Grassmann Matrices

Abstract

We explore systems with a large number of fermionic degrees of freedom subject to non-local interactions. We study both vector and matrix-like models with quartic interactions. The exact thermal partition function is expressed in terms of an ordinary bosonic integral, which has an eigenvalue repulsion term in the matrix case. We calculate real time correlations at finite temperature and analyze the thermal phase structure. When possible, calculations are performed in both the original Hilbert space as well as the bosonic picture, and the exact map between the two is explained. At large $N$, there is a phase transition to a highly entropic high temperature phase from a low temperature low entropy phase. Thermal two-point functions decay in time in the high temperature phase.

25 pages, 4 figures

References in corpus (3)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• The complete $1/N$ expansion of a SYK--like tensor model
• Matrix Quantum Mechanics from Qubits

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• Matrix integrals $\&$ finite holography
• An invitation to the principal series
• Areas and entropies in BFSS/gravity duality
• Matrix models for classical groups and Toeplitz$\pm$Hankel minors with applications to Chern-Simons theory and fermionic models
• Hagedorn Temperature in Large $N$ Majorana Quantum Mechanics
• Polynomial solution of quantum Grassmann matrices
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Schur expansion of random-matrix reproducing kernels
• Fermionic Matrix Models and Bosonization