Chern-Simons theory encoded on a spin chain

Abstract

We construct a 1d spin chain Hamiltonian with generic interactions and prove that the thermal correlation functions of the model admit an explicit random matrix representation. As an application of the result, we show how the observables of $U(N)$ Chern-Simons theory on $S^3$ can be reproduced with the thermal correlation functions of the 1d spin chain, which is of the XX type, with a suitable choice of exponentially decaying interactions between infinitely many neighbours. We show that for this model, the correlation functions of the spin chain at a finite temperature $\beta =1$ give the Chern-Simons partition function, quantum dimensions and the full topological $S$-matrix.

v2, 11 pages. Expanded, more detailed version. Misprints corrected

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Cited by in corpus (5)

• Matrix models for classical groups and Toeplitz$\pm$Hankel minors with applications to Chern-Simons theory and fermionic models
• Phase transition in complex-time Loschmidt echo of short and long range spin chain
• Dynamical quantum phase transitions from random matrix theory
• Unitary matrix integrals, symmetric polynomials, and long-range random walks
• Hawking-Page transition on a spin chain