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Strongly Interacting Fermions Are Nontrivial yet Nonglassy

Eric R. Anschuetz1,2,*, Chi-Fang Chen1,3,†, Bobak T. Kiani4,‡, and Robbie King1,5,§

  • 1Institute for Quantum Information and Matter, Caltech, Pasadena, California, 91125, USA
  • 2Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California, 91125, USA
  • 3University of California, Berkeley, California, 94720, USA
  • 4John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, 02134, USA
  • 5Computational and Mathematical Sciences, Caltech, Pasadena, California, 91125, USA

  • *Contact author: eans@caltech.edu
  • †Contact author: achifchen@gmail.com
  • ‡Contact author: bkiani@seas.harvard.edu
  • §Contact author: wking@caltech.edu
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Phys. Rev. Lett. 135, 030602 – Published 17 July, 2025

DOI: https://doi.org/10.1103/cbqf-d24r

Abstract

Random spin systems at low temperatures are glassy and feature computational hardness in finding low-energy states. We study the random all-to-all interacting fermionic Sachdev-Ye-Kitaev model and prove that, in contrast, the low-energy states have polynomial circuit depth, yet the annealed and quenched free energies agree to polynomially inverse low temperatures, ruling out a glassy phase transition in this sense. These results are derived by showing that fermionic and spin systems significantly differ in their “commutation index,” which quantifies the noncommutativity of Hamiltonian terms. Our results suggest that low-temperature strongly interacting fermions, unlike spins, belong in a classically nontrivial yet quantumly easy phase.

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Phys. Rev. Lett. 135, 030602– Published 17 July, 2025
  • Received 18 October 2024
  • Revised 25 February 2025
  • Accepted 19 May 2025
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