Strongly Interacting Fermions Are Nontrivial yet Nonglassy
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1.
California Institute of Technology
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2.
Harvard University
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.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
E. R. A. is funded in part by the Walter Burke Institute for Theoretical Physics at Caltech. C.-F. C. is supported by a Simons-CIQC postdoctoral fellowship through NSF QLCI Grant No. 2016245. R. K. is funded by NSF Grant No. CCF-2321079. The authors thank Chokri Manai, who pointed out an error in an earlier draft and shared his insights on its solution.
Contributions
R. K. and C.-F. C. conceived the commutation index and provided initial proofs for the main results. B. T. K. and E. R. A. simplified and extended the proofs. All authors contributed to writing and editing the manuscript.
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Additional details
Funding
- California Institute of Technology
- Walter Burke Institute for Theoretical Physics -
- National Science Foundation
- QLCI 2016245
- National Science Foundation
- CCF-2321079