Strongly Interacting Fermions Are Nontrivial yet Nonglassy

Area of Science:

• Quantum physics
• Condensed matter theory
• Computational complexity

Background:

• Random spin systems exhibit glassy behavior and computational hardness at low temperatures.
• The Sachdev-Ye-Kitaev (SYK) model is a key theoretical framework for studying quantum many-body systems.

Purpose of the Study:

• To investigate the low-energy properties of the random all-to-all interacting fermionic SYK model.
• To compare the computational complexity and phase behavior of fermionic SYK models with random spin systems.

Main Methods:

• Analysis of the fermionic SYK model using techniques from quantum information and complexity theory.
• Calculation of free energies (annealed and quenched) and comparison at low temperatures.
• Quantification of noncommutativity between Hamiltonian terms using a "commutation index".

Main Results:

• Low-energy states of the fermionic SYK model possess polynomial circuit depth, indicating quantum ease.
• The annealed and quenched free energies of the fermionic SYK model agree at low temperatures.
• Fermionic and spin systems exhibit significant differences in their commutation indices.

Conclusions:

• The fermionic SYK model does not undergo a glassy phase transition in the studied sense.
• Fermions in the SYK model reside in a phase that is classically nontrivial but quantumly easy.
• The commutation index is a crucial differentiator between the low-temperature behavior of fermionic and spin systems.