Low-rank Sachdev-Ye-Kitaev models
Abstract
Motivated by recent proposals of experimental realization of fast scramblers, we study a family of solvable variants of the (q =4 ) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix Ji j ,k l are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate an extensively degenerate or negative semidefinite coupling matrix. More generic distributions give rise to "almost Fermi liquids" with a scaling dimension Δ =1 /2 , but which differ from a genuine Fermi liquid in quasiparticle decay rate, quantum Lyapunov exponent, and/or specific heat.
- Publication:
-
Physical Review B
- Pub Date:
- March 2020
- DOI:
- 10.1103/PhysRevB.101.125112
- arXiv:
- arXiv:1910.10173
- Bibcode:
- 2020PhRvB.101l5112K
- Keywords:
-
- Condensed Matter - Strongly Correlated Electrons;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 5+10 pages, 10 figures