Topological Sachdev-Ye-Kitaev model

Abstract

In this Rapid Communication, we construct a large-$N$ exactly solvable model to study the interplay between interaction and topology, by connecting the Sachdev-Ye-Kitaev (SYK) model with constant hopping. The hopping forms a band structure that can exhibit both topologically trivial and nontrivial phases. Starting from a topologically trivial insulator with zero Hall conductance, we show that the interaction can drive a phase transition to a topologically nontrivial insulator with quantized nonzero Hall conductance, and a single gapless Dirac fermion emerges when the interaction is fine tuned to the critical point. The finite temperature effect is also considered, and we show that the topological phase with a stronger interaction is less stable against temperature. Our model provides a concrete example to illustrate the interacting topological phases and phase transitions, and can shed light on similar problems in physical systems.