Interacting 1D Chiral Fermions with Pairing: Transition from Integrable to Chaotic

Abstract

We study a generic one-dimensonal quantum model of two flavors (pseudospins) chiral complex fermions by exact diagonalization, which can have local interflavor interaction and superconducting pairings (with all irrelevant terms ignored). Analytically, the model has two solvable (integrable) points in the parameter space: it is a free fermion model when the fermion interaction is zero, and is a free boson Luttinger liquid when there is a global U(1)${}^{(\uparrow )}\times$U(1)${}^{(\downarrow )}$ symmetry (with nonzero interaction). When the global symmetry of the interacting model is lowered by turning on symmetry breaking parameters, the model undergoes a transition from a quantum integrable model to a fully quantum chaotic model, as we demonstrate by examining the level spacing statistics (LSS) of the many-body energy spectrum. In particular, there is a possibly integrable regime with intermediate global symmetries, where the model is neither free bosons nor free fermions, but shows Poisson LSS in each global symmetry charge sector. This implies the existence of hidden (quasi)local conserved quantities. When the global symmetries are further lowered, the LSS in each charge sector becomes Wigner-Dyson, implying quantum chaos.

A Chapter for the Chen-Ning Yang Centenary Festschrift

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