Universal subdiffusive behavior at band edges from transfer matrix exceptional points

TL;DR

This paper reveals a universal subdiffusive conductance behavior at band edges in open quantum systems, linked to transfer matrix exceptional points and PT-symmetry, with implications for quantum phase transitions.

Contribution

It establishes a deep connection between PT-symmetric optical systems and quantum transport, showing that transfer matrix exceptional points correspond to band edges and induce subdiffusive scaling.

Findings

Subdiffusive conductance scaling with exponent 2 at band edges.

Existence of a dissipative quantum phase transition across band edges.

Universality of this behavior regardless of potential details.

Abstract

We discover a deep connection between parity-time (PT) symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of $2 \times 2$ transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the PT-symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent $2$, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.