Sub-diffusive phases in open clean long-range systems

TL;DR

This paper uncovers two sub-diffusive phases in open one-dimensional fermionic systems with long-range hopping, revealing phase transitions driven by chemical potential differences and demonstrating the robustness of these phases against interactions.

Contribution

It introduces the existence of sub-diffusive phases in open long-range fermionic systems, a phenomenon absent in isolated systems, and characterizes their microscopic origin and stability.

Findings

Sub-diffusive phases exhibit conductance scaling with system size.

Phase transitions occur between sub-diffusive and ballistic regimes.

Sub-diffusive phases are robust against many-body interactions.

Abstract

We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing sub-diffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e, in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven sub-diffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known non-equilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the sub-diffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing sub-diffusive scaling of conductance with system size in a two-terminal set-up are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.