Unbinding transition in semi-infinite two-dimensional localized systems

TL;DR

This paper predicts an unbinding transition in two-dimensional localized systems with different edge and bulk transfer integrals, showing a change in conductance distribution at criticality and linking the behavior to Tracy-Widom distributions and KPZ universality.

Contribution

It introduces the concept of an unbinding transition in 2D localized systems with variable edge transfer integrals and connects conductance distributions to Tracy-Widom laws and KPZ universality class.

Findings

Conductance distribution follows $F_1$ Tracy-Widom at criticality.

Distribution is $F_4$ Tracy-Widom for equal edge and bulk transfer.

Numerical verification for Anderson and Nguyen-Spivak-Shklovskii models.

Abstract

We consider a two-dimensional strongly localized system defined in a half-space and whose transfer integral in the edge can be different than in the bulk. We predict an unbinding transition, as the edge transfer integral is varied, from a phase where conduction paths are distributed across the bulk to a bound phase where propagation is mainly along the edge. At criticality the logarithm of the conductance follows the $F_1$ Tracy-Widom distribution. We verify numerically these predictions for both the Anderson and the Nguyen, Spivak and Shklovskii models. We also check that for a half-space, i.e., when the edge transfer integral is equal to the bulk transfer integral, the distribution of the conductance is the $F_4$ Tracy-Widom distribution. These findings are strong indications that random signs directed polymer models and their quantum extensions belong to the Kardar-Parisi- Zhang universality class. We have analyzed finite-size corrections at criticality and for a half-plane.