Unbinding transition in semi-infinite two-dimensional localized systems

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.

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• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line
• Glassy properties of Anderson localization: pinning, avalanches and chaos
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class
• Genuine localisation transition in a long-range hopping model
• Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
• The crossing probability for directed polymers in random media
• Crossing probability for directed polymers in random media: exact tail of the distribution
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• KPZ fluctuations in finite volume
• Mutually avoiding paths in random media and largests eigenvalues of random matrices
• Green functions of interacting systems in the strongly localized regime
• Tracy-Widom fluctuations in 2D random Schrodinger operators
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain