Unconventional scaling at non-Hermitian critical points

TL;DR

This paper explores the unique critical phenomena in non-Hermitian systems, revealing fractional order phase transitions and unconventional scaling behaviors using a thermodynamic approach, exemplified by the non-Hermitian SSH model.

Contribution

It introduces a thermodynamic framework for analyzing non-Hermitian critical points and uncovers fractional order phase transitions and scaling anomalies.

Findings

Fractional order topological phase transitions in the complex energy plane.

Unconventional scaling relations at highly degenerate critical points.

Emergence of an extra length scale from skin mode accumulation.

Abstract

Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or temporal divergences render the thermodynamic limit ill-defined. In this work, we show that a thermodynamic grand potential can still be defined in pseudo-Hermitian Hamiltonians, and can be used to characterize aspects of criticality unique to non-Hermitian systems. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) model as a paradigmatic example, we demonstrate the fractional order of topological phase transitions in the complex energy plane. These fractional orders add up to the integer order expected of a Hermitian phase transition when the model is doubled and Hermitianized. More spectacularly, gap preserving highly degenerate critical points known as non-Bloch band collapses possess fractional order that are not constrained by conventional scaling relations, testimony to the emergent extra length scale from the skin mode accumulation. Our work showcases that a thermodynamic approach can prove fruitful in revealing unconventional properties of non-Hermitian critical points.