Topological phase transition in fluctuating imaginary gauge fields

TL;DR

This paper explores topological phase transitions in non-Hermitian lattice models with fluctuating imaginary gauge fields, revealing new spectral invariants and edge localization phenomena through analytical gauge transformations.

Contribution

It introduces a method to predict spectral topological invariance and boundary localization in disordered nonperiodic lattices using gauge transformations, uncovering a novel topological phase transition.

Findings

Spectral equivalence between lattices with and without gauge fields under open boundaries.

Identification of a new topological phase transition at λ≈2 in quasiperiodic gauge fields.

All eigenstates localize at edges depending on gauge strength, with delocalization at critical point.

Abstract

We investigate the exact solvability and point-gap topological phase transitions in non-Hermitian lattice models. These models incorporate site-dependent nonreciprocal hoppings $J e^{\pm g_n}$, facilitated by a spatially fluctuating imaginary gauge field $ig_n \hat~x$ that disrupts translational symmetry. By employing suitable imaginary gauge transformations, it is revealed that a lattice characterized by any given $g_n$ is spectrally equivalent to a lattice devoid of fields, under open boundary conditions. Furthermore, a system with closed boundaries can be simplified to a spectrally equivalent lattice featuring a uniform mean field $i\bar{g}\hat~x$. This framework offers a comprehensive method for analytically predicting spectral topological invariance and associated boundary localization phenomena for bond-disordered nonperiodic lattices. These predictions are made by analyzing gauge-transformed isospectral periodic lattices. Notably, for a lattice with quasiperiodic $g_n= \ln |\lambda \cos 2\pi \alpha n|$ and an irrational $\alpha$, a previously unknown topological phase transition is unveiled. It is observed that the topological spectral index $W$ assumes values of $-N$ or $+N$, leading to all $N$ open-boundary eigenstates localizing either at the right or left edge, solely dependent on the strength of the gauge field, where $\lambda<2$ or $\lambda>2$. A phase transition is identified at the critical point $\lambda\approx2$, at which all eigenstates undergo delocalization. The theory has been shown to be relevant for long-range hopping models and for higher dimensions.