Exotic quantum holonomy and non-Hermitian degeneracies in two-body Lieb-Liniger model

TL;DR

This paper explores the relationship between exotic quantum holonomy and exceptional points in a one-dimensional Bose system, revealing how eigenenergy anholonomy relates to the structure of Riemann surfaces and non-Hermitian degeneracies.

Contribution

It demonstrates the connection between eigenenergy anholonomy and exceptional points, interpreting degeneracies as branch points on Riemann surfaces in the Lieb-Liniger model.

Findings

Eigenenergy anholonomy corresponds to Riemann surface branch points.

Exceptional points are divergence points of the non-Abelian gauge connection.

Gauge covariant quantities can be obtained via anti-path-ordered exponentials.

Abstract

An interplay of an exotic quantum holonomy and exceptional points is examined in one-dimensional Bose systems. The eigenenergy anholonomy, in which Hermitian adiabatic cycle induces nontrivial change in eigenenergies, can be interpreted as a manifestation of eigenenergy's Riemann surface structure, where the branch points are identified as the exceptional points which are degeneracy points in the complexified parameter space. It is also shown that the exceptional points are the divergent points of the non-Abelian gauge connection for the gauge theoretical formulation of the eigenspace anholonomy. This helps us to evaluate anti-path-ordered exponentials of the gauge connection to obtain gauge covariant quantities.