Exact duality relations in correlated electron systems

TL;DR

This paper derives exact duality relations between different order parameters in correlated electron systems, revealing mappings between unconventional and conventional density-wave orders and providing insights into the phase diagram.

Contribution

It introduces gauge transformation-based duality relations in correlated electron models, especially in the two-leg Hubbard ladder, highlighting new mappings between phases.

Findings

Duality relations between unconventional and conventional density-waves

Exact phase diagram results for the Hubbard ladder

Mappings between dual phases

Abstract

Using gauge transformations on electron bond operators, we derive exact duality relations between various order parameters for correlated electron systems. Applying these transformations, we find two duality relations in the generalized two-leg Hubbard ladder at arbitrary filling. The relations show that unconventional density-wave orders such as staggered flux or circulating spin-current are dual to conventional density-wave orders and there are direct mappings between dual phases. Several exact results on the phase diagram are also concluded.