Duality relations and exotic orders in electronic ladder systems

TL;DR

This paper explores duality relations in electronic ladder systems, revealing how exotic density-wave orders relate to conventional ones and unifying different phases through symmetry considerations.

Contribution

It introduces exact and asymptotic duality relations in Hubbard ladders and extends the SO(5) symmetry framework to include circulating spin current order.

Findings

Exotic density-wave orders map to conventional orders via duality.

Duality relations connect circulating spin-current order with s-wave superconductivity.

Unification of phases through extended SO(5) symmetry.

Abstract

We discuss duality relations in correlated electronic ladder systems to clarify mutual relations between various conventional and unconventional phases. For the generalized two-leg Hubbard ladder, we find two exact duality relations, and also one asymptotic relation which holds in the low-energy regime. These duality relations show that unconventional (exotic) density-wave orders such as staggered flux or circulating spin-current are directly mapped to conventional density-wave orders, which establishes the appearance of various exotic states with time-reversal and/or spin symmetry breaking. We also study duality relations in the SO(5) symmetry that was proposed to unify antiferromagnetism and d-wave superconductivity. We show that the same SO(5) symmetry also unifies circulating spin current order and s-wave superconductivity.