Competing orders in the generalized Hund chain model at half-filling

TL;DR

This paper explores the complex phase diagram of the generalized Hund model at half-filling, revealing multiple Mott insulating phases and their correspondence with two-leg Hubbard ladders using combined analytical and numerical methods.

Contribution

It provides a comprehensive analysis of the phase diagram of the generalized Hund model, identifying eight Mott phases and establishing their relation to two-leg Hubbard ladders through a duality approach.

Findings

Eight Mott insulating phases identified

Quantitative agreement between weak coupling analysis and numerical results

Correspondence established with two-leg Hubbard ladder phases

Abstract

By using a combination of several non-perturbative techniques -- a one-dimensional field theoretical approach together with numerical simulations using density matrix renormalization group -- we present an extensive study of the phase diagram of the generalized Hund model at half-filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3/2, other cold gases like Ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg Hubbard ladder with interchain hopping. Our results obtained from a weak coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.