Non-local order parameters for the 1D Hubbard model

TL;DR

This paper introduces non-local order parameters based on parity correlators to distinguish phases in the 1D Hubbard model, revealing insights into the nature of Mott insulator and Luther-Emery phases and their phase transition.

Contribution

It proposes a novel characterization of 1D Hubbard phases using parity-based non-local correlators, linking them to an effective free fermion model.

Findings

Parity correlators order in gapped phases and vanish at critical point

Mott insulator involves bound doublon-holon pairs

Behavior of correlators explained by free spinless fermion model

Abstract

We characterize the Mott insulator and Luther-Emery phases of the 1D Hubbard model through correlators that measure the parity of spin and charge strings along the chain. These non-local quantities order in the corresponding gapped phases and vanish at the critical point $U_c=0$. The Mott insulator consists of bound doublon-holon pairs, which in the Luther-Emery phase turn into electron pairs with opposite spins, both unbinding at $U_c$. The behavior of the parity correlators can be captured by an effective free spinless fermion model.