How Hidden Orders Generate Gaps in 1D Fermionic Systems

TL;DR

This paper shows that hidden long-range order exists in gapped phases of 1D interacting fermionic systems, characterized by nonlocal correlations, and confirms these findings through numerical simulations of specific models.

Contribution

It provides a classification of microscopic hidden orders in 1D fermionic systems and demonstrates their universal presence in gapped phases.

Findings

Hidden long-range order is always present in gapped phases.

Correlation functions of nonlocal operators remain finite asymptotically.

Numerical simulations confirm the theoretical classification.

Abstract

We demonstrate that hidden long range order is always present in the gapped phases of interacting fermionic systems on one dimensional lattices. It is captured by correlation functions of appropriate nonlocal charge and/or spin operators, which remain asymptotically finite. The corresponding microscopic orders are classified. The results are confirmed by DMRG numerical simulation of the phase diagram of the extended Hubbard model, and of a Haldane insulator phase.