Confined phases of one-dimensional spinless fermions coupled to $Z_2$ gauge theory

TL;DR

This paper explores a one-dimensional system of spinless fermions coupled to a $Z_2$ gauge field, revealing confinement phenomena, emergent Luttinger liquid behavior, and potential experimental signatures like doubled Friedel oscillations.

Contribution

It introduces an exactly solvable effective theory for confined fermion dimers and demonstrates fractionalization and confinement effects in a $Z_2$ gauge coupled fermion system.

Findings

Formation of a Luttinger liquid despite confinement

Doubling of Friedel oscillation period as an experimental signature

Potential Mott phase at 2/3 filling

Abstract

We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical $Z_2$ gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the Density Matrix Renormalization Group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling $2/3$.