Fractons from confinement in one dimension

TL;DR

This paper reveals a fundamental connection between fracton behavior and confinement in one-dimensional quantum systems, showing how confining theories can exhibit effective fracton dynamics with immobile particles and conserved dipole moments.

Contribution

It demonstrates that confining one-dimensional models can naturally exhibit fracton-like behavior, linking two previously distinct mechanisms for non-ergodicity.

Findings

Confined charges show immobility, while dipolar bound states move freely.

Effective fracton Hamiltonian with conserved dipole moment derived.

Connection between confinement and fracton dynamics explained through string motion.

Abstract

Recent work has shown that two seemingly different physical mechanisms, namely fracton behavior and confinement, can give rise to non-ergodicity in one-dimensional quantum many-body systems. In this work, we demonstrate an intrinsic link between these two mechanisms by studying the dynamics of one-dimensional confining theories, such as a U(1) gauge theory and a quantum Ising model. We show that, within certain parameter regimes, these models exhibit effective fracton dynamics, characterized by immobility of stable single-particle excitations and free motion of dipolar bound states. By perturbatively integrating out the linearly confining field, we obtain an effective fracton Hamiltonian for the confined charges which exhibits conservation of dipole moment. We discuss an intuitive understanding of these results in terms of the motion of the confining strings, leading to potential extensions to higher dimensions. We thereby interpret recent observations of nonthermal eigenstates and glassy dynamics in confining theories in terms of corresponding results in the fracton literature.