# Anomalous domain wall condensation in a modified Ising chain

## TL;DR

This paper introduces a one-dimensional spin Hamiltonian with an anomalous non-local $Z_2$ symmetry, revealing a rich phase diagram with gapless, ferromagnetic, and antiferromagnetic phases through domain wall condensation analysis.

## Contribution

It constructs a novel Hamiltonian with an intrinsically non-local symmetry and analyzes its phase diagram, highlighting unconventional domain wall properties and phase transitions.

## Key findings

- Identifies a gapless phase separated by BKT transition from ferromagnetic phase.
- Discovers a first-order transition between the gapless and antiferromagnetic phases.
- Demonstrates the role of domain wall condensation in the phase structure.

## Abstract

We construct a one-dimensional local spin Hamiltonian with an intrinsically non-local, and therefore anomalous, global $\mathbb{Z}_2$ symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and contains a parameter that can be tuned to spontaneously break the non-local $\mathbb{Z}_2$ symmetry. The Hamiltonian is constructed to capture the unconventional properties of the domain walls in the symmetry broken phase. Using uniform matrix product states, we obtain the phase diagram that results from condensing the domain walls. We find that the complete phase diagram includes a gapless phase that is separated from the ordered ferromagnetic phase by a Berezinskii-Kosterlitz-Thouless transition, and from the ordered antiferromagnetic phase by a first order phase transition.