# Non-equilibrium magnetic phases in spin lattices with gain and loss

## TL;DR

This paper investigates non-equilibrium magnetic phases in a spin chain with competing coherent interactions and alternating gain and loss, revealing novel phase transition phenomena driven by parity-time-reversal symmetry breaking.

## Contribution

It introduces a new model demonstrating atypical non-equilibrium phase transitions, including first-order and mixed-order types, extending the understanding of driven-dissipative spin systems.

## Key findings

- Transitions between magnetically aligned and highly mixed phases.
- First-order transitions without phase co-existence.
- Mixed-order transitions preserving $U(1)$ symmetry.

## Abstract

We study the magnetic phases of a non-equilibrium spin chain, where coherent interactions between neighboring lattice sites compete with alternating gain and loss processes. This competition between coherent and incoherent dynamics induces transitions between magnetically aligned and highly mixed phases, across which the system changes from a low- to an effective infinite-temperature state. We show that the origin of these transitions can be traced back to the dynamical effect of parity-time-reversal symmetry breaking, which has no counterpart in the theory of equilibrium phase transitions. This mechanism also results in very atypical features and we find first-order transitions without phase co-existence and mixed-order transitions which do not break the underlying $U(1)$ symmetry, even in the appropriate thermodynamic limit. Thus, despite its simplicity, the current model considerably extends the phenomenology of non-equilibrium phase transitions beyond that commonly assumed for driven-dissipative spins and related systems.

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Source: https://tomesphere.com/paper/1908.02290