# Nonequilibrium phase transition in an open quantum spin system with long-range interaction

## TL;DR

This paper explores a nonequilibrium phase transition in a long-range quantum spin system with both coherent and incoherent processes, revealing new universality classes at tricritical points through mean-field analysis.

## Contribution

It introduces a long-range quantum contact process model with long-distance interactions, extending previous nearest-neighbor models and identifying novel universality classes at tricritical points.

## Key findings

- Mean-field phase diagram similar to nearest-neighbor QCP.
- Continuous and discontinuous transitions in weak and strong quantum regimes.
- Discovery of a new universality class at the tricritical point.

## Abstract

We investigate a nonequilibrium phase transition in a dissipative and coherent quantum spin system using the quantum Langevin equation and mean-field theory. Recently, the quantum contact process (QCP) was theoretically investigated using the Rydberg antiblockade effect, in particular, when the Rydberg atoms were excited in s-states so that their interactions were regarded as being between the nearest neighbors. However, when the atoms are excited to d-states, the dipole-dipole interactions become effective, and long-range interactions must be considered. Here, we consider a quantum spin model with a long-range QCP, where the branching and coagulation processes are allowed not only for the nearest-neighbor pairs, but also for long-distance pairs, coherently and incoherently. Using the semiclassical approach, we show that the mean-field phase diagram of our long-range model is similar to that of the nearest-neighbor QCP, where the continuous (discontinuous) transition is found in the weak (strong) quantum regime. However, at the tricritical point, we find a new universality class, which was neither that of the QCP at the tricritical point nor that of the classical directed percolation model with long-range interactions. Implementation of the long-range QCP using interacting cold gases is discussed.