# Purely Long-Range Coherent Interactions in Two-Dimensional Structured Baths

## TL;DR

This paper investigates how quantum emitters interact coherently over long distances within a two-dimensional hexagonal bosonic bath, revealing unique relaxation and interaction behaviors near the Dirac point.

## Contribution

It demonstrates the emergence of long-range coherent interactions and logarithmic relaxation laws for quantum emitters in a 2D structured bath with Dirac points.

## Key findings

- Single emitter relaxation follows a logarithmic law in time.
- Emitters exhibit inverse-distance decay of coherent interactions.
- Long-range interactions occur without exponential attenuation.

## Abstract

In this work we study the quantum dynamics emerging when quantum emitters exchange excitations with a two-dimensional bosonic bath with hexagonal symmetry. We show that a single quantum emitter spectrally tuned to the middle of the band relaxes following a logarithmic law in time due to the existence of a singular point with vanishing density of states, i.e., the Dirac point. Moreover, when several emitters are coupled to the bath at that frequency, long-range coherent interactions between them appear which decay inversely proportional to their distance without exponential attenuation. We analyze both the finite and infinite system situation using both perturbative and non-perturbative methods.