Many-body spin interactions and the ground state of a dense Rydberg lattice gas

TL;DR

This paper investigates a one-dimensional Rydberg lattice gas, revealing a parameter regime where the system's Hamiltonian simplifies to a spin model with many-body interactions, allowing an exact ground state solution and showing a phase crossover.

Contribution

It introduces a class of spin models with many-body interactions that admit an exact analytic ground state, advancing understanding of complex quantum phases in Rydberg systems.

Findings

Exact analytic ground state for a class of many-body spin models.

Identification of a phase crossover between paramagnetic and crystalline states.

Detailed analysis of the superposition state and correlation properties.

Abstract

We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well-approximated by a spin Hamiltonian with quasi-local many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a cross-over between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.