Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation

TL;DR

This paper demonstrates how a chain of trapped ions can simulate a dipolar XXZ spin chain, revealing a complete devil's staircase of crystal states and unique correlation behaviors, advancing quantum simulation of long-range interacting systems.

Contribution

It introduces a trapped ion quantum simulation platform for a dipolar XXZ model and maps out its complex phase diagram including the devil's staircase and correlation properties.

Findings

Complete devil's staircase extends to lobes similar to Mott lobes.

No clear evidence of supersolidity near melting transition.

Inside lobes, correlations decay algebraically, not exponentially.

Abstract

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose--Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations.