Observation of a finite-energy phase transition in a one-dimensional quantum simulator

TL;DR

This paper reports the first experimental observation of a finite-energy phase transition in a one-dimensional quantum system using a trapped-ion quantum simulator, demonstrating access to previously inaccessible phases.

Contribution

It experimentally demonstrates a finite-energy phase transition in 1D, previously thought impossible without long-range interactions, using a quantum simulator with up to 23 spins.

Findings

Observed ferromagnetic phase transition at finite energy

Identified crossover from polarized to unpolarized paramagnet

Results agree with numerical simulations

Abstract

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to $23$ spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.