Probing the conformal Calabrese-Cardy scaling with cold atoms

TL;DR

This paper shows how cold atom experiments can verify conformal field theory predictions by measuring entanglement entropy, enabling estimation of the central charge and testing Calabrese-Cardy scaling.

Contribution

It introduces methods to use cold atom setups for probing CFT predictions and compares numerical models with experimental conditions to validate the scaling laws.

Findings

S_2 entanglement entropy follows Calabrese-Cardy scaling with c=1

Methods to estimate and subtract classical entropy are effective

Numerical models agree with experimental results for open boundary conditions

Abstract

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Renyi entanglement entropy S_2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half-filling where we expect a CFT with c=1. This can be accomplished with a very small hoping parameter J, in contrast to existing studies with density one where a much larger J is needed. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a 1+1 dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S_2 is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8)\ln(N_s), for N_s sites with open boundary conditions, provided that the large subleading corrections are taken into account.