Microscopic characterization of Ising conformal field theory in Rydberg chains

TL;DR

This paper establishes a detailed microscopic understanding of Ising conformal field theory in Rydberg chains, linking lattice operators to low-energy critical fields and analyzing how interactions influence criticality and phase transitions.

Contribution

It constructs a lattice-to-CFT dictionary for Rydberg chains at the Ising transition, including primary fields and fermions, and studies interaction effects on critical behavior.

Findings

Microscopic Rydberg operators correlate with Ising CFT fields.

Second-neighbor interactions tune four-fermion couplings.

Identification of how four-fermion couplings lead to tricriticality.

Abstract

Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. We first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions -- a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays, and can inform the design of novel higher-dimensional phases based on coupled critical chains.