Surface criticality in the mixed-field Ising model with sign-inverted next-nearest-neighbor interaction

TL;DR

This paper proposes a method to implement sign-inverted next-nearest-neighbor interactions in Rydberg atom systems and studies the resulting surface criticality near a quantum phase transition using analytical and numerical approaches.

Contribution

It introduces a way to realize sign-inverted NNN interactions in Rydberg systems and analyzes the associated surface critical phenomena.

Findings

Sign-inverted NNN interactions can be achieved via weak coupling of Rydberg states.

Surface criticality manifests as a logarithmic divergence of the healing length.

Theoretical analysis combines Ginzburg-Landau theory with mean-field numerical methods.

Abstract

Rydberg atoms in an optical tweezer array have been used as a quantum simulator of the spin-$1/2$ antiferromagnetic Ising model with longitudinal and transverse fields. We suggest how to implement the next-nearest-neighbor (NNN) interaction whose sign is opposite to that of the nearest neighbor one in the Rydberg atom systems. We show that this can be achieved by weakly coupling one Rydberg state with another Rydberg state. We further study the surface criticality associated with the first-order quantum phase transition between the antiferromagnetic and paramagnetic phases, which emerges due to the sign-inverted NNN interaction. From the microscopic model, we derive a Ginzburg-Landau (GL) equation, which describes static and dynamic properties of the antiferromagnetic order parameter near the transition. Using both analytical GL theory and numerical method based on a mean-field theory, we calculate the order parameter in the proximity of a boundary of the system in order to show that the healing length of the order parameter logarithmically diverges, signaling the surface criticality.