Exact solvability and asymptotic aspects of generalized XX0 spin chains

TL;DR

This paper introduces generalized XX0 spin chains, constructs a long-range Selberg model, and analyzes phase transitions using matrix integrals and asymptotic methods, revealing Tracy-Widom and Gross-Witten transitions.

Contribution

It presents a new class of generalized XX0 models, explicitly constructs the Selberg long-range spin chain, and analyzes their phase structure with asymptotic techniques.

Findings

Identified Tracy-Widom distribution tails govern phase transitions.

Reproduced the Gross-Witten phase transition in the XX0 model.

Proposed universal features for phase structures of generalized XX0 models.

Abstract

Building on our earlier work \unscite{Sa-Za}, we introduce and study generalized XX0 models. We explicitly construct a long-range interacting spin chain, referred to as the Selberg model, and study the correlation functions of the Selberg and XX0 models. Using a matrix integral representation of the generalized XX0 model and applying asymptotic analysis in non-intersecting Brownian motion, the phase structure of the Selberg model is determined. We find that tails of the Tracy-Widom distribution, of Gaussian unitary ensemble, govern a discrete-to-continuous third-order phase transition in Selberg model. The same method also reproduces the Gross-Witten phase transition of the original XX0 model. Finally, we conjecture universal features for the phase structure of the generalized XX0 model.