Ring frustration and factorizable correlation functions of critical spin rings

TL;DR

This paper investigates the effects of ring frustration on the nonlocality and correlation functions in critical spin rings, using exactly solvable models to deepen understanding of many-body quantum systems.

Contribution

It introduces the concept of nonlocality in many-body systems via factorizable correlation functions and reexamines finite-size scaling in the presence of ring frustration.

Findings

Nonlocal factors embedded in correlation functions are established.

Ring frustration significantly affects correlation functions.

Finite-size scaling analysis is reappraised in this context.

Abstract

Basing on the exactly solvable prototypical model, the critical transverse Ising ring with or without ring frustration, we establish the concept of nonlocality in a many-body system in the thermodynamic limit by defining the nonlocal factors embedded in its factorizable correlation functions. In the context of nonlocality, the valuable traditional finite-size scaling analysis is reappraised. The factorizable correlation functions of the isotropic $XY$ and the spin-1/2 Heisenberg models are also demonstrated with the emphasis on the effect of ring frustration.