Quantum-classical equivalence and ground-state factorization

TL;DR

This paper analytically explores the connection between quantum $XY$-spin chains and classical models, revealing how factorizing fields correspond to natural boundaries in classical mappings, and proposes a method to find these fields.

Contribution

It establishes a novel link between quantum ground-state factorization and classical boundary phenomena, offering a new approach to determine factorizing fields in quantum systems.

Findings

Factorizing line corresponds to the natural boundary in classical mapping

Quantum systems with non-factorizable ground states cannot be mapped to classical Ising models

Proposes a method to find factorizing fields via Hamiltonian and transfer matrix commutation

Abstract

We have performed an analytical study of quantum-classical equivalence for quantum $XY$-spin chains with arbitrary interactions to explore the classical counterpart of the factorizing magnetic fields that drive the system into a separable ground state. We demonstrate that the factorizing line in parameter space of a quantum model is equivalent to the so-called natural boundary that emerges in mapping the quantum $XY$-model onto the two dimensional classical Ising model. As a result, we show that the quantum systems with the non-factorizable ground state could not be mapped onto the classical Ising model. Based on the presented correspondence we suggest a promising method for obtaining the factorizing field of quantum systems through the commutation of the quantum Hamiltonian and the transfer matrix of the classical model.