Quantum-classical equivalence and ground-state factorization

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.

5 pages, 2 figures

References in corpus (7)

• Theory of ground state factorization in quantum cooperative systems
• Separability and ground state factorization in quantum spin systems
• Entanglement of finite cyclic chains at factorizing fields
• Criticality, factorization and long-range correlations in the anisotropic XY-model
• Ground-state factorization and quantum phase transition in dimerized spin chains
• Separability and entanglement in finite dimer-type chains in general transverse fields
• Exact models for trimerization and tetramerization in spin chains