Disorder from disorder and confinement in the quantum Ising model in the pyrochlore lattice

TL;DR

This paper studies how a transverse magnetic field induces quantum confinement and changes the spin correlation in the classical pyrochlore lattice Ising model, revealing a transition from a deconfined to a confined phase.

Contribution

It demonstrates the quantum confinement of magnetic monopoles in the pyrochlore lattice Ising model under a transverse field, extending understanding of disorder and confinement in quantum spin systems.

Findings

Turning on a transverse field induces exponential decay in spin correlations.

Quantum confinement causes the monopole binding energy to be proportional to their separation.

The system transitions adiabatically to a paramagnetic state at large fields.

Abstract

At zero temperature, the classical antiferromagnetic Ising model on the pyrochlore lattice is a spin disorder phase of the critical spin correlation. It is a deconfined phase in that the binding energy of the monopole-anti-monopole pair is independent of their distance of separation. We show that turning on a transverse magnetic field turns it into the cooperative paramagnet, and the spin correlation becomes exponential decay. Furthermore, it introduces the quantum confinement (of magnetic monopoles), where the binding energy of the pair is proportional to their distance of separation. This disorder state undergoes adiabatic transition to the paramagnetic state in the large field limit. The effective Hamiltonian (without magnetic monopoles) in small field is the Ising Hamiltonian plus ring exchange interaction.