Order-by-disorder and quantum Coulomb phase in quantum square ice

TL;DR

This paper maps the phase diagram of quantum square ice, revealing quantum fluctuation-induced phases and a thermally induced Coulomb phase with deconfined spinons, using advanced computational and theoretical methods.

Contribution

It provides a comprehensive analysis of quantum square ice, identifying new quantum phases and connecting them to lattice gauge theories through perturbation theory and Monte Carlo simulations.

Findings

Identification of two quantum order-by-disorder phases: plaquette valence-bond solid and canted Neel state.

Discovery of a thermally induced quantum Coulomb phase supporting deconfined spinons.

Mapping of the phase diagram using quantum Monte Carlo, perturbation theory, and gauge mean-field theory.

Abstract

We reconstruct the equilibrium phase diagram of quantum square ice, realized by the transverse-field Ising model on the checkerboard lattice, using a combination of quantum Monte Carlo, degenerate perturbation theory and gauge mean-field theory. The extensive ground-state degeneracy of classical square ice is lifted by the transverse field, leading to two distinct order-by-disorder phases, a plaquette valence-bond solid for low field, and a canted Neel state for stronger fields. These two states appear via a highly non-linear effect of quantum fluctuations, and they can be identified with the phases of a lattice gauge theory (quantum link model) emerging as the effective Hamiltonian of the system within degenerate perturbation theory up to the 8th order. The plaquette valence-bond solid melts at a very low temperature, above which the system displays a thermally induced quantum Coulomb phase, supporting deconfined spinons.