Bosonic Many-body Theory of Quantum Spin Ice

TL;DR

This paper provides an analytical bosonic many-body theory of quantum spin ice, analyzing the stability of the U(1) quantum spin liquid phase and estimating phase boundaries in the parameter space.

Contribution

It introduces a bosonic representation of spinons and a phenomenological gauge field Hamiltonian to study quantum spin ice stability.

Findings

Determines the stability region of the U(1) quantum spin liquid phase.

Calculates the one-loop spinon self-energy proportional to J_{zeta}^2.

Estimates phase boundaries between spin liquid and ordered phases.

Abstract

We carry out an analytical study of quantum spin ice, a U$(1)$ quantum spin liquid close to the classical spin ice solution for an effective spin $1/2$ model with anisotropic exchange couplings $J_{zz}$, $J_{\pm}$ and $J_{z\pm}$ on the pyrochlore lattice. Starting from the quantum rotor model introduced by Savary and Balents in Phys. Rev. Lett. 108, 037202 (2012), we retain the dynamics of both the spinons and gauge field sectors in our treatment. The spinons are described by a bosonic representation of quantum XY rotors while the dynamics of the gauge field is captured by a phenomenological Hamiltonian. By calculating the one-loop spinon self-energy, which is proportional to $J_{z\pm}^2$, we determine the stability region of the U$(1)$ quantum spin liquid phase in the $J_{\pm}/J_{zz}$ vs $J_{z\pm}/J_{zz}$ zero temperature phase diagram. From these results, we estimate the location of the boundaries between the spin liquid phase and classical long-range ordered phases.