Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries

TL;DR

This paper investigates how $ heta$-terms, related to magnetoelectric effects, can emerge in the internal electromagnetism of a quantum spin ice, revealing new microscopic interactions and symmetry conditions for observable responses.

Contribution

It identifies a seven-spin interaction term that induces a $ heta$-electromagnetic phase in quantum spin ice and analyzes the symmetry conditions necessary for its emergence.

Findings

Seven-spin term leads to $ heta$-phase in lattice gauge theory.

Next-nearest-neighbor interactions are essential for $ heta$-term.

Conditions for significant magnetoelectric response are established.

Abstract

$U(1)$ gauge theories, including conventional Maxwell electromagnetism, allow $\theta$-terms when parity and time-reversal symmetry are broken. In condensed matter systems, the physics of $\theta$ as a magnetoelectric response has been explored extensively within the context of topological insulators and multiferroics. We show how $\theta$-terms can arise in the internal dynamics of the emergent electromagnetism in a $U(1)$ quantum spin liquid. In its Coulomb phase, the minimal model of pyrochlore quantum spin ice is governed by a six-spin ring exchange Hamiltonian. We identify the next-order contribution to the microscopic Hamiltonian when parity, time-reversal, and all improper spatial symmetries are broken -- a seven-spin term which leads to a two-parameter lattice gauge theory with a $\theta$-electromagnetic phase. We derive how the seven-spin term is generated perturbatively within each of the three symmetry classes of short-range pyrochlore spin ice. Within a complete microscopic symmetry analysis, we find that the most general nearest-neighbor Hamiltonians fail to generate the seven-spin term, and one must include next-nearest-neighbor interactions to obtain an emergent $\theta$. Using gauge mean-field theory we compute additional contributions to the $\theta$-term from the spinon sector. Finally, we determine the conditions required for an internal $\theta$-term to generate a significant external magnetoelectic response.