G. Naik: Theta electromagnetism in quantum spin ice

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. In this talk, I will 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.