Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice

Abstract

Understanding the nature and behaviour of excitations in quantum spin liquids, and in topological phases of matter in general, is of fundamental importance and has proven crucial for experimental detection and characterisation of candidate materials. Current theoretical and numerical techniques, however, have limited capabilities, especially when it comes to studying gapped excitations. Here, we propose a semiclassical numerical method to study systems whose spin liquid behaviour is underpinned by perturbative ring-exchange Hamiltonians. Our method can readily access both thermodynamic and spectral properties. We focus in particular on quantum spin ice and its photon and vison excitations. After benchmarking the method against existing results on photons, we use it to characterise visons and their thermodynamic behaviour, which remained hitherto largely unexplored. We find that visons, in contrast to spinons in classical spin ice, form a weak electrolyte: vison pairs are the dominant population at low temperatures. This is reflected in the behaviour of thermodynamic quantities, such as pinch point motifs in the relevant correlators. Visons also appear to strongly hybridise with the photon background, a phenomenon that affects the way these quasiparticles may show up in inelastic response measurements. Our results demonstrate that the method, and generalisations thereof, can substantially help our understanding of quasiparticles and their interplay in quantum spin ice and other quantum spin liquids, quantum dimer models, and lattice gauge theories in general.

Vison-generated photon mass in quantum spin ice: A theoretical framework

“…The above vison self-energy and Coulomb interaction agree with the results of Ref. [26] in the quadratic approximation. (Note that our definition of g and the definition given in Ref.…”

“…These quantum corrections also go beyond the recent classical description of visons in Ref. [26] and endow them with a finite mass (exponentially small in s), which we have calculated.…”

“…Because visons are sources of emergent electric field, they are not easily accessible to experimental probes. Perhaps, magnetostriction or Dzyaloshinskii-Moriya effects can couple real electric fields to the emergent electric field of the visons [26,[34][35][36], in which case visons can leave a signature in electric response measurements. In this paper, we have instead focused on how the dynamics of the vison's emergent electric field couple to the dynamics of the physical magnetic field, via electromagnetic induction.…”

“…Classical Monte Carlo calculations of Ref. [26] found that the energy of a nearest-neighbor vison pair is actually lower than that of a single vison, so that at low temperatures, vison pairs are the dominant species and the visons form a weak electrolyte. Here, we argue that the model can be mapped, by integrating out tightly bound vison pairs, to a coarse-grained 3D Coulomb gas where free visons are the dominant species.…”

“…In this context, the work of Ref. [26], made recent progress by looking at visons through classical Monte Carlo, characterising their effect on emergent field correlators and the heat capacity. This work analysed vison signatures in the classical s = ∞ limit.…”