Semiclassical approach to quantum spin ice

Abstract

International audienceWe propose a semiclassical description of the low-energy properties of quantum spin ice in the strong Ising limit. Within the framework of a semiclassical, perturbative Villain expansion, that can be truncated at arbitrary order, we give an analytic and quantitative treatment of the deconfining phase. We find that photon-photon interactions significantly renormalize the speed of light and split the two transverse photon polarizations at intermediate wave vectors. We calculate the photon velocity and the ground-state energy to first and second order in perturbation theory, respectively. Both are in good agreement with recent numerical simulations. We further compute the classical energy of the vison excitation

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

“…[33], we evaluated the correlator Dynamical structure factor S zz (q, ω) along high symmetry directions in the semiclassical QSI model at T = 10 −4 g. Photons manifest as a sharp, gapless, linearly dispersing branch of classical normal modes. The frequency of these modes matches excellently with large-S analytic predictions (green line) [38,58]. The integrated structure factor of the modes (red dots) is independent of q, as expected on grounds of equipartition.…”

“…A single set of remarkably sharp normal modes appear in the data [58]. The frequencies of the numerically obtained modes match perfectly with analytic results for the large-S photon dispersion [38] (green line in Fig. 2), confirming that the CSL simulated by our method is indeed equivalent to large-S QSI.…”

“…These states are stable against transverse fluctuations, removing any dynamics analogous to QSI. The ring exchange Hamiltonian (5), however, remains in a QSL phase for arbitrary S [22,38]: Since it only contains transverse terms, its classical ground state is easy-plane and the electric field appears as small fluctuations of σ z , which are amenable to continuous time evolution (cf. Fig.…”

“…This is due to interactions between visons and photons arising from corrections to the gauge theory beyond quadratic order. The next order in the Villain expansion [38] consists of negative quartic terms which, in the presence of a (thermal) population of photons, lead to a negative renormalisation of vison energies and interactions; see Appendix E for a more detailed discussion of both the mechanism and its effect on the effective vison gap. This mechanism is at work at intermediate temperatures, reducing the gap of visons compared to the zero-temperature value, resulting in larger thermal populations.…”

Generalized route to effective field theories for quantum systems with local constraints

“…[13,14], namely c √ 0.8J(J − V). We expect higher-order corrections in the 1/S expansion to substantialy reduce this discrepancy [16]. The ground state of the S → ∞ model was obtained as a function of V/J by comparing the large-S minimum energy of ordered and resonating phases suggested in the literature [13,14,33].…”