Peering into the darkness: vison-generated photon mass in quantum spin ice

Abstract

Describing experimental signatures of quantum spin ice has been the focus of many theoretical efforts, as definitive experimental verification of this candidate quantum spin liquid is yet to be achieved. Gapped excitations known as visons have largely eluded those efforts. We provide a theoretical framework, which captures their dynamics and predicts new signatures in the magnetic response. We achieve this by studying the ring-exchange Hamiltonian of quantum spin ice in the large-$s$ approximation, taking into account the compact nature of the emergent $U(1)$ gauge theory. We find the stationary solutions of the action -- the instantons -- which correspond to visons tunneling between lattice sites. By integrating out the instantons, we calculate the effective vison Hamiltonian, including their mass. We show that in the ground state virtual vison pairs simply renormalise the speed of light. At low temperatures, however, thermally activated visons form a Debye plasma and introduce a mass gap in the photon spectrum, equal to the plasma frequency, which we calculate as a function of temperature. We demonstrate that this dynamical mass gap should be visible in energy-resolved neutron scattering spectra but not in the energy-integrated ones. We also show that it does not lead to confinement of static spinons.

References in corpus (5)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Bosonic Many-body Theory of Quantum Spin Ice
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Coulomb liquid phases of bosonic cluster Mott insulators on a pyrochlore lattice

Cited by in corpus (8)

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• The Emergent Fine Structure Constant of Quantum Spin Ice Is Large
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
• Vison crystal in quantum spin ice on the breathing pyrochlore lattice
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Quantum Spin Liquids Stabilized by Disorder in Non-Kramers Pyrochlores