Abstract
"Magnetic monopole" is an exotic quantum excitation in pyrochlore U(1) spin liquid, and its emergence is purely of quantum origin and has no classical analogue. We predict topological thermal Hall effect (TTHE) of "magnetic monopoles" and present this prediction through non-Kramers doublets. We observe that, when the external magnetic field polarizes the Ising component of the local moment, internally this corresponds to the induction of emergent dual U(1) gauge flux for the "magnetic monopoles". The motion of "magnetic monopoles" is then twisted by the induced dual gauge flux. This emergent Lorentz force on "magnetic monopoles" is the fundamental origin of TTHE. Therefore, TTHE would be a direct evidence of the "monopole"-gauge coupling and the emergent U(1) gauge structure in pyrochlore U(1) spin liquid. Our result does not depend strongly on our choice of non-Kramers doublets for our presentation, and can be well extended to Kramers doublets. Our prediction can be readily tested among the pyrochlore spin liquid candidate materials. We give a detailed discussion about the expectation for different pyrochlore magnets.
Highlights
Emergent gauge structure and theory comprise an important subject in modern condensed-matter physics, for strongly correlated quantum matter [1]
We develop a theory to predict the phenomenon of the topological thermal Hall effect (TTHE) in the pyrochlore U(1) quantum spin liquids (QSLs) and propose it as a positive evidence of the emergent U(1) gauge structure
A weak external magnetic field polarizes the spins in each pyrochlore tetrahedron partially, and throughout we work in the weak-field regime such that the U(1) QSL state is preserved, namely the lattice gauge theory is in its deconfined phase
Summary
Emergent gauge structure and theory comprise an important subject in modern condensed-matter physics, for strongly correlated quantum matter [1]. The external magnetic field, which couples linearly with the spins through a simple Zeeman coupling, polarizes the internal electric field and thereby modifies the dual U(1) gauge flux that is experienced by the “magnetic monopoles.”. Our key observation is that the external field could generate an internal dual U(1) gauge flux for the “magnetic monopoles.” A weak external magnetic field polarizes the spins in each pyrochlore tetrahedron partially, and throughout we work in the weak-field regime such that the U(1) QSL state is preserved, namely the lattice gauge theory is in its deconfined phase. We observe that the external field modifies the internal dual U(1) gauge flux and thereby generates an emergent Lorentz force on the “magnetic monopoles.”. The Hamiltonian in Eq (12) describes the hopping of “magnetic monopoles” in the presence of a dual U(1) gauge field, whose fluctuation has been ignored
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