Chiral Topological Elasticity and Fracton Order

We analyze the “higher rank” gauge theories that capture some of the phenomenology of the fracton order. It is shown that these theories lose gauge invariance when an arbitrarily weak and smooth curvature is introduced. We propose a resolution to this problem by introducing a theory invariant under area-preserving diffeomorphisms, which reduce to the higher rank gauge transformations upon linearization around a flat background. The proposed theory is geometric in nature and is interpreted as a theory of chiral topological elasticity. This theory exhibits some of the fracton phenomenology. We explore the conservation laws, topological excitations, linear response, various kinematical constraints, and canonical structure of the theory. Finally, we emphasize that the very structure of Riemann-Cartan geometry, which we use to formulate the theory, encodes some of the fracton phenomenology, suggesting that the fracton order itself is geometric in nature.

Note:

6 pages, 1 Fig; v2 Improved presentation, to appear in PRL

Condensed Matter: Electronic Properties, etc.
excited state: topological
invariance: gauge
geometry: Riemann-Cartan
kinematics: constraint
fractional
gauge field theory
conservation law
diffeomorphism

References(52)

Figures(1)

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This must be the case since the r.h.s. of (2) is a rank-2 tensor

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The reader may be tempted to argue that our observation implies that higher rank gauge theory is only welldefined in flat space, because it is related to the microscopic model that is very sensitive to the lattice effects. We believe that the effective gauge theory cannot make sense if adding arbitrarily small and smooth gaussian curvature breaks the gauge invariance. Alternative would imply that the number of degrees of freedom depends on whether the space is curved

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Sensitivity of the lattice Fracton models to geometry was remarked in [11] however the relation to our observation (5) is not clear

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In fact, we believe that it is not possible to reconcile the higher rank gauge invariance with the reparametrisation invariance, unless the former is interpreted as a subset of the latter

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