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Article overview
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Emergent Fracton Dynamics in a Non-Planar Dimer Model | | Johannes Feldmeier
; Frank Pollmann
; Michael Knap
; | | Date: |
19 Nov 2020 | | Abstract: | We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge
theory in the form of a dimer model on a bilayer geometry. To this end, we
first develop a proper notion of hydrodynamic transport in such a system by
constructing a global conservation law that can be attributed to the presence
of topological solitons. The correlation functions of local objects charged
under this conservation law can then be used to study the universal properties
of the dynamics at late times, applicable to both quantum and classical
systems. Performing the time evolution via classically simulable automata
circuits unveils a rich phenomenology of the system’s non-equilibrium
properties: For a large class of relevant initial states, local charges are
effectively restricted to move along one-dimensional ’tubes’ within the
quasi-two-dimensional system, displaying fracton-like mobility constraints. The
time scale on which these tubes are stable diverges with increasing systems
size, yielding a novel mechanism for non-ergodic behavior in the thermodynamic
limit. We further explore the role of geometry by studying the system in a
quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due
to the emergence of an extensive number of conserved quantities. This provides
an instance of a recently introduced concept of ’statistically localized
integrals of motion’, whose universal anomalous hydrodynamics we determine by a
mapping to a problem of classical tracer diffusion. We conclude by discussing
how our approach might generalize to study transport in other lattice gauge
theories. | | Source: | arXiv, 2011.10055 | | Services: | Forum | Review | PDF | Favorites | |
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