Title: Glassy quantum dynamics in translation invariant fracton models,
Abstract: We investigate relaxation in the recently discovered "fracton" models and
discover that these models naturally host glassy quantum dynamics in the
absence of quenched disorder. We begin with a discussion of "type I" fracton
models, in the taxonomy of Vijay, Haah, and Fu. We demonstrate that in these
systems, the mobility of charges is suppressed exponentially in the inverse
temperature. We further demonstrate that when a zero temperature type I fracton
model is placed in contact with a finite temperature heat bath, the approach to
equilibrium is a logarithmic function of time over an exponentially wide window
of time scales. Generalizing to the more complex "type II" fracton models, we
find that the charges exhibit subdiffusion upto a relaxation time that diverges
at low temperatures as a super-exponential function of inverse temperature.
This behaviour is reminiscent of "nearly localized" disordered systems, but
occurs with a translation invariant three-dimensional Hamiltonian. We also
conjecture that fracton models with conserved charge may support a phase which
is a thermal metal but a charge insulator.