Einstein relation for subdiffusive relaxation in Stark chains
arxiv(2024)
Abstract
We investigate chains of interacting spinless fermions subject to a finite
external field F (also called Stark chains) and focus on the regime where the
charge thermalization follows the subdiffusive hydrodynamics. First, we study
reduced models conserving the dipole moment and derive an explicit Einstein
relation which links the subdiffusive transport coefficient with the
correlations of the dipolar current. This relation explains why the decay rate,
Γ_q, of the density modulation with wave-vector q shows
q^4-dependence. In the case of the Stark model, a similar Einstein relation
is also derived and tested using various numerical methods. They confirm an
exponential reduction of the transport coefficient with increasing F. On the
other hand, our study of the Stark model indicates that upon increasing q
there is a crossover from subdiffusive behavior, Γ_q ∝ q^4, to the
normal diffusive relaxation, Γ_q ∝ q^2, at the wave vector q^*
which vanishes for F → 0.
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