Abstract
We study the dynamics of the energy fluctuations in the Hubbard chain with strong potential disorder that preserves the SU(2) spin symmetry. Within the effective spin-only model that correctly captures relaxation in the situation of localized charges, we show that the decay of local energy correlations is suppressed and is at least marginally nonergodic, being qualitatively different from the subdiffusive dynamics and relaxation of local spins. The anomalous behavior can be traced back to the singular distribution of effective exchange couplings. Numerical results for the dynamical thermal conductivity within the full Hubbard model confirm that the energy (thermal) transport is closer to the charge dynamics, which appears to be also marginally localized in a wide parameter range.
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