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arXiv:1903.03770 · Physical review. B./Physical review. B

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

M. Środa, Peter Prelovšek, Marcin Mierzejewski

Published Mar 20, 2019• 21 citations
arXivHTMLPDF

Abstract

We study spin transport in a Hubbard chain with a strong, random, on-site potential and with spin-dependent hopping integrals ${t}_{\ensuremath{\sigma}}$. For the SU(2) symmetric case ${t}_{\ensuremath{\uparrow}}={t}_{\ensuremath{\downarrow}}$, such a model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spin asymmetry, ${t}_{\ensuremath{\uparrow}}\ensuremath{\ne}{t}_{\ensuremath{\downarrow}}$, localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak ${t}_{\ensuremath{\uparrow}}\ensuremath{\ne}{t}_{\ensuremath{\downarrow}}$. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.

DOI
10.1103/physrevb.99.121110

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We study spin transport in a Hubbard chain with a strong, random, on-site potential and with spin-dependent hopping integrals t\ensuremathσ{t}_{\ensuremath{\sigma}}t\ensuremathσ​. For the SU(2) symmetric case t\ensuremath↑=t\ensuremath↓{t}_{\ensuremath{\uparrow}}={t}_{\ensuremath{\downarrow}}t\ensuremath↑​=t\ensuremath↓​, such a model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spin asymmetry, t\ensuremath↑\ensuremath≠t\ensuremath↓{t}_{\ensuremath{\uparrow}}\ensuremath{\ne}{t}_{\ensuremath{\downarrow}}t\ensuremath↑​\ensuremath=t\ensuremath↓​, localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak t\ensuremath↑\ensuremath≠t\ensuremath↓{t}_{\ensuremath{\uparrow}}\ensuremath{\ne}{t}_{\ensuremath{\downarrow}}t\ensuremath↑​\ensuremath=t\ensuremath↓​. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.
We derive and study an effective spin model that explains the anomalous spin dynamics in the one-dimensional Hubbard model with strong potential disorder. Assuming that charges are localized, we show that spins are delocalized and their subdiffusive transport originates from a singular random distribution of spin exchange interactions. The exponent relevant for the subdiffusion is determined by the Anderson localization length and the density of the electrons. Although the analytical derivations are valid for low particle density, numerical results for the full model reveal a qualitative agreement up to half filling.
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.
The ttt-model represents the Hubbard model in the limit U→∞U \to \inftyU→∞ and is one of the basic models of strongly correlated electrons. On a one-dimensional chain, the model is integrable, and the charge dynamics corresponds to that of free spinless fermions. However, the sequence of spins is frozen, leading to the Hilbert space fragmentation and nontrivial spin dynamics. We consider integrable and perturbed models with perturbations that break integrability while preserving fragmentation, and show that they exhibit various types of spin dynamics, from ballistic transport to anomalous diffusion in the integrable case, and from diffusion to subdiffusion in the perturbed case. Due to fragmentation, in all cases considered, spin transport is mediated by charge transport, with a particular magnetization dependence, most notably leading to subdiffusion in the grandcanonical average of the perturbed model, with a mechanism distinct from subdiffusion in disordered or dipole-conserving models.
Motivated by the recent experiments that reported signatures of many-body localization of ultracold atoms in optical lattices [M. Schreiber et al., Science 349, 842 (2015)], we study dynamics of highly excited states in the strongly disordered Hubbard model in one dimension. Owing to the SU(2)SU(2)SU(2) spin symmetry, spin degrees of freedom form a delocalized thermal bath with a narrow bandwidth. The spin bath mediates slow particle transport, eventually leading to delocalization of particles. The particle hopping rate is exponentially small in t/W(t,Wt/W\phantom{\rule{4pt}{0ex}}(t,Wt/W(t,W being hopping and disorder scales) owing to the narrow bandwidth of the spin bath. We find the optimal length scale for particle hopping and show that the particle transport rate depends strongly on the density of singly occupied sites in the initial state. The delocalization rate is zero for initial states with only doubly occupied or empty sites, suggesting that such states are truly many-body localized, and therefore the Hubbard model may host both localized and delocalized states. Full many-body localization can be induced by breaking spin rotational symmetry.
We study transport in the boundary-driven XX spin chain with onsite disorder and randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. We then present an exactly solvable semiclassical model of conductors and insulators, which exhibits both diffusive and subdiffusive phases, and qualitatively reproduces the results of the quantum system. The subdiffusion in these models is a consequence of rare insulating regions, and they therefore exhibit, in a more controlled setup, the physics of which have been conjectured to cause the subdiffusive transport observed in interacting many-body localizable systems. For the quantum model we show that finite-size effects come from the interplay of three characteristic lengths: one associated with disorder (the localization length), one with dephasing, and the third with the percolation problem defining large, rare, insulating regions. The latter grows logarithmically with system size, and we conjecture that this may be the reason why the heavy-tailed distributions typical of Griffiths effects have not been observed in subdiffusive interacting systems.
The t model represents the Hubbard model in the limit U →∞and is one of the basic models of stronglycorrelated electrons. On a one-dimensional chain, the model is integrable, and its charge dynamics is equivalentto that of free spinless fermions. However, within its dynamics the sequence of spins is frozen, implyingHilbert-space fragmentation and nontrivial spin dynamics. We focus primarily on perturbed versions of themodel in which the perturbations break integrability while preserving fragmentation. Considered examplesof such perturbations are spin-dependent hopping and additional spin interaction. We show that these modelsexhibit a variety of spin-transport regimes. In contrast to the integrable model, which displays either ballistictransport or dissipationless diffusion, the perturbed systems exhibit either normal diffusion or subdiffusion. Dueto Hilbert-space fragmentation, spin transport is mediated by charge transport in all cases considered. This leadsto a characteristic dependence on the magnetization, most notably resulting in subdiffusive spin transport in thegrand-canonical ensemble of the perturbed model. The underlying mechanism is distinct from the subdiffusionobserved in disordered systems or in models with dipole conservation.