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Physical review. B./Physical review. B

Suppressed energy transport in the strongly disordered Hubbard chain

Maciej Kozarzewski, Marcin Mierzejewski, Peter Prelovšek

Published Jun 28, 2019• 7 citations
Publisher

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.

DOI
10.1103/physrevb.99.241113

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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.
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 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.
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.
We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-Abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite-temperature spin autocorrelation function decays at long times as ${t}^{\ensuremath{-}\ensuremath{\beta}}$ with $\ensuremath{\beta}<0.5$, indicating subdiffusive transport at strong disorders.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.
The transport quantities of a classical spin chain with quenched disorder in antiferromagnetic coupling Ji{J}_{i}Ji​ are evaluated using a dynamical simulation at finite temperatures T>0T>0T>0. Since the classical model is nonintegrable, spin and thermal conductivities remain finite even in the pure case. On the other hand, the role of disorder becomes crucial at low TTT, leading to a vanishing transport due to Anderson localization within the linearized regime. The crossover from the insulator to the conductor appears both for spin and thermal transport at quite low ${T}^{*}\ensuremath{\ll}J$. Still the many-body localization regime at T>0T>0T>0 evidenced by extremely short mean free paths can be strongly enhanced by introducing into the model an additional staggered field.