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Spin subdiffusion in perturbed infinite-? Hubbard chain

J. Rękas, Marcin Mierzejewski, Zala Lenarčič, Peter Prelovšek

Published Sep 16, 2026• 0 citations
OpenAlex

Abstract

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.

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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.
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 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.
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 $t\text{\ensuremath{-}}V$ disordered spinless fermionic chain in the strong-coupling regime, $t/V\ensuremath{\rightarrow}0$. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: blocks with only one mover and ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show a many-body localized (MBL) transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe subdiffusive dynamics at finite timescales and find indications that this might be only a transient behavior before crossing over to diffusion.
In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ\mathit{XXZ}XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ\mathit{XXZ}XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.
We study Family-Vicsek scaling of charge, spin, and energy fluctuations in the one-dimensional Hubbard model at infinite temperature. Using a quantum generating function approach, we compute time-dependent cumulants of transferred conserved quantities and analyze how the corresponding roughness depends on subsystem size and time. We start by focusing on a single interface at half the chain and determine the transport exponents. Then we turn to fluctuations of a small finite interval and study the Family-Vicsek universality of fluctuations over an extended timescale. We find that the long-time scaling behavior is controlled by integrability. In the free limit, charge, spin, and energy all display ballistic transport. In the interacting integrable Hubbard chain, charge and spin cross over to a KPZ scaling regime, while the energy sector remains ballistic. Once integrability is broken by a next-nearest-neighbor density interaction, the long-time dynamics becomes diffusive in all sectors. In every case we also observe a short-time microscopic regime with apparently universal ballistic growth before the hydrodynamic scaling window sets in. The Family-Vicsek setup allows us to determine the growth, the saturation as well as the dynamical exponents.