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arXiv:2609.04814

Spin-Charge Subordination in the Infinite-$U$ $SU(N)$ Hubbard Chain

Cătălin Paşcu Moca, Ovidiu I. Pâţu, Gergely Zaránd, Balázs Dóra

Published Sep 4, 2026• 0 citations
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Abstract

We obtain the exact full counting statistics of charge and flavor transport in the one-dimensional infinite-$U$ $SU(N)$ Hubbard model. The no-passing constraint freezes the ordered flavor sequence while the particle coordinates evolve as free spinless fermions. Consequently, charge transfer is governed by a free-fermion determinant, whereas flavor transfer is exactly subordinated to the number of particles crossing the observation cut. For an arbitrary traceless Cartan generator this yields an exact relation between the charge and flavor cumulants. The complete asymptotic flavor distribution is a universal non-Gaussian M-Wright law. Together, these results establish spin--charge subordination as a kinematic mechanism for anomalously slow internal-state transport in one-dimensional impenetrable quantum gases.

DOI
10.48550/arxiv.2609.04814

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We obtain the exact full counting statistics of charge and flavor transport in the one-dimensional infinite-UUU SU(N)SU(N)SU(N) Hubbard model. The no-passing constraint freezes the ordered flavor sequence while the particle coordinates evolve as free spinless fermions. Consequently, charge transfer is governed by a free-fermion determinant, whereas flavor transfer is exactly subordinated to the number of particles crossing the observation cut. For an arbitrary traceless Cartan generator this yields an exact relation between the charge and flavor cumulants. The complete asymptotic flavor distribution is a universal non-Gaussian M-Wright law. Together, these results establish spin--charge subordination as a kinematic mechanism for anomalously slow internal-state transport in one-dimensional impenetrable quantum gases.
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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 SU(N)\mathrm{SU}(N)SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.
We study quantum quench dynamics in the Fermi-Hubbard model, and its SU(N)\mathrm{SU}(N)SU(N) generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized N\'eel order, namely, initial states in which there is a periodic NNN-spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) N\'eel domain walls. Those correlations resemble the ones in the ground state of the SU(N)\mathrm{SU}(N)SU(N) model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting SU(N)\mathrm{SU}(N)SU(N) gas into the rapidity distribution after long times. Finally, we study equilibration in SU(N)\mathrm{SU}(N)SU(N) gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated SU(N)\mathrm{SU}(N)SU(N) fermions at large UUU.
We introduce a numerical tensor-network method to compute the statistics of the charge transferred across an interface partitioning an interacting one-dimensional many-body lattice system with U(1)U(1)U(1) symmetry. Our approach is based on a matrix-product state representation of the process tensor (also known as influence functional or influence matrix) describing the effect of the bulk system on the degrees of freedom at the interface, allowing us to evaluate a multi-time correlation function that yields the moment-generating function of charge transfer. We develop a scheme to truncate non-Markovian correlations which preserves the proper normalization of the process tensor and ensures the correct physical properties of the generating function. We benchmark our approach by simulating magnetization transport within the Heisenberg spin-1/21/21/2 XXZ brickwork circuit model at infinite temperature. Our results recover the correct transport exponent describing ballistic, superdiffusive, and diffusive transport in different regimes of the model. We also demonstrate anomalous transport encoded by a self-similar scaling form of the moment-generating function outside of the ballistic regime. In particular, we confirm the breakdown of Kardar-Parisi-Zhang universality in higher-order transport cumulants at the isotropic point. Our work paves the way for process-tensor descriptions of non-Markovian open quantum systems to address current fluctuations in strongly interacting systems far from equilibrium.
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.