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arXiv:2509.20498 · Physical review. B./Physical review. B

Quantum coherence in a maximally hot Hubbard chain

Anonymous, Ovidiu I. Pâţu, Balázs Dóra, Gergely Zaránd

Published Aug 27, 2026• 0 citations
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Abstract

We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle Green's function and analyze its dynamics across a broad range of interaction strengths. To complement the time-domain approach, we develop a high-resolution Chebyshev expansion method within the density matrix formalism, enabling direct access to spectral functions in the frequency domain. In the non-interacting limit, we derive exact analytical expressions for the Green's function, providing a benchmark for our numerical methods. As interactions are introduced, we observe a transition in the spectral function from a sharp peak at the free dispersion to a broadened two-band structure associated with hole and doublon excitations. These features are well captured by a Hubbard-I mean-field approximation, even at intermediate coupling. At infinite interaction strength ($U = \infty$), we exploit a determinant representation of the Green's function to access both real-time and spectral properties. In this regime, the system retains a sharp, cosine-like momentum dispersion in frequency space, while the dynamics display nontrivial light-cone spreading with sub-ballistic scaling. Our results demonstrate that strong correlations and nontrivial quantum coherence can persist even at infinite temperature.

DOI
10.1103/b8v1-f7zb

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We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle Green's function and analyze its dynamics across a broad range of interaction strengths. To complement the time-domain approach, we develop a high-resolution Chebyshev expansion method within the density matrix formalism, enabling direct access to spectral functions in the frequency domain. In the non-interacting limit, we derive exact analytical expressions for the Green's function, providing a benchmark for our numerical methods. As interactions are introduced, we observe a transition in the spectral function from a sharp peak at the free dispersion to a broadened two-band structure associated with hole and doublon excitations. These features are well captured by a Hubbard-I mean-field approximation, even at intermediate coupling. At infinite interaction strength (U=∞U = \inftyU=∞), we exploit a determinant representation of the Green's function to access both real-time and spectral properties. In this regime, the system retains a sharp, cosine-like momentum dispersion in frequency space, while the dynamics display nontrivial light-cone spreading with sub-ballistic scaling. Our results demonstrate that strong correlations and nontrivial quantum coherence can persist even at infinite temperature.
We investigate the spectral properties and the dynamics of doublons in the one-dimensional Hubbard model at infinite temperature. Using a Chebyshev expansion approach formulated in the superfermionic representation, we compute the momentum- and frequency-resolved doublon spectral function across a wide range of interaction strengths UUU and in the presence of an external electric field. Increasing the interaction, the spectrum gradually splits into separate bands associated with two-hole and two-particle excitations. Despite the presence of strong correlations, we find that doublons retain their coherence and undergo long-lived Bloch oscillations, as well as rich quantum walk dynamics characterized by light-cone spreadings at strong coupling, which we analyze through the time-and space-resolved Green's function.
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We study dynamical correlations of interacting hard-core anyons on a one-dimensional lattice at infinite temperature. This is a setting in which the many-body spectrum is independent of the statistical phase θ , while dynamical correlators remain sensitive to θ through nonlocal Jordan-Wigner strings. We compute single-particle Green's functions, spectral functions, and density-density correlators, thereby separating the effects of fractional statistics on one-body coherence from those on density transport in a maximally mixed ensemble. In the noninteracting case V = 0 , high-temperature averaging leads to inversion-symmetric Green's functions for all θ despite the presence of anyonic strings. Finite nearest-neighbor interactions V generate, however, a pronounced left-right asymmetry in the Green's functions for 0 < θ < π , with the strongest chirality appearing at intermediate couplings V ∼ J where interactions and hopping compete most effectively. In this regime, the Green's function decays exponentially in time with a statistical-angle-dependent decay rate. At strong coupling, the dynamics crosses over to an atomic-limit regime in which the dependence on θ is reduced. Here, the Green's function decays universally as t − 1 and the corresponding spectral function displays a three-band structure. In contrast, density-density correlations are insensitive to statistics and recover the known infinite-temperature transport regimes of the XXZ chain, including ballistic, superdiffusive, and diffusive behaviors. These results identify dynamical correlation functions as direct probes of fractional statistics in high-entropy quantum systems.
The dynamical correlations of a strongly correlated system are an essential ingredient to describe its nonequilibrium properties. We present a general method to calculate exactly the dynamical correlations of hard-core anyons in one-dimensional lattices, valid for any type of confining potential and any temperature. We obtain exact explicit expressions of the Green's function, the spectral function, and the out-of-time-ordered correlators (OTOCs). We find that the anyonic spectral function displays three main singularity lines which can be explained as a double spectrum in analogy to the Lieb-Liniger gas. The dispersion relations of these lines can be given explicitly and they cross at a hot point $({q}_{m},{\ensuremath{\omega}}_{m})$, which induces a peak in the momentum distribution function at qm{q}_{m}qm​ and a power-law singularity in the local spectral function at ${\ensuremath{\omega}}_{m}$. We also find that the anyonic statistics can induce spatial asymmetry in the Green's function, its spectrum, and the OTOC. Moreover, the information spreading characterized by the OTOCs shows light-cone dynamics, asymmetric for general statistics and low temperatures, but symmetric at infinite temperature. Our results pave the way toward studying the nonequilibrium dynamics of hard-core anyons and experimentally probing anyonic statistics through spectral functions.