Kazuya Fujimoto

Fluctuations of integrated currents have attracted considerable interest over the past decades in the context of statistical mechanics. Recently, anomalous current fluctuations, characterized by the M-Wright function, were obtained exactly in a classical automaton [\ifmmode \check{Z}\else \v{Z}\fi{}. Krajnik et al., Phys. Rev. Lett. 128, 160601 (2022)], and previous studies have shown that this anomalous behavior can arise in a variety of classical systems. Despite the rapidly growing interest in such anomalous behaviors, which capture a universal aspect of one-dimensional many-body transport, the exact derivation of the M-Wright function in quantum many-body systems has remained elusive. In this Letter, we present the first exact microscopic derivation of the M-Wright function in quantum many-body dynamics by analyzing the integrated spin current in a one-dimensional Fermi-Hubbard model with infinitely strong repulsive interactions. Our results lay the groundwork for exploring anomalous integrated currents in a broad class of quantum many-body systems.

We present an exact integral formula for the multi-particle propagator of the one-dimensional Fermi–Hubbard model on an infinite lattice. The proof is based on the nested Bethe ansatz without relying on the string hypothesis. Our formula enables an explicit integral representation of the time evolution of arbitrary finite-particle wave functions and thereby provides a foundation for the exact analysis of nonequilibrium dynamics in the Hubbard model. It can further be applied to related open quantum models.

We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii (GP) model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes Π ϵ ( k ) and Π N ( k ) , we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade’s momentum distribution amplitude n 0 and the energy flux ε in the steady state. We find that in our regime of “mixed” turbulence—where both vortices and waves play a significant role— n 0 ∝ ε 0.67 ( 2 ) , a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states.

We theoretically study quantum spin transport in a one-dimensional folded XXZ model with an alternating domain-wall initial state via the Bethe ansatz technique, exactly demonstrating that a probability distribution of finding a leftmost up spin with an appropriate scaling variable converges to the Tracy-Widom distribution for the Gaussian unitary ensemble (GUE), which is a universal distribution for the largest eigenvalue of GUE under a soft-edge scaling limit. Our finding presented here offers a first exact derivation of the GUE Tracy-Widom distribution in the dynamics of the interacting quantum model not being mapped to noninteracting fermions via the Jordan-Wigner transformation. On the basis of the exact solution of the folded XXZ model and our numerical analysis of the XXZ model, we discuss a universal behavior for the probability of finding the leftmost up spin in the XXZ model.

Emergence of hydrodynamics in quantum many-body systems has recently garnered growing interest. The recent experiment of ultracold atoms [J. F. Wienand et al., Nat. Phys. 20, 1732 (2024)NPAHAX1745-247310.1038/s41567-024-02611-z] studied emergent hydrodynamics in hard-core bosons using a bipartite fluctuation, which quantifies how the particle number fluctuates in a subsystem. In this Letter, we theoretically study the variance of a bipartite fluctuation in one-dimensional noninteracting fermionic dynamics starting from an alternating state, deriving the exact solution of the variance and its asymptotic linear growth law for the long-time dynamics. To compare the theoretical prediction with the experiment, we generalize our exact solution by incorporating the incompleteness of the initial alternating state, deriving the general linear growth law analytically. We find that it shows good agreement with the experimentally observed variance growth without any fitting parameters. Furthermore, we estimate a timescale for the local equilibration using our exact solution, finding that the timescale is independent of the initial incompleteness. To investigate the interaction effect, we implement numerical studies for the variance growth in interacting fermions, which has yet to be explored experimentally. As a result, we find that the presence of interactions breaks the linear variance growth derived in the noninteracting fermions. Our exact solutions and numerical findings here lay a foundation for growing bipartite fluctuations in quantum many-body dynamics.

We theoretically study propagating correlation fronts in noninteracting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime, all the moments of dynamical fluctuations around the correlation fronts are described by the universal correlation functions of Gaussian orthogonal and symplectic random matrices at the soft edge. Our finding here sheds light on a hitherto unknown connection between random matrix theory and correlation propagation in quantum dynamics.

Recent theoretical and experimental works have explored universal dynamics related to surface growth physics in isolated quantum systems. In this Letter, we theoretically elucidate that dissipation drastically alters universal particle-number-fluctuation dynamics associated with surface-roughness growth in one-dimensional free fermions and bosons. In a system under dephasing that causes loss of spatial coherence, we numerically find that a universality class of surface-roughness dynamics changes from the ballistic class to a class with the Edwards-Wilkinson scaling exponents and an unconventional scaling function. We provide the analytical derivation of the diffusion equation from the dephasing Lindblad equation via a renormalization-group technique and succeed in explaining the drastic change. Furthermore, we numerically find the same change of the universality class under a more nontrivial dissipation, i.e., symmetric incoherent hopping.

Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically study dynamics of fermions on disordered one-dimensional potentials exhibiting localization and find dynamical one-parameter scaling for surface roughness, which represents particle-number fluctuations at a given length scale, and for entanglement entropy when the system is in delocalized phases. This dynamical scaling corresponds to the Family-Vicsek scaling originally developed in classical surface growth, and the associated scaling exponents depend on the type of disorder. Notably, we find that partially localized states in the delocalized phase of the random-dimer model lead to anomalous scaling, where destructive interference unique to quantum systems leads to exponents unknown for classical systems and clean systems.