Abstract In this work we investigate discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple function of the magnetization profile and which elegantly captures transport properties of the system. From this quantity we extract transport exponents, revealing behaviors across the phase diagram consistent with localized, diffusive, and - most interestingly for a disordered system - superdiffusive regimes. Investigation of this superdiffusive regime reveals the existence of a prethermal ''swappy'' regime unique to discrete-time systems in which excitations propagate coherently; even in the presence of strong disorder.
High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven systems, its fate in the complete absence of time-translation symmetry, particularly in interacting random quantum circuits, has remained unclear. Here we construct integrable random quantum circuits built from inhomogeneous XXZ R-matrices. Remarkably, integrability is preserved for arbitrary sequences of gate layers, ranging from quasiperiodic to fully random, thereby explicitly breaking both continuous and discrete time-translation symmetry. Using large-scale time-dependent density-matrix renormalization group simulations at infinite temperature and half filling, we map out the resulting spin-transport phase diagram and identify ballistic, superdiffusive, and diffusive regimes controlled by the spectral parameters of the R-matrices. The spatiotemporal structure of spin correlations within each regime depends sensitively on the inhomogeneity, exhibiting spatial asymmetry and sharp peak structures tied to near-degenerate quasiparticle velocities. To account for these findings, we develop a generalized hydrodynamics framework adapted to time-dependent integrable circuits, yielding Euler-scale predictions for correlation functions, Drude weights, and diffusion bounds. This approach identifies the quasiparticles governing transport and quantitatively captures both the scaling exponents and fine structures of the correlation profiles observed numerically. Our results demonstrate that exact Yang-Baxter integrability is compatible with stochastic quantum dynamics and establish generalized hydrodynamics as a predictive framework for transport in time-dependent integrable systems.
Symmetries strongly influence transport properties of quantum many-body systems and can lead to deviations from the generic case of diffusion. In this work, we study the impact of time-reversal symmetry breaking on the transport and its universal aspects in integrable chiral spin ladders. We observe that the infinite-temperature spin transport is superdiffusive with a dynamical critical exponent z = 3 / 2 matching the one of the Kardar-Parisi-Zhang (KPZ) universality class, which also lacks the time reversal symmetry. However, we find that fluctuations of the net magnetization transfer deviate from the KPZ predictions. Moreover, the full probability distribution of the associated spin current obeys fluctuation symmetry despite broken time-reversal and space-reflection symmetries. To further investigate the role of conserved quantities, we introduce an integrable quantum circuit that shares the essential symmetries with the chiral ladder and which exhibits analogous dynamical behavior in the absence of energy conservation. Our work shows that time-reversal symmetry breaking is compatible with superdiffusion but insufficient to stabilize the KPZ universality in integrable systems. This suggests that additional fundamental features are missing in order to identify the emergence of such dynamics in quantum matter.
We study discrete-time quantum walks with Fourier, Grover, and Hadamard coin operators on disordered square lattices, alongside classical random walks. Edges in the lattice are absent with a probability,
p. In this case, both classical and quantum walks exhibit an essentially identical degradation of transport. We then study a general version of this model, in which the existing edges are retained. However, the absent edges are no longer absent, but now become partially transmitting, with a transmission coefficient
f. We find that the response is now quite sensitive to the walk protocol and coin symmetry. The classical walk exhibits asymptotic stability of the anomalous diffusion exponent,
β(t). In comparison, quantum walks exhibit a monotonically decaying
β(t) beyond the initial transient regime, leading to the absence of quantum diffusion in two dimensions. We map the transport regimes in the
(f,p) plane and identify the contour for
β=1, which separates the subdiffusive and superdiffusive regimes. We also examine the effective diffusion coefficient, the inverse participation ratio, and the first two moments of edge transmission. We restrict ourselves to analyzing bulk propagation prior to finite-size boundary reflections. The results indicate that quantum transport depends significantly on coin-specific interference and cannot be fully described by transmission statistics alone.
We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\ensuremath{\alpha}$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a nonequilibrium steady-state charge transport, and (ii) time dynamics of an initially localized single-particle excitation in the absence of boundary reservoirs. In both variants, anomalous superdiffusive behavior is observed for $1<\ensuremath{\alpha}<1.5$, and for $\ensuremath{\alpha}>1.5$ the setup is effectively short ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behavior in open quantum systems.
Emergent hydrodynamics (EHD) bridges short-time unitarity with late-time thermodynamics, universal transport phenomena characterize the manner and speed of transport and thermalization. Typical non-integrable systems with few conserved local quantities are expected to be diffusive. In contrast, strongly disordered systems which admit phases such as many-body localization, are predicted to inhibit thermalization and thus slow dynamical transport. Disordered systems represent a uniquely poised platform to probe the quantum-to-classical transition and the emergence of irreversible thermodynamics from the underlying unitary structure. Here, we study a strongly disordered nuclear spin ensemble, using local measurements enabled by the disordered-state technique. We observe an apparent phase transition into a sub-diffusive regime, which we model as a random walk on the emergent fractal structure of a percolating network in the dipolar spin ensemble. Our novel theoretical model provides a framework for characterizing the emergence of thermalization in closed quantum systems, even in the presence of strong disorder.
We use ultracold atoms in a quasiperiodic lattice to study two outstanding problems in the physics of disordered systems: a) the anomalous diffusion of a wavepacket in the presence of disorder, interactions and noise; b) the transport of a disordered superfluid.a) Our results show that the subdiffusion, observed when interaction alone is present, can be modelled with a nonlinear diffusion equation and the peculiar shape of the expanding density profiles can be connected to the microscopic nonlinear diffusion coefficients.Also when noise alone is present we can describe the observed normal diffusion dynamics by existing microscopic models.In the unexplored regime in which noise and interaction are combined, instead, we observe an anomalous diffusion, that we model with a generalized diffusion equation, where noise-and interaction-induced contributions add each other.b) We find that an instability appearing at relatively large momenta can be employed to locate the fluid-insulator crossover driven by disorder.By investigating the momentum-dependent transport, we observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum.The set of critical disorder and interaction strengths for which such critical momentum vanishes, can be identified with the separation between a fluid regime and an insulating one and can be related to the predicted zero-temperature superfluid-Bose glass transition.