Emergent dipole moment conservation and subdiffusion in tilted chains

We study the transport dynamics of an interacting tilted (Stark) chain. We show that the crossover between diffusive and subdiffusive dynamics is governed by $F\sqrt{L}$, where $F$ is the strength of the field, and $L$ is the wave-length of the excitation. While the subdiffusive dynamics persist for large fields, the corresponding transport coefficient is exponentially suppressed with $F$ so that the finite-time dynamics appear almost frozen. We explain the crossover scale between the diffusive and subdiffusive transport by bounding the dynamics of the dipole moment for arbitrary initial state. We also prove its emergent conservation at infinite temperature. Consequently, the studied chain is one of the simplest experimentally realizable models for which numerical data are consistent with the hydrodynamics of fractons.Comment: 8 pages, 4 figures (including Supplementary Material). Changes in the second version: The typo of the first version in the arrow directions of Fig. 1 panel (b) and Fig. S1 (upper panel) is correcte

Spin diffusion in perturbed isotropic Heisenberg spin chain

The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization $m\ne0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\cal D}_0(\Delta)$ on the spin anisotropy $\Delta$, with a pronounced maximum at $\Delta =1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\Delta=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.Comment: 5+5 pages, 4+5 figure

Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach

In the last two decades non-equilibrium spectroscopies have evolved from avant-garde studies to crucial tools for expanding our understanding of the physics of strongly correlated materials. The possibility of obtaining simultaneously spectroscopic and temporal information has led to insights that are complementary to (and in several cases beyond) those attainable by studying the matter at equilibrium. From this perspective, multiple phase transitions and new orders arising from competing interactions are benchmark examples where the interplay among electrons, lattice and spin dynamics can be disentangled because of the different timescales that characterize the recovery of the initial ground state. For example, the nature of the broken-symmetry phases and of the bosonic excitations that mediate the electronic interactions, eventually leading to superconductivity or other exotic states, can be revealed by observing the sub-picosecond dynamics of impulsively excited states. Furthermore, recent experimental and theoretical developments have made it possible to monitor the time-evolution of both the single-particle and collective excitations under extreme conditions, such as those arising from strong and selective photo-stimulation. These developments are opening the way for new, non-equilibrium phenomena that can eventually be induced and manipulated by short laser pulses. Here, we review the most recent achievements in the experimental and theoretical studies of the non-equilibrium electronic, optical, structural and magnetic properties of correlated materials. The focus will be mainly on the prototypical case of correlated oxides that exhibit unconventional superconductivity or other exotic phases. The discussion will also extend to other topical systems, such as iron-based and organic superconductors, (Formula presented.) and charge-transfer insulators. With this review, the dramatically growing demand for novel experimental tools and theoretical methods, models and concepts, will clearly emerge. In particular, the necessity of extending the actual experimental capabilities and the numerical and analytic tools to microscopically treat the non-equilibrium phenomena beyond the simple phenomenological approaches represents one of the most challenging new frontiers in physics