The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour Heisenberg
chain, with temperature as tuning parameter. Our numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where we observe strong evidence either of spin super-diffusion or an extremely slow crossover to diffusion. This difference also governs the equilibration after a quench, and, remarkably, is apparent even at very high temperatures.
We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multi-chromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping from strong
ly interacting bosons to weakly interacting fermions, and provide exact numerical results for hard-core bosons in and out of equilibrium. In equilibrium, we find that the system behaves like a quasi-condensate (insulator) depending on whether the Fermi surface of the corresponding fermionic system lies in a spectral region where the single-particle states are delocalized (localized). We also study non-equilibrium expansion dynamics of initially trapped bosons, and demonstrate that the extent of partial localization is determined by the single-particle spectrum.
In the study of trapped two-component Bose gases, a widely used dynamical protocol is to start from the ground state of a one-component condensate and then switch half the atoms into another hyperfine state. The slightly different intra-component and
inter-component interactions can then lead to highly nontrivial dynamics. We study and classify the possible subsequent dynamics, over a wide variety of parameters spanned by the trap strength and by the inter- to intra-component interaction ratio. A stability analysis suited to the trapped situation provides us with a framework to explain the various types of dynamics in different regimes.
We study the interplay between magnetic frustration and itinerant electrons. For example, how does the coupling to mobile charges modify the properties of a spin liquid, and does the underlying frustration favor insulating or conducting states? Suppo
rted by Monte Carlo simulations, our goal is in particular to provide an analytical picture of the mechanisms involved. The models under considerations exhibit Coulomb phases in two and three dimensions, where the itinerant electrons are coupled to the localized spins via double exchange interactions. Because of the Hund coupling, magnetic loops naturally emerge from the Coulomb phase and serve as conducting channels for the mobile electrons, leading to doping-dependent rearrangements of the loop ensemble in order to minimize the electronic kinetic energy. At low electron density rho, the double exchange coupling mainly tends to segment the very long loops winding around the system into smaller ones while it gradually lifts the extensive degeneracy of the Coulomb phase with increasing rho. For higher doping, the results are strongly lattice dependent, displaying loop crystals with a given loop length for some specific values of rho, which can melt into another loop crystal by varying rho. Finally, we contrast this to the qualitatively different behavior of analogous models on kagome or triangular lattices.
We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regi
me of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a new direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements.
We present a new approach to obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall states from finite-size wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied,
we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary. This approach allows us to extract the topological entanglement entropy with an accuracy superior to what is possible on the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological information, the study of entanglement scaling is also useful as an indicator of the difficulty posed by fractional quantum Hall states for various numerical techniques.
For a Bose-Hubbard dimer, we study quenches of the site energy imbalance, taking a highly asymmetric Hamiltonian to a fully symmetric one. The ramp is carried out over a finite time that interpolates between the instantaneous and adiabatic limits. We
provide results for the excess energy of the final state compared to the ground state energy of the final Hamiltonian, as a function of the quench rate. This excess energy serves as the analog of the defect density that is considered in the Kibble-Zurek picture of ramps across phase transitions. We also examine the fate of quantum `self-trapping when the ramp is not instantaneous.
