Dynamics of the (spin-) Hall effect in topological insulators and graphene

A single two-dimensional Dirac cone with a mass gap produces a quantized (spin-) Hall step in the absence of magnetic field. What happens in strong electric fields? This question is investigated by analyzing time evolution and dynamics of the (spin-) Hall effect. After switching on a longitudinal electric field, a stationary Hall current is reached through damped oscillations. The Hall conductivity remains quantized as long as the electric field (E) is too weak to induce Landau-Zener transitions, but quantization breaks down for strong fields and the conductivity decreases as 1/sqrt{E}. These apply to the (spin-) Hall conductivity of graphene and the Hall and magnetoelectric response of topological insulators.Comment: 4 pages, 3 figure

Control of effective free energy landscape in a frustrated magnet by a field pulse

Thermal fluctuations can lift the degeneracy of a ground state manifold, producing a free energy landscape without accidentally degenerate minima. In a process known as order by disorder, a subset of states incorporating symmetry-breaking may be selected. Here, we show that such a free energy landscape can be controlled in a non-equilibrium setting as the slow motion within the ground state manifold is governed by the fast modes out of it. For the paradigmatic case of the classical pyrochlore XY antiferromagnet, we show that a uniform magnetic field pulse can excite these fast modes to generate a tunable effective free energy landscape with minima at thermodynamically unstable portions of the ground state manifold.Comment: 10 pages, 6 figures; minor revision

Out-of-time-ordered density correlators in Luttinger liquids

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behaviour combining robustly universal and non-universal features. The OTO commutators display temperature and initial state independent behaviour, and grow as $t^2$ for short times. For the short wavelength density operator, they reach a sizeable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. We benchmark our findings numerically on an interacting spinless fermion model in 1D, and find persistence of central features even in the non-integrable case. As a non-universal feature, the short time growth exhibits a distance dependent power.Comment: 6 pages, 2 figure

The fate of a discrete time crystal in an open system

Following the recent realisation that periodically driven quantum matter can support new types of spatiotemporal order, now known as discrete time crystals (DTCs), we consider the stability of this phenomenon. Motivated by its conceptual importance as well as its experimental relevance we consider the effect of coupling to an external environment. We use this to argue, both analytically and numerically, that the DTC in disordered one-dimensional systems is destroyed at long times by any such natural coupling. This holds true even in the case where the coupling is such that the system is prevented from heating up by an external thermal bath

Disordered flat bands on the kagome lattice

We study two models of correlated bond- and site-disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly flat ground state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the flat band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic groundstates in the presence of repulsive interactions, an example of disordered flat band ferromagnetism.Comment: 7+3 pages, 4+2 figures, accepted versio

The Coulomb potential V(r)=1/r and other radial problems on the Bethe lattice

We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of a generalized radial potential problem defined on the Bethe lattice to an infinite number of one dimensional problems that are easily accessible numerically. The latter method is particularly useful when the problem admits no analytical solution.Comment: 5 pages + reference

Non-equilibrium dynamics in Bose-Hubbard ladders

Motivated by a recent experiment on the non-equilibrium dynamics of interacting bosons in ladder-shaped optical lattices, we report exact calculations on the sweep dynamics of Bose-Hubbard systems in finite two-leg ladders. The sweep changes the energy bias between the legs linearly over a finite time. As in the experiment, we study the cases of [a] the bosons initially all in the lower-energy leg (ground state sweep) and [b] the bosons initially all in the higher-energy leg (inverse sweep). The approach to adiabaticity in the inverse sweep is intricate, as the transfer of bosons is non-monotonic as a function of both sweep time and intra-leg tunnel coupling. Our exact study provides explanations for these non-monotonicities based on features of the full spectrum, without appealing to concepts (e.g., gapless excitation spectrum) that are more appropriate for the thermodynamic limit. We also demonstrate and study Stueckelberg oscillations in the finite-size ladders.Comment: 8 pages, 10 figure

Persistence of the flat band in a kagome magnet with dipolar interactions

The weathervane modes of the classical Heisenberg antiferromagnet on the kagome lattice constitute possibly the earliest and certainly the most celebrated example of a flat band of zero-energy excitations. Such modes arise from the underconstraint that has since become a defining criterion of strong geometrical frustration. We investigate the fate of this flat band when dipolar interactions are added. These change the nearest-neighbour model fundamentally as they remove the Heisenberg spin-rotational symmetry while also introducing a long- range component to the interaction. We explain how the modes continue to remain approximately dispersionless, while being lifted to finite energy as well as being squeezed: they change their ellipticity described by the ratio of the amplitudes of the canonically conjugate variables comprising them. This phenomenon provides interesting connections between concepts such as constraint counting and self-screening underpinning the field of frustrated magnetism. We discuss variants of these phenomena for different interactions, lattices and dimension.Comment: 12 pages, 7 figure

Onset of Floquet Thermalisation

In presence of interactions, a closed, homogeneous (disorder-free) many-body system is believed to generically heat up to an `infinite temperature' ensemble when subjected to a periodic drive: in the spirit of the ergodicity hypothesis underpinning statistical mechanics, this happens as no energy or other conservation law prevents this. Here we present an interacting Ising chain driven by a field of time-dependent strength, where such heating onsets only below a threshold value of the drive amplitude, above which the system exhibits non-ergodic behaviour. The onset appears at {\it strong, but not fast} driving. This in particular puts it beyond the scope of high-frequency expansions. The onset location shifts, but it is robustly present, across wide variations of the model Hamiltonian such as driving frequency and protocol, as well as the initial state. The portion of nonergodic states in the Floquet spectrum, while thermodynamically subdominant, has a finite entropy. We find that the magnetisation as an {\it emergent} conserved quantity underpinning the freezing; indeed the freezing effect is readily observed, as initially magnetised states remain partially frozen {\it up to infinite time}. This result, which bears a family resemblance to the Kolmogorov-Arnold-Moser theorem for classical dynamical systems, could be a valuable ingredient for extending Floquet engineering to the interacting realm.Comment: 10 pages, including Supplemental Materia