Topological electrostatics

We present a theory of optimal topological textures in nonlinear sigma-models with degrees of freedom living in the GrassmannianGr(M,N)manifold. These textures describe skyrmion lattices ofN-component fermions in a quantising magnetic field, relevant to the physics of graphene, bilayer and other multicomponent quantum Hall systems near integer filling factorsν > 1. We derive analytically the optimality condition, minimizing topological charge density fluctuations, for a general Grassmannian sigma modelGr(M,N)on a sphere and a torus, together with counting arguments which show that for any filling factor and number of components there is a critical value of topological chargedcabove which there are no optimal textures. Belowdca solution of the optimality condition on a torus is unique, while in the case of a sphere one has, in general, a continuum of solutions corresponding to new non-Goldstone zero modes, whose degeneracy is not lifted (via a order from disorder mechanism) by any fermion interactions depending only on the distance on a sphere. We supplement our general theoretical considerations with the exact analytical results for the case ofGr(2,4), appropriate for recent experiments in graphene.

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.

Disorder-Free Localization

The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

Raman scattering signatures of Kitaev spin liquids in A(2)IrO(3) iridates with A=Na or Li

We show how Raman spectroscopy can serve as a valuable tool for diagnosing quantum spin liquids (QSL). We find that the Raman response of the gapless QSL of the Kitaev-Heisenberg model exhibits signatures of spin fractionalization into Majorana fermions, which give rise to a broad signal reflecting their density of states, and Z(2) gauge fluxes, which also contribute a sharp feature. We discuss the current experimental situation and explore more generally the effect of breaking the integrability on response functions of Kitaev spin liquids.

Multicomponent Skyrmion lattices and their excitations

We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrized by a d-component spinor field. In the absence of anisotropies we find a hexagonal Skyrmion lattice that completely breaks the underlying SU(d) symmetry with the low-lying excitation spectrum separating into d(2) - 1 gapless acoustic magnetic modes and a magnetophonon. The ground state charge density modulations, which inevitably exist in these lattices, vanish exponentially in d. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant to experiments with AlAs quantum wells. Here we find a transition which breaks a sixfold rotational symmetry of the triangular lattice, followed by the formation of a square lattice at large values of anisotropy strength.

Relaxation in driven integer quantum Hall edge states

A highly nonthermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al., Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations.

Anomalous tunneling of phonon excitations between two Bose-Einstein condensates

We discuss the tunneling of phonon excitations across a potential barrier separating two condensates. It is shown that a strong barrier proves to be transparent for the excitations at low energy epsilon. Moreover, the transmission is reduced with increasing epsilon in contrast to the standard dependence. This anomalous behavior is due to the existence of a quasiresonance interaction. The origin of this interaction is a result of the formation of a special well determined by the density distribution of the condensate in the vicinity of a high barrier.