D. L. Kovrizhin

Dynamics of a Two-Dimensional Quantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes

We provide a complete and exact theoretical study of the dynamical structure factor of a twodimensional quantum spin liquid in gapless and gapped phases, as realized in Kitaev’s honeycomb model. We show that there are direct signatures—qualitative and quantitative—of the Majorana fermions and gauge fluxes emerging in this model. These include counterintuitive manifestations of quantum number fractionalization, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalization of electron spin. Our analysis identifies new varieties of the venerable x-ray edge problem and explores connections to the physics of quantum quenches.

Fermionic response from fractionalization in an insulating two-dimensional magnet

An intriguing state of matter known as a quantum spin liquid has been predicted to host Majorana fermions. A detailed theoretical and numerical analysis re-interprets existing Raman data for α-RuCl3 and uncovers direct evidence of a fermionic response.

Friction and Diffusion of Matter-Wave Bright Solitons

We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless; however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter-wave bright soliton immersed in a thermal cloud.

Density wave and supersolid phases of correlated bosons in an optical lattice

Motivated by the recent experiment on the Bose-Einstein condensation of 52Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground-state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, i.e., the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them.

Dynamics of fractionalization in quantum spin liquids

We present the theory of dynamical spin response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin fractionalization into emergent quasiparticles: Majorana fermions and fluxes of Z2 gauge field. In addition to a broad continuum from spin fractionalization, we find sharp (δ-function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions, and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase.

Equilibration of integer quantum Hall edge states

We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial non-equilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: its properties depend on the full functional form of the initial electron distribution, and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an over-estimate or an under-estimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor \nu=1 we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor \nu=2 we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at \nu=2 from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.

“Cherenkov radiation” of a sound in a Bose condensed gas

Abstract In terms of linearized Gross–Pitaevskii equation we have studied the process of sound emission arises from a supersonic particle motion in a Bose condensed gas. By analogy with the method used for description of Vavilov–Cherenkov phenomenon, we have found a friction work created by the particle generated condensate polarization. For comparison we have found radiation intensity of excitations. Both methods gives the same result.

Exact form of the Bogoliubov excitations in one-dimensional nonlinear Schrödinger equation

Abstract In this Letter we present the exact solutions of one-dimensional nonlinear Schrodinger equation. The solutions correspond to the Bogoliubov excitations in Bose-gas with a local interaction. The obtained expression is used for evaluating the transmission coefficient of the excitations across a δ -functional potential barrier.

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.

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.