From Floquet to Dicke: quantum spin-Hall insulator interacting with quantum light

Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter interaction on the edge state of a quantum spin-Hall insulator. A Dicke-type superradiant phase transition occurs at arbitrary weak coupling, the electronic spectrum acquires a finite gap and the resulting ground state manifold is topological with Chern number $\pm 1$. When the total number of excitations is conserved, a photocurrent is generated along the edge, being pseudo-quantized as $\omega\ln(1/\omega)$ in the low frequency limit, and decaying as $1/\omega$ for high frequencies with $\omega$ the photon frequency. The photon spectral function exhibits a clean Goldstone mode, a Higgs like collective mode at the optical gap and the polariton continuum.Comment: 5 pages, 3 figures, revised versio

Local Classical and Quantum Criticality due to Electron-Vibration Interaction

We study the local classical and quantum critical properties of electron-vibration interaction, represented by the Yu-Anderson model. It exhibits an instability, similar to the Wentzel-Bardeen singularity, whose nature resembles to weakly first order quantum phase transitions at low temperatures, and crosses over to Gaussian behaviour with increasing temperature. We determine the dominant energy scale separating the quantum from classical criticality, study the effect of dissipation and analyze its impact on correlation functions. Similar phenomenon should be observable in carbon nanotubes around local defects.Comment: 5 pages, 1 figure, 1 tabl

Escort distribution function of work done and diagonal entropies in quenched Luttinger liquids

We study the escort probability distribution function of work done during an interaction quantum quench of Luttinger liquids. It crosses over from the thermodynamic to the small system limit with increasing $a$, the order of the escort distribution, and depends on the universal combination $(|K_i-K_f|/(K_i+K_F))^a$ with $K_i$, $K_f$ the initial and final Luttinger liquid parameters, respectively. From its characteristic function, the diagonal R\'enyi entropies and the many body inverse participation ratio (IPR) are determined to evaluate the information content of the time evolved wavefunction in terms of the eigenstates of the final Hamiltonian. The hierarchy of overlaps is dominated by that of the ground states. The IPR exhibits a crossover from Gaussian to power law decay with increasing interaction quench parameter.Comment: 5 pages, 2 figures, positive comments are welcom

Thermodynamics and optical conductivity of unconventional spin density waves

We consider the possibility of formation of an unconventional spin density wave (USDW) in quasi-one dimensional electronic systems. In analogy with unconventional superconductivity, we develop a mean field theory of SDW allowing for the momentum dependent gap $\Delta({\bf k})$ on the Fermi surface. Conditions for the appearence of such a low temperature phase are investigated. The excitation spectrum and basic thermodynamic properties of the model are found to be very similar to those of d-wave superconductors in spite of the different topology of their Fermi surfaces. Several correlation functions are calculated, and the frequency dependent conductivity is evaluated for various gap functions. The latter is found to reflect the maximum gap value, however with no sharp onset for absorbtion.Comment: 13 pages, 11 figures, submitted to Phys. Rev.

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

Inelastic Scattering from Local Vibrational Modes

We study a nonuniversal contribution to the dephasing rate of conduction electrons due to local vibrational modes. The inelastic scattering rate is strongly influenced by multiphonon excitations, exhibiting oscillatory behaviour. For higher frequencies, it saturates to a finite, coupling dependent value. In the strong coupling limit, the phonon is almost completely softened, and the inelastic cross section reaches its maximal value. This represents a magnetic field insensitive contribution to the dephasing time in mesoscopic systems, in addition to magnetic impurities.Comment: 5 pages, 3 figure

Unusual spin dynamics in topological insulators

The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as $\omega^{d-1}$ with $d=2$ and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as $d=2K-1$ with $K$ the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems. These parallel with the optical conductivity of neutral graphene.Comment: 5 pages, 3 figure

Absence of orthogonality catastrophe after a spatially inhomogeneous interaction quench in Luttinger liquids

We investigate the Loschmidt echo, the overlap of the initial and final wavefunctions of Luttinger liquids after a spatially inhomogeneous interaction quench. In studying the Luttinger model, we obtain an analytic solution of the bosonic Bogoliubov-de Gennes equations after quenching the interactions within a finite spatial region. As opposed to the power law temporal decay following a potential quench, the interaction quench in the Luttinger model leads to a finite, hardly time dependent overlap, therefore no orthogonality catastrophe occurs. The steady state value of the Loschmidt echo after a sudden inhomogeneous quench is the square of the respective adiabatic overlaps. Our results are checked and validated numerically on the XXZ Heisenberg chain.Comment: 5 pages, 4 figures, published versio