Publications (138)392.71 Total impact
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ABSTRACT: Timeperiodic 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 lightmatter interaction on the edge state of a quantum spin Hall insulator. A Dicketype superradiant phase transition occurs at arbitrary weak coupling, the electronic spectrum acquires a finite gap, and the resulting groundstate manifold is topological with a Chern number of ±1. When the total number of excitations is conserved, a photocurrent is generated along the edge, being pseudoquantized as ωln(1/ω) in the lowfrequency limit and decaying as 1/ω for high frequencies with ω the photon frequency. The photon spectral function exhibits a clean Goldstone mode, a Higgslike collective mode at the optical gap and the polariton continuum.  [Show abstract] [Hide abstract]
ABSTRACT: Luttinger liquids (LLs) are one dimensional systems with wellunderstood instabilities due to umklapp or backscattering. We study a generalization of the Luttinger model, which incorporates a time reversal symmetry breaking interaction producing a complex forward scattering amplitude ($g_2$ process). The resulting low energy state is still a LL, and belongs to the family of interacting SchulzShastry models. Remarkably, it becomes increasingly robust against additional perturbations  for purely imaginary $g_2$, both umklapp and local backscattering are always irrelevant. Changing the phase of the interaction generates a nontrivial Berry phase, with a universal geometric phase difference between ground and a one boson excited state depending only on the LL parameter.  [Show abstract] [Hide abstract]
ABSTRACT: By combining the Baeriswyl wavefunction with equilibrium and timedependent variational principles, we develop a nonequilibrium formalism to study quantum quenches for two dimensional spinless fermions with nearestneighbour hopping and repulsion. The variational ground state energy and the short time dynamics agree convincingly with the results of numerically exact simulations. We find that depending on the initial and final interaction strength, the quenched system either exhibits undamped oscillations or relaxes to a time independent steady state. The time averaged expectation value of the CDW order parameter rises sharply when crossing from the steady state regime to the oscillating regime, indicating that the system, being nonintegrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively.  [Show abstract] [Hide abstract]
ABSTRACT: The nonequilibrium dynamics beyond linear response of Weyl semimetals is studied after a sudden switching on of a DC electric field. The resulting current is a nonmonotonic function of time, with an initial quick increase of polarization current followed by a powerlaw decay. Particlehole creation \`a la Schwinger dominates for long times when the conduction current takes over the leading role, with the total current increasing again. The conductivity estimated from a dynamical calculation within a Drude picture agrees with the one obtained from Kubo's formula. The full distribution function of electronhole pairs changes from Poissonian for short perturbations to a Gaussian in the long perturbation (LandauZener) regime. The vacuum persistence probability of high energy physics manifests itself in a finite probability of no pair creation and no induced current at all times.  [Show abstract] [Hide abstract]
ABSTRACT: Timeperiodic 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 lightmatter interaction on the edge state of a quantum spinHall insulator. A Dicketype superradiant phase transition occurs at arbitrary weak coupling, and 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 pseudoquantized 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.  [Show abstract] [Hide abstract]
ABSTRACT: 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 nonLorentzian 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 $\omega^{d1}$ with $d=2$ and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as $d=2K1$ with $K$ the Luttingerliquid 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.  [Show abstract] [Hide abstract]
ABSTRACT: 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 Bogoliubovde 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.  [Show abstract] [Hide abstract]
ABSTRACT: Dynamical phase transitions (DPT) are characterized by nonanalytical time evolution of the dynamical free energy. For general 2band systems in one and two dimensions (eg. SSH model, Kitaevchain, Haldane model, p+ip superconductor, etc.), we show that the time evolution of the dynamical free energy is crucially affected by the ground state topology of both the initial and final Hamiltonians, implying DPTs when the topology is changed under the quench. Similarly to edge states in topological insulators, DPTs can be classified as being topologically protected or not. In 1D systems the number of topologically protected nonequilibrium time scales are determined by the difference between the initial and final winding numbers, while in 2D no such relation exists for the Chern numbers. The singularities of dynamical free energy in the 2D case are qualitatively different from those of the 1D case, the cusps appear only in the first time derivative. 
Article: Escort distribution function of work done and diagonal entropies in quenched Luttinger liquids
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ABSTRACT: 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 $(K_iK_f/(K_i+K_F))^a$ 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.  [Show abstract] [Hide abstract]
ABSTRACT: Topological excitations keep fascinating physicists since many decades. While individual vortices and solitons emerge and have been observed in many areas of physics, their most intriguing higher dimensional topological relatives, skyrmions (smooth, topologically stable textures) and magnetic monopoles  emerging almost necessarily in any grand unified theory and responsible for charge quantization  remained mostly elusive. Here we propose that loading a threecomponent nematic superfluid such as $^{23}$Na into a deep optical lattice and thereby creating an insulating core, one can create topologically stable skyrmion textures and investigate their properties in detail. We show furthermore that the spectrum of the excitations of the superfluid and their quantum numbers change dramatically in the presence of the skyrmion, and they reflect the presence of a trapped monopole, as imposed by the skyrmion's topology.  [Show abstract] [Hide abstract]
ABSTRACT: A (single flavor) quadratic band crossing in two dimensions is known to have a generic instability towards a quantum anomalous Hall (QAH) ground state for infinitesimal repulsive interactions. Here we introduce a generalization of a quadratic band crossing which is protected only by rotational symmetry. By focusing on the representative case of a parabolic and flat band touching, which also allows for a straightforward lattice realization, the interaction induced nematic phase is found generally to compete successfully with the QAH insulator, and to become the dominant instability in certain parts of the phase diagram already at weak coupling. The full phase diagram of the model, together with its topological properties, is mapped out using a perturbative renormalization group, strong coupling analysis, the meanfield theory. Interestingly, the Berry flux varies continuously in the single flavour limit with various control parameters.  [Show abstract] [Hide abstract]
ABSTRACT: Dynamical phase transitions (DPT) occur after quenching some global parameters in quantum systems and are signalled by the nonanalytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between the initial and time evolved states. In a recent letter (M. Heyl et al., Phys. Rev. Lett. \textbf{110}, 135704 (2013)), it was suggested that DPTs are closely related to equilibrium phase transitions (EPT) for the transverse field Ising model. By studying a minimal model, the XY chain in transverse magnetic field, we show analytically that this connection does not hold generally. We present examples where DPT occurs without crossing any equilibrium critical lines by the quench, and a nontrivial example with no DPT but crossing a critical line by the quench. Albeit the nonanalyticities of the dynamical free energy on the real time axis do not indicate the presence or absence of an EPT, the structure of Fisherlines for complex times reveal a qualitative difference.  [Show abstract] [Hide abstract]
ABSTRACT: Spintronics is an emerging paradigm with the aim to replace conventional electronics by using electron spins as information carriers. Its utility relies on the magnitude of the spinrelaxation, which is dominated by spinorbit coupling (SOC). Yet, SOC induced spinrelaxation in metals and semiconductors is discussed for the seemingly orthogonal cases when inversion symmetry is retained or broken by the socalled ElliottYafet and D'yakonovPerel' spinrelaxation mechanisms, respectively. We unify the two theories on general grounds for a generic twoband system containing intra and interband SOC. While the previously known limiting cases are recovered, we also identify parameter domains when a crossover occurs between them, i.e. when an inversion symmetry broken state evolves from a D'yakonovPerel' to an ElliottYafet type of spinrelaxation and conversely for a state with inversional symmetry. This provides an ultimate link between the two mechanisms of spinrelaxation.  [Show abstract] [Hide abstract]
ABSTRACT: We study the nonequilibrium dynamics of the Luttinger model after a quantum quench, when the initial state is a finite temperature thermal equilibrium state. The diagonal elements of the density matrix in the steady state show thermal features for high temperature initial states only, otherwise retain highly nonthermal character. The time evolution of Uhlmann fidelity, which measures the distance between the time evolved and initial states, is evaluated for arbitrary initial temperatures and quench protocols. In the long time limit, the overlap between the time evolved and initial system decreases exponentially with the temperature with a universal prefactor. Within perturbation theory, the statistics of final total energy and work are numerically evaluated in the case of a sudden quench, which yield identical distributions at zero temperature. In both statistics, temperature effects are more significant in small systems. The Diracdelta peak at the adiabatic ground state energy remains present in the probability distribution of the total energy, but disappears from the work distribution at nonzero initial temperatures. 
Article: Loschmidt Echo and the ManyBody Orthogonality Catastrophe in a QubitCoupled Luttinger Liquid
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ABSTRACT: We investigate the manybody generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bangbang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrixproduct state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry.  [Show abstract] [Hide abstract]
ABSTRACT: The persistent current in strictly onedimensional Dirac systems is investigated within two different models, defined in the continuum and on a lattice, respectively. The object of the study is the effect of a single magnetic or nonmagnetic impurity in the two systems. In the continuum Dirac model, an analytical expression for the persistent current flowing along a ring with a single deltalike magnetic impurity is obtained after regularization of the unbounded negative energy states. The predicted decay of the persistent agrees with the lattice simulations. The results are generalized to finite temperatures. To realize a single Dirac massless fermion, the lattice model breaks the timereversal symmetry, and, in contrast with the continuum model, a pointlike nonmagnetic impurity can lead to a decay in the persistent current.  [Show abstract] [Hide abstract]
ABSTRACT: The manipulation and movement of Dirac points in the Brillouin zone by the electronelectron interaction is considered within leading order perturbation theory. At the merging point, an infinitesimal interaction is shown to cause opening of the gap or splitting of the Dirac points, depending on the inter or intrasublattice nature of the merging and the sign of the interaction. The topology of the spectrum can therefore be efficiently changed by simply tuning the interaction between particles, as opposed to the usual careful band structure engineering. This is illustrated around the merging transition of one, two, and three dimensional DiracWeyl fermions. A simple Weyllike Hamiltonian that describes the quadratic bandcrossing in three dimensions is also proposed, and its stability under interactions is addressed. 
Article: Diverging dc conductivity due to a flat band in disordered pseudospin1 DiracWeyl fermions
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ABSTRACT: Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin1 DiracWeyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hubsite does not reveal the presence of the flat band, the sublattice resolved DOS on the noncentral sites exhibits a narrow peak with height ~ 1/\sqrt{g} with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as ln(1/g) with decreasing disorder due to interband transitions around the band touching point between the propagating and the flat band. Generalizations to higher pseudospin are given. 
Article: Floquet topological insulators
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ABSTRACT: Topological insulators represent unique phases of matter with insulating bulk and conducting edge or surface states, immune to small perturbations such as backscattering due to disorder. This stems from their peculiar band structure, which provides topological protections. While conventional tools (pressure, doping etc.) to modify the band structure are available, time periodic perturbations can provide tunability by adding time as an extra dimension enhanced to the problem. In this short review, we outline the recent research on topological insulators in non equilibrium situations. Firstly, we introduce briefly the Floquet formalism that allows to describe steady states of the electronic system with an effective timeindependent Hamiltonian. Secondly, we summarize recent theoretical work on how light irradiation drives semimetallic graphene or a trivial semiconducting system into a topological phase. Finally, we show how photons can be used to probe topological edge or surface states.  [Show abstract] [Hide abstract]
ABSTRACT: We study variablerate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest neighbour interaction for hardcore bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spinflip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system timeevolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and muchneeded test of Luttinger liquid theory in a nonequilibrium situation.
Publication Stats
1k  Citations  
392.71  Total Impact Points  
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Institutions

20002015

Budapest University of Technology and Economics
 Department of Physics
Budapeŝto, Budapest, Hungary


20082012

Hungarian Academy of Sciences
Budapeŝto, Budapest, Hungary 
Max Planck Institute of Physics
München, Bavaria, Germany


20062009

Max Planck Institute for Dynamics of Complex Technical Systems
Magdeburg, SaxonyAnhalt, Germany


2004

Abdus Salam International Centre for Theoretical Physics
Trst, Friuli Venezia Giulia, Italy
