arXiv subjects

Gergely Zaránd

Publications and source records attributed to Gergely Zaránd.

At least 55 records · Page 3Linked to original sources

arXiv2019

Magnetic degeneracy points in interacting two-spin systems: geometrical patterns, topological charge distributions, and their stability

Spectral degeneracies of quantum magnets are often described as diabolical points or magnetic Weyl points, which carry topological charge. Here, we study a simple, yet experimentally relevant quantum magnet: two localized interacting electrons subject to spin-orbit coupling. In this setting, the degeneracies are not necessarily isolated points, but can also form a line or a surface. We identify ten different possible geometrical patterns formed by these degeneracy points, and study their stability under small perturbations of the Hamiltonian. Stable structures are found to depend on the relative sign of the determinants of the two $g$-tensors, $\cal S$. Both for ${\cal S}=+1$ and ${\cal S}=-1$, two stable configurations are found, and three out of these four configurations are formed by pairs of Weyl points. These stable regions are separated by a surface of almost stable configurations, with a structure akin to co-dimension one bifurcations.

cond-mat.mes-hall↗

arXiv2019

Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench

We use a semiclassical approach to study out of equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space and time dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a `second front' that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of non-trivial scattering processes in the $O(3)$ non-linear sigma model by performing Monte Carlo simulations, and observe local equilibration around the second front in terms of the densities of the particle species.

cond-mat.stat-mech↗

arXiv2019

Hybrid semiclassical theory of quantum quenches in one dimensional systems

We develop a hybrid semiclassical method to study the time evolution of one dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time evolving block decimation method, while treating orbital quasiparticle motion classically. We can follow dynamics up to timescales well beyond the reach of standard numerical methods to observe the crossover between pre-equilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel coupled one dimensional Bose condensates. We demonstrate the emergence of soliton-collision induced phase propagation, soliton-entropy production and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.

cond-mat.stat-mech↗

arXiv2019

Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory

We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum mechanically. We analyze the non-equilibrium time evolution of the distribution of the total spin in half of the system and compare the predictions of the semi-semiclassical theory with those of a non-Abelian time evolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry. We show that while the standard semiclassical approach using the universal low energy scattering matrix cannot describe the dynamics, the hybrid semiclassical method based on the full scattering matrix gives excellent agreement with the first principles TEBD simulation.

cond-mat.stat-mech↗

arXiv2018

Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals

We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and reveals the crossover between the orthogonal and unitary critical states in weak random magnetic fields. The flow of the QGT near the critical points determines the critical exponents. Critical distributions of the QGT are universal and exhibit a remarkable isotropy even in a homogeneous magnetic field. We predict universal and isotropic Hall conductance fluctuations at the metal-insulator transition in an external magnetic field.

cond-mat.dis-nn↗

arXiv2018

Observation of spin-orbit coupling induced Weyl points and topologically protected Kondo effect in a two-electron double quantum dot

Recent years have brought an explosion of activities in the research of topological aspects of condensed-matter systems. Topologically non-trivial phases of matter are typically accompanied by protected surface states or exotic degenerate excitations such as Majorana end states or Haldane's localized spinons. Topologically protected degeneracies can, however, also appear in the bulk. An intriguing example is provided by Weyl semimetals, where topologically protected electronic band degeneracies and exotic surface states emerge even in the absence of interactions. Here we demonstrate experimentally and theoretically that Weyl degeneracies appear naturally in an interacting quantum dot system, for specific values of the external magnetic field. These magnetic Weyl points are robust against spin-orbit coupling unavoidably present in most quantum dot devices. Our transport experiments through an InAs double dot device placed in magnetic field reveal the presence of a pair of Weyl points, exhibiting a robust ground state degeneracy and a corresponding protected Kondo effect.

cond-mat.mes-hall↗

arXiv2018

Exploring the Kondo model in and out of equilibrium with alkaline-earth atoms

We propose a scheme to realize the Kondo model with tunable anisotropy using alkaline-earth atoms in an optical lattice. The new feature of our setup is Floquet engineering of interactions using time-dependent Zeeman shifts, that can be realized either using state-dependent optical Stark shifts or magnetic fields. The properties of the resulting Kondo model strongly depend on the anisotropy of the ferromagnetic interactions. In particular, easy-plane couplings give rise to Kondo singlet formation even though microscopic interactions are all ferromagnetic. We discuss both equilibrium and dynamical properties of the system that can be measured with ultracold atoms, including the impurity spin susceptibility, the impurity spin relaxation rate, as well as the equilibrium and dynamical spin correlations between the impurity and the ferromagnetic bath atoms. We analyze the non-equilibrium time evolution of the system using a variational non-Gaussian approach, which allows us to explore coherent dynamics over both short and long timescales, as set by the bandwidth and the Kondo singlet formation, respectively. In the quench-type experiments, when the Kondo interaction is suddenly switched on, we find that real-time dynamics shows crossovers reminiscent of poor man's renormalization group flow used to describe equilibrium systems. For bare easy-plane ferromagnetic couplings, this allows us to follow the formation of the Kondo screening cloud as the dynamics crosses over from ferromagnetic to antiferromagnetic behavior. On the other side of the phase diagram, our scheme makes it possible to measure quantum corrections to the well-known Korringa law describing the temperature dependence of the impurity spin relaxation rate. Theoretical results discussed in our paper can be measured using currently available experimental techniques.

cond-mat.quant-gas↗

arXiv2017

Selective final state spectroscopy and multifractality in two-component ultracold Bose-Einstein condensates: a numerical study

We propose to use the method introduced by Volchkov et al., based on state dependent disordered ultracold bosons, to address the critical state at the mobility edge of the Anderson localization transition, and to observe its intriguing multifractal structure. An optimally designed external radio frequency pulse can be applied to generate transitions to eigenstates in a narrow energy window close to the mobility edge, where critical scaling and multifractality emerge. Two-photon laser scanning microscopy will be used to address individual localized states even close to the transition. The projected image of the cloud is shown to inherit multifractality and to display universal density correlations. Time of flight images of the excited states are predicted to show interference fringes in the localized phase, while they allow one to map equal energy surfaces deep in the metallic phase.

cond-mat.dis-nn↗

arXiv2017

Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems

We develop the theoretical framework for calculating magnetic noise from conducting two-dimensional (2D) materials. We describe how local measurements of this noise can directly probe the wave-vector dependent transport properties of the material over a broad range of length scales, thus providing new insight into a range of correlated phenomena in 2D electronic systems. As an example, we demonstrate how transport in the hydrodynamic regime in an electronic system exhibits a unique signature in the magnetic noise profile that distinguishes it from diffusive and ballistic transport and how this can be used to measure the viscosity of the electronic fluid. We employ a Boltzmann approach in a two-time relaxation-time approximation to compute the conductivity of graphene and quantitatively illustrate these transport regimes and the experimental feasibility of observing them. Next, we discuss signatures of isolated impurities lodged inside the conducting 2D material. The noise near an impurity is found to be suppressed compared to the background by an amount that is directly proportional to the cross-section of electrons/holes scattering off of the impurity. We use these results to outline an experimental proposal to measure the temperature dependent level-shift and line-width of the resonance associated with an Anderson impurity.

cond-mat.str-el↗

arXiv2016

Confinement induced interlayer molecules: a route to strong interatomic interactions

We study theoretically the interaction between two species of ultracold atoms confined into two layers of a finite separation, and demonstrate the existence of new types of confinement-induced interlayer bound and quasi-bound molecules: these novel exciton-like interlayer molecules appear for both positive and negative scattering lengths, and exist even for layer separations many times larger than the interspecies scattering length. The lifetime of the quasi-bound molecules grows exponentially with increasing layer separation, and they can therefore be observed in simple shaking experiments, as we demonstrate through detailed many-body calculations. These quasi-bound molecules can also give rise to novel interspecies Feshbach resonances, enabling one to control geometrically the interaction between the two species by changing the layer separation. Rather counter-intuitively, the species can be made strongly interacting, by increasing their spatial separation. The separation induced interlayer resonances provide a powerful tool for the experimental control of interspecies interactions and enables one to realize novel quantum phases of multicomponent quantum gases.

cond-mat.quant-gas↗

arXiv2016

Floquet topological phases coupled to environments and the induced photocurrent

We consider the fate of a helical edge state of a spin Hall insulator and its topological transition in presence of a circularly polarized light when coupled to various forms of environments. A Lindblad type equation is developed to determine the fermion occupation of the Floquet bands. We find by using analytical and numerical methods that non-secular terms, corresponding to 2-photon transitions, lead to a mixing of the band occupations, hence the light induced photocurrent is in general not perfectly quantized in the presence of finite coupling to the environment, although deviations are small in the adiabatic limit. Sharp crossovers are identified at frequencies $Ω$ and $\frac{1}{2}Ω$ ($Ω$ is the strength of light-matter coupling) with the former resembling to a phase transition.

cond-mat.str-el↗

arXiv2015

Quantum quenches in the sine--Gordon model: a semiclassical approach

We compute the time evolution of correlation functions after quantum quenches in the sine--Gordon model within the semiclassical approximation which is expected to yield accurate results for small quenches. We demonstrate this by reproducing results of a recent form factor calculation of the relaxation of expectation values. Extending these results, we find that the expectation values of most vertex operators do not decay to zero. We give analytic expressions for the relaxation of dynamic correlation functions, and we show that they have diffusive behavior for large timelike separation.

cond-mat.stat-mech↗

arXiv2014

Anderson Localization and Quantum Hall Effect: Numerical Observation of Two Parameter Scaling

A two dimensional disordered system of non-interacting fermions in a homogeneous magnetic field is investigated numerically. By introducing a new magnetic gauge, we explore the renormalization group (RG) flow of the longitudinal and Hall conductances with higher precision than previously studied, and find that the flow is consistent with the predictions of Pruisken and Khmelnitskii. The extracted critical exponents agree with the results obtained by using transfer matrix methods. The necessity of a second parameter is also reflected in the level curvature distribution. Near the critical point the distribution slightly differs from the prediciton of random matrix theory, in agreement with previous works. Close to the quantum Hall fixed points the distribution is lognormal since here states are strongly localized.

cond-mat.dis-nn↗

arXiv2014

Nonperturbative phase diagram of interacting disordered Majorana nanowires

We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong coupling regime. This method allows for a non-perturbative treatment in the disorder strength, electron- electron interactions and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase, and a glassy, non-topological localized phase, characterized by replica symmetry breaking.

cond-mat.mes-hall↗

arXiv2014

Stabilizing the false vacuum: Mott skyrmions

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 three-component 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.

cond-mat.quant-gas↗

arXiv2013

Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid

We investigate the many-body 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 behaviour: the steady state exponent after quenching back and forth n-times between 2 LLs (bang-bang 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 matrix-product 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.

cond-mat.str-el↗

arXiv2012

Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid

We analyze the probability distribution function (PDF) of work done on a Luttinger liquid for an arbitrary finite duration interaction quench and show that it can be described in terms a generalized Gibbs ensemble. We construct the corresponding density matrix with explicit intermode correlations, and determine the duration and interaction dependence of the probability of an adiabatic transition and the PDF of non-adiabatic processes. In the thermodynamic limit, the PDF of work exhibits a non-Gaussian maximum around the excess heat, carrying almost all spectral weight. In contrast, in the small system limit most spectral weight is carried by a delta peak at the energy of the adiabatic process, and an oscillating PDF with dips at energies commensurate to the quench duration and with an exponential envelope develops. Relevance to cold atom experiments is also discussed.

cond-mat.str-el↗

arXiv2011

Fluctuation-exchange approximation theory of the non-equilibrium singlet-triplet transition

As a continuation of a previous work [B. Horváth et al., Phys. Rev. B {\bf 82}, 165129 (2010)], here we extend the so-called Fluctuation Exchange Approximation (FLEX) to study the non-equilibrium singlet-triplet transition. We show that, while being relatively fast and a conserving approximation, FLEX is able to recover all important features of the transition, including the evolution of the linear conductance throughout the transition, the two-stage Kondo effect on the triplet side, and the gradual opening of the singlet-triplet gap on the triplet side of the transition. A comparison with numerical renormalization group calculations also shows that FLEX captures rather well the width of the Kondo resonance. FLEX thus offers a viable route to describe correlated multi-level systems under non-equilibrium conditions, and, in its rather general form, as formulated here, it could find a broad application in molecular electronics calculations.

cond-mat.str-el↗