arXiv subjects

Karyn Le Hur

Publications and source records attributed to Karyn Le Hur.

At least 91 records · Page 5Linked to original sources

arXiv2012

Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi--metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi--metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.

cond-mat.quant-gas↗

arXiv2012

Non-equilibrium quantum transport through a dissipative resonant level

The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett. 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization group approach is applied to compute the non-equilibrium current in the presence of a finite bias voltage V. In the linear response regime V ->0, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the non-equilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the non-equilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V< T, while it obeys a distinct non-equilibrium profile for V>T. We furthermore provide new signatures of the transition in the finite-frequency current noise and AC conductance via the recently developed Functional Renormalization Group (FRG) approach. The generalization of our analysis to non-equilibrium transport through a resonant level coupled to two chiral Luttinger-liquid leads, generated by the fractional quantum Hall edge states, is discussed. Our work on dissipative resonant level has direct relevance to the experiments in a quantum dot coupled to resistive environment, such as H. Mebrahtu et al., Nature 488, 61, (2012).

cond-mat.mes-hall↗

arXiv2012

Heisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions

Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $ΔxΔp$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamics

quant-ph↗

arXiv2012

Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice

We theoretically investigate a photonic Kagome lattice which can be realized in microwave cavity arrays using current technology. The Kagome lattice exhibits an exotic band structure with three bands one of which can be made completely flat. The presence of artificial gauge fields allows to emulate topological phases and induce chiral edge modes which can coexist inside the energy gap with the flat band that is topologically trivial. By tuning the artificial fluxes or in the presence of disorder, the flat band can also acquire a bandwidth in energy allowing the coexistence between chiral edge modes and bulk extended states; in this case the chiral modes become fragile towards scattering into the bulk. The photonic system then exhibits equivalents of both a quantum Hall effect without Landau levels, and an anomalous Hall effect characterized by a non-quantized Chern number. We discuss experimental observables such as local density of states and edge currents. We show how synthetic uniform magnetic fields can be engineered, which allows an experimental probe of Landau levels in the photonic Kagome lattice. We then draw on semiclassical Boltzmann equations for transport to devise a method to measure Berry's phases around loops in the Brillouin zone. The method is based solely on wavepacket interference and can be used to determine band Chern numbers or the photonic equivalent of the anomalous Hall response. We demonstrate the robustness of these measurements towards on-site and gauge-field disorder. We also show the stability of the anomalous quantum Hall phase for nonlinear cavities and for (artificial) atom-photon interactions.

cond-mat.quant-gas↗

arXiv2012

Noninvasive Probe of Charge Fractionalization in Quantum Spin-Hall Insulators

When an electron with well-defined momentum tunnels into a nonchiral Luttinger liquid, it breaks up into two separate wave packets that carry fractional charges and move in opposite directions. A direct observation of this phenomenon has proven elusive, mainly due to single-particle and plasmon backscattering caused by measurement probes. This paper theoretically introduces two topological insulator devices that are naturally suited for detecting fractional charges and their velocities directly and in a noninvasive fashion.

cond-mat.mes-hall↗

arXiv2012

Quantum Spin Hall Insulators with Interactions and Lattice Anisotropy

We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice combining the cellular dynamical mean-field theory and its real space extension with analytical approaches. We provide a thorough analysis of the phase diagram and temperature effects at weak spin-orbit coupling. We systematically discuss the stability of the quantum spin Hall phase toward interactions and lattice anisotropy resulting in the plaquette-honeycomb model. We also show the evolution of the helical edge states characteristic of quantum spin Hall insulators as a function of Hubbard interaction and anisotropy. At very weak spin-orbit coupling and intermediate electron-electron interactions, we substantiate the existence of a quantum spin liquid phase.

cond-mat.str-el↗

arXiv2012

Kondo Resonance of a Microwave Photon

We emulate renormalization group models, such as the Spin-Boson Hamiltonian or the anisotropic Kondo model, from a quantum optics perspective by considering a superconducting device. The infra-red confinement involves photon excitations of two tunable transmission lines entangled to an artificial spin-1/2 particle or double-island charge qubit. Focusing on the propagation of microwave light, in the underdamped regime of the Spin-Boson model, we identify a many-body resonance where a photon is absorbed at the renormalized qubit frequency and reemitted forward in an elastic manner. We also show that asymptotic freedom of microwave light is reached by increasing the input signal amplitude at low temperatures which allows the disappearance of the transmission peak.

cond-mat.mes-hall↗

arXiv2012

Detecting Quantum Critical Points using Bipartite Fluctuations

We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state of the art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows to find quantum critical points with a much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.

cond-mat.str-el↗

arXiv2012

Giant Charge Relaxation Resistance in the Anderson Model

We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resistance at intermediate magnetic fields related to the destruction of the Kondo singlet. The scaling properties of this peak are computed analytically in the Kondo regime. We also show that the resistance peak fades away at the particle-hole symmetric point.

cond-mat.mes-hall↗

arXiv2011

d-wave Superfluid with Gapless Edges in a Cold Atom Trap

We consider a strongly repulsive fermionic gas in a two-dimensional optical lattice confined by a harmonic trapping potential. To address the strongly repulsive regime, we consider the $t-J$ Hamiltonian. The presence of the harmonic trapping potential enables the stabilization of coexisting and competing phases. In particular, at low temperatures, this allows the realization of a d-wave superfluid region surrounded by purely (gapless) normal edges. Solving the Bogoliubov-de Gennes equations and comparing with the local density approximation, we show that the proximity to the Mott insulator is revealed by a downturn of the Fermi liquid order parameter at the center of the trap where the d-wave gap has a maximum. The density profile evolves linearly with distance.

cond-mat.supr-con↗

arXiv2011

Bipartite Fluctuations as a Probe of Many-Body Entanglement

We investigate in detail the behavior of the bipartite fluctuations of particle number $\hat{N}$ and spin $\hat{S}^z$ in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

cond-mat.mes-hall↗

arXiv2011

Effective thermodynamics of strongly coupled qubits

Interactions between a quantum system and its environment at low temperatures can lead to violations of thermal laws for the system. The source of these violations is the entanglement between system and environment, which prevents the system from entering into a thermal state. On the other hand, for two-state systems, we show that one can define an effective temperature, placing the system into a `pseudo-thermal' state where effective thermal laws are upheld. We then numerically explore these assertions for an n-state system inspired by the spin-boson environment.

cond-mat.other↗

arXiv2011

Effective Equilibrium Description of Nonequilibrium Quantum Transport I: Fundamentals and Methodology

The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through a quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian, thus facilitating the implementation of equilibrium many-body techniques. We provide an alternative derivation of the effective Hamiltonian of Hershfield using the concept of an "open system". Furthermore, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach. For the study of transport, the non-equilibrium spectral function of the dot is identified as the quantity of principal interest and we derive general expressions for the current (the Meir-Wingreen formula) and the charge occupation of the dot. We introduce a finite temperature formalism which is used as a tool for computing real time Green's functions. In a companion paper we elucidate a generic scheme for perturbative calculations of interacting models, with particular reference to the Anderson model.

cond-mat.str-el↗

arXiv2011

Designing Heterostructures with Higher Temperature Superconductivity

We propose to increase the superconducting transition temperature Tc of strongly correlated materials by designing heterostructures which exhibit a high pairing energy as a result of magnetic fluctuations. More precisely, applying an effective theory of the doped Mott insulator, we envisage a bilayer Hubbard system where both layers exhibit prominent intralayer (intraband) d-wave superconducting correlations. Introducing a finite asymmetry between the hole densities of the two layers such that one layer becomes slightly more underdoped and the other more overdoped, we evidence a visible enhancement of Tc compared to the optimally doped isolated layer. Using the bonding and antibonding band basis, we show that the mechanism behind this enhancement of Tc is the interband pairing correlation mediated by the hole asymmetry which strives to decrease the paramagnetic nodal contribution to the superfluid stiffness. For two identical layers, Tc remains comparable to that of the isolated layer until moderate values of the interlayer single-particle tunneling term. These heterostructures shed new light on fundamental questions related to superconductivity.

cond-mat.supr-con↗

arXiv2011

Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet

We compute the von Neumann and generalized Rényi entanglement entropies in the ground-state of the spin-1/2 antiferromagnetic Heisenberg model on the square lattice using the modified spin-wave theory for finite lattices. The addition of a staggered magnetic field to regularize the Goldstone modes associated with symmetry-breaking is shown to be essential for obtaining well-behaved values for the entanglement entropy. The von Neumann and Rényi entropies obey an area law with additive logarithmic corrections, and are in good quantitative agreement with numerical results from valence bond quantum Monte Carlo and density matrix renormalization group calculations. We also compute the spin fluctuations and observe a multiplicative logarithmic correction to the area law in excellent agreement with quantum Monte Carlo calculations.

cond-mat.str-el↗

arXiv2010

Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins

We analyze the static and dynamical properties of two Ising-coupled quantum spins embedded in a common bosonic bath as an archetype of dissipative quantum mechanics. First, we elucidate the ground state phase diagram for an ohmic and a subohmic bath using a combination of bosonic numerical renormalization group (NRG), analytical techniques and intuitive arguments. Second, employing the time-dependent NRG we investigate the system's rich dynamical behavior arising from the complex interplay between spin-spin and spin-bath interactions. Interestingly, spin oscillations can synchronize due to the proximity of the common non-Markovian bath and the system displays highly entangled steady states for certain nonequilibrium initial preparations. We complement our non-perturbative numerical results by exact analytical solutions when available and provide quantitative limits on the applicability of the perturbative Bloch-Redfield approach at weak coupling.

cond-mat.mes-hall↗

arXiv2010

Time-reversal symmetry breaking in circuit-QED based photon lattices

Breaking time-reversal symmetry is a prerequisite for accessing certain interesting many-body states such as fractional quantum Hall states. For polaritons, charge neutrality prevents magnetic fields from providing a direct symmetry breaking mechanism and similar to the situation in ultracold atomic gases, an effective magnetic field has to be synthesized. We show that in the circuit QED architecture, this can be achieved by inserting simple superconducting circuits into the resonator junctions. In the presence of such coupling elements, constant parallel magnetic and electric fields suffice to break time-reversal symmetry. We support these theoretical predictions with numerical simulations for realistic sample parameters, specify general conditions under which time-reversal is broken, and discuss the application to chiral Fock state transfer, an on-chip circulator, and tunable band structure for the Kagome lattice.

cond-mat.mes-hall↗

arXiv2010

Universality in dissipative Landau-Zener transitions

We introduce a random variable approach to investigate the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of the time evolution of a quantum state vector subject to a Hamiltonian containing random noise fields. This numerically exact, non-perturbative formalism is particularly well suited in the context of time-dependent Hamiltonians, both at zero and finite temperature. As an important example, we consider the renowned Landau-Zener problem in the presence of an Ohmic environment with a large cutoff frequency at finite temperature. We investigate the 'scaling' limit of the problem at intermediate times, where the decay of the upper spin state population is universal. Such a dissipative situation may be implemented using a cold-atom bosonic setup.

cond-mat.other↗