arXiv subjects

Álvaro Gómez-León

Publications and source records attributed to Álvaro Gómez-León.

At least 37 records · Page 2Linked to original sources

arXiv2020

Designing adiabatic time-evolution from high frequency bichromatic sources

We investigate the quantum dynamics of a two-level system driven by a bichromatic field, using a non-perturbative analysis. We make special emphasis in the case of two large frequencies, where the Magnus expansion can fail, and in the case of a large and a small frequency, where resonances can dominate. In the first case, we show that two large frequencies can be combined to produce an effective adiabatic evolution. In the second case, we show that high frequency terms (which naturally arise as corrections to the adiabatic evolution obtained in the first case) can be used to produce a highly tunable adiabatic evolution over the whole Bloch sphere, controlled by multi-photon resonances.

cond-mat.mes-hall↗

arXiv2019

Correlation effects in spin models in the presence of a spin bath

We analyze the effect of a bath of spins interacting with a spin system in terms of the equation of motion technique. We show that this formalism can be used with general spin systems and baths, and discuss the concrete case of a Quantum Ising model longitudinally coupled to the bath. We show how the uncorrelated solutions change when spin-spin correlations are included, the properties of the quasiparticle excitations and the effect of internal dynamics in the spin bath.

cond-mat.str-el↗

arXiv2019

Simulation of 1D topological phases in driven quantum dot arrays

We propose a driving protocol which allows to use quantum dot arrays as quantum simulators for 1D topological phases. We show that by driving the system out of equilibrium, one can imprint bond-order in the lattice (producing structures such as dimers, trimers, etc) and selectively modify the hopping amplitudes at will. Our driving protocol also allows for the simultaneous suppression of all the undesired hopping processes and the enhancement of the necessary ones, enforcing certain key symmetries which provide topological protection. In addition, we have discussed its implementation in a 12-QD array with two interacting electrons and found correlation effects in their dynamics, when configurations with different number of edge states are considered.

cond-mat.mes-hall↗

arXiv2019

Spin bath dynamics and dynamical Renormalization Group

Abstract We discuss the quantum dynamics of the central spin model in a regime where the central spin and bath are slaved to each other. The exact solution is found when the bath is static, and is compared with the effect of an external field, finding that they are inequivalent due to the quantum nature of the environment. When the bath has dynamics, we analyze the differences between the numerical simulation using time-dependent perturbation theory and the equation of motion technique, which shows better accuracy. We demonstrate that the use of dynamical Renormalization Group (dRG), simultaneously with the equation of motion technique, provides a suitable analytical tool to understand the physics, to capture the main physical processes, and a powerful method to eliminate secular terms. In addition, this approach allows to separate classical non-linear behavior from corrections due to quantum correlations.

cond-mat.str-el↗

arXiv2019

Floquet engineering of Dirac cones on the surface of a topological insulator

We propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator. We show that a large tunability of the Fermi velocity can be achieved as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experimental evidences. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators. In our work we use the full Hamiltonian for the three-dimensional system instead of effective surface Hamiltonians, which are usually considered in the literature. Our findings show that the Dirac cones in the quasienergy spectrum remain robust even in the presence of bulk states and, therefore, they validate the usage of effective surface Hamiltonians to explore the properties of Floquet-driven topological boundaries. Furthermore, our model allows us to introduce new out-of-plane field configurations, which cannot be accounted for by effective surface Hamiltonians.

cond-mat.mes-hall↗

arXiv2019

Interplay between long range hopping and disorder in topological systems

We extend the standard SSH model to include long range hopping and disorder, and study how the electronic and topological properties are affected. We show that long range hopping can change the symmetry class and the topological invariant, while diagonal and off-diagonal disorder lead to Anderson localization. Interestingly we find that the Lyapunov exponent $γ(E)$ can be linked in two ways to the topological properties in the presence of disorder: Either due to the different response of mid-gap states to increasing disorder, or due to an extra contribution to $γ$ due to the presence of edge modes. Finally we discuss its implications in realistic transport measurements.

cond-mat.mes-hall↗

arXiv2018

SSH model with long-range hoppings: topology, driving and disorder

The Su-Schrieffer-Heeger (SSH) model describes a finite one-dimensional dimer lattice with first-neighbour hoppings populated by non-interacting electrons. In this work we study a generalization of the SSH model including longer-range hoppings, what we call the extended SSH model. We show that the presence of odd and even hoppings has a very different effect on the topology of the chain. On one hand, even hoppings break particle-hole and sublattice symmetry, making the system topologically trivial, but the Zak phase is still quantized due to the presence of inversion symmetry. On the other hand, odd hoppings allow for phases with a larger topological invariant. This implies that the system supports more edge states in the band's gap. We propose how to engineer those topological phases with a high-frequency driving. Finally, we include a numerical analysis on the effect of diagonal and off-diagonal disorder in the edge states properties.

cond-mat.mes-hall↗

arXiv2017

Hierarchy of correlations for the Ising model in the Majorana representation

We study the quantum Ising model in D dimensions with the equation of motion technique, in combination with the Majorana representation for spins. The decoupling scheme used for the Green's functions is based on the hierarchy of correlations in position space. To lowest order this method reproduces the well known mean field phase diagram and critical exponents. When correlations between spins are included, we show how the appearance of thermal fluctuations and magnons strongly affect the physical properties. We demonstrate that in 1D and for B=0, thermal fluctuations completely destroy the ordered phase, and that near the quantum critical point, the quantum model displays different behavior than its classical counterpart. We discuss the connection with the Dyson's equation formalism and the explicit form of the self-energies.

cond-mat.str-el↗

arXiv2017

Transport signatures in topological systems coupled to AC fields

We study the transport properties of a topological system coupled to an AC electric field by means of Floquet-Keldysh formalism. We consider a semi-infinite chain of dimers coupled to a semi-infinite metallic lead, and obtain the density of states and current when the system is out of equilibrium. Our formalism is non-perturbative and allows us to explore, in the thermodynamic limit, a wide range of regimes for the AC field, arbitrary values of the coupling strength to the metallic contact and corrections to the wide-band limit. We find that hybridization with the contact can change the dimerization phase, and that the current dependence on the field amplitude can be used to discriminate between them. We also show the appearance of side-bands and non-equilibrium zero-energy modes, characteristic of Floquet systems. Our results directly apply to the stability of non-equilibrium topological phases, when transport measurements are used for their detection.

cond-mat.mes-hall↗

arXiv2017

Dynamical Quantum Phase Transitions in presence of a spin bath

We derive an effective time independent Hamiltonian for the transverse Ising model coupled to a spin bath, in the presence of a high frequency AC magnetic field. We show that the spin blocking mechanism that removes the quantum phase transition can be suppressed by the AC field, allowing high tunability of the quantum critical point. Finally, we calculate the phase diagram within the RPA approximation for the case of spin $7/2$ nuclei, appropriate to the $LiHo_{x}Y_{1-x}F_{4}$ system.

cond-mat.str-el↗

arXiv2016

Hierarchy of correlations: Application to Green's functions and interacting topological phases

We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to calculate double-time Green's functions, and due to its non-perturbative nature, we describe quantum phase transition and topological features characteristic of strongly correlated phases. As concrete examples we consider spinless fermions in a dimers chain and in a honeycomb lattice. We present analytical results which are valid for any dimension and can be generalized to different types of interactions (e.g., long range interactions), which allows us to shed light on the effect of quantum correlations in a very systematic way. Furthermore, we show that this approach provides an efficient framework for the calculation of topological invariants in interacting systems.

cond-mat.str-el↗

arXiv2015

Reply to "Comment on `Floquet Fractional Chern Insulators'"

We respond to the comments expressed by L. D'Alessio in arXiv:1412.3481 on our work "Floquet Fractional Chern Insulators" [Phys. Rev. Lett. 112, 156801 (2014)]. We confirm the central result that the ground state of the effective Hamiltonian is an interacting fractional Chern insulator.

cond-mat.str-el↗

arXiv2015

Floquet engineering of long-range p-wave superconductivity

Floquet Majorana Fermions appear as steady states at the boundary of time-periodic topological phases of matter. In this work, we theoretically study the main features of these exotic topological phases in the periodically driven one-dimensional Kitaev model. By controlling the ac fields, we can predict new topological phase transitions that should give rise to signatures of Majorana states in experiments. Moreover, the knowledge of the time-dependence of these Majorana states allows one to manipulate them. Our work contains a complete analysis of the monochromatic driving in different frequency regimes.

cond-mat.str-el↗

arXiv2014

Engineering Quantum Anomalous Hall Plateaus and Anti-Chiral States with AC Fields

We investigate the AC electric field induced quantum anomalous Hall effect in honeycomb lattices and derive the full phase diagram for arbitrary field amplitude and phase polarization. We show how to induce anti-chiral edge modes as well as topological phases characterized by a Chern number larger than $1$ by means of suitable drivings. In particular, we find that the Chern number develops plateaus as a function of the frequency, providing an time-dependent analogue to the ones in the quantum Hall effect.

cond-mat.mes-hall↗

arXiv2014

Merging of Dirac points and Floquet topological transitions in AC driven graphene

We investigate the effect of an in-plane AC electric field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points can be controlled by the amplitude and the polarization of the field for high frequency drivings, providing a new platform to achieve their merging, a topological transition which has not been observed yet in electronic systems. Importantly, for lower frequencies we find that the multi-photon absorptions and emissions processes yield the creation of additional pairs of Dirac points. This provides an additional method to achieve the merging transition by just tuning the frequency of the driving. Our approach, based on Floquet formalism, is neither restricted to specific choice of amplitude or polarization of the field, nor to a low energy approximation for the Hamiltonian.

cond-mat.mes-hall↗

arXiv2013

Floquet Fractional Chern Insulator in Doped Graphene

Fractional Chern insulators are theoretically predicted states of electronic matter with emergent topological order. They exhibit the same universal properties as the fractional quantum Hall effect, but dispose of the need to apply a strong magnetic field. However, despite intense theoretical work, an experimental realization for these exotic states of matter is still lacking. Here we show that doped graphene turns into a fractional Chern insulator, when irradiated with high-intensity circularly polarized light. We derive the effective steady state band structure of light-driven graphene using Floquet theory and subsequently study the interacting system with exact numerical diagonalization. The fractional Chern insulator state equivalent to the 1/3 Laughlin state appears at 7/12 total filling of the honeycomb lattice (1/6 filling of the upper band). The state also features spontaneous ferromagnetism and is thus an example of the spontaneous breaking of a continuous symmetry along with a topological phase transition.

cond-mat.str-el↗

arXiv2013

Topological phases in adiabatic and nonadiabatic driven systems

In this work we study the geometrical and topological properties of non-equilibrium quantum systems driven by ac fields. We consider two tunnel coupled spin qubits driven by either spatially homogeneous or inhomogeneous ac fields. Our analysis is an extension of the classical model introduced by Berry with he addition of the spatial degree of freedom. We calculate the Berry and Aharonov-Anandan geometric phases, and demonstrate the influence of the different field parameters in the geometric properties. We also discuss the topological properties associated with the different driving regimes, and show that by tuning the different parameters one can induce topological phase transitions, even in the non-adiabatic regime.

quant-ph↗

arXiv2012

Transport blocking and topological phases using ac magnetic fields

We analyze electron dynamics and topological properties of open double quantum dots (DQDs) driven by circularly polarized ac-magnetic fields. In particular we focus on the system symmetries which can be tuned by the ac-magnetic field. Remarkably, we show that in the electron spin resonance (ESR) configuration, where the magnetic fields in each dot oscillate with a phase difference of $π$, charge localization occurs giving rise to transport blocking at arbitrary intensities of the ac field. The conditions for charge localization are obtained by means of Floquet theory and related with quasienergies degeneracy. We also demonstrate that a topological phase transition can be induced in the adiabatic regime for a phase difference of $π$, either by tuning the coupling between dots or by modifying the intensity of the driving magnetic field.

cond-mat.mes-hall↗