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Journal of Physics Conference Series

Theory of photon-driven correlated electrons in one dimension

Matteo Ballerini Puviani, F. Manghi

Published May 1, 2017• 0 citations
Publisher

Abstract

In this paper we present a general theoretical framework to study interacting electrons under the influence of an external time-periodic driving, such as a homogeneous laser field. This is performed through a true many-body calculation and the use of Floquet theory. In particular, we consider a linear atomic chain using the Hubbard model to describe the short-ranged Coulomb interactions between electrons, plus Cluster Perturbation Theory to embed the many-body exact solution for a finite system into both an extended and an infinite lattice. Due to the presence of the external time-periodic perturbation, the electronic problem can be mapped into the study of photon-dressed quasiparticles thanks to Floquet theorem, keeping into account of all the virtual processes (absorption and emission of photons by electrons) with the laser field. This leads to an extension of the many-body static theories to out-of-equilibrium systems. This theoretical approach allowed us to show how the electronic properties of the system can be controlled and tuned varying the laser parameters. Above all, an inverse insulator-to-metal transition can be obtained for the one dimensional infinite lattice, and edge localized states appear as a finite size effect in an extended truncated chain.

DOI
10.1088/1742-6596/841/1/012021

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In this paper we present a general theoretical framework to study interacting electrons under the influence of an external time-periodic driving, such as a homogeneous laser field. This is performed through a true many-body calculation and the use of Floquet theory. In particular, we consider a linear atomic chain using the Hubbard model to describe the short-ranged Coulomb interactions between electrons, plus Cluster Perturbation Theory to embed the many-body exact solution for a finite system into both an extended and an infinite lattice. Due to the presence of the external time-periodic perturbation, the electronic problem can be mapped into the study of photon-dressed quasiparticles thanks to Floquet theorem, keeping into account of all the virtual processes (absorption and emission of photons by electrons) with the laser field. This leads to an extension of the many-body static theories to out-of-equilibrium systems. This theoretical approach allowed us to show how the electronic properties of the system can be controlled and tuned varying the laser parameters. Above all, an inverse insulator-to-metal transition can be obtained for the one dimensional infinite lattice, and edge localized states appear as a finite size effect in an extended truncated chain.
We propose a method to study the time evolution of correlated electrons driven by a harmonic perturbation. Combining Floquet formalism to include the time-dependent field and cluster perturbation theory to solve the many-body problem in the presence of short-range correlations, we treat the electron double dressing, by photons and by $e\text{\ensuremath{-}}e$ interactions, on the same footing. We apply the method to an extended Hubbard chain at half occupation, and we show that in the regime of small field frequency and for given values of field strength, the zero-mode Floquet band is no longer gapped and the system recovers a metallic state. Our results are indicative of an omnipresent mechanism for insulator-to-metal transitions in one-dimensional systems.
We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-band noninteracting systems. As a demonstration, we have applied the method to the Falicov-Kimball model in intense ac fields to calculate the spectral function. The result shows that photoinduced midgap states emerge from strong ac fields, triggering an insulator-metal transition.
Controlling and manipulating complex many-body quantum systems will be a key ingredient \nfor the development of next-generation technologies. While the realisation of a \nuniversal quantum machine is still out of reach, in recent years experimental systems of \nultracold atoms have already evolved into a vivid field of research for quantum simulation. \nCrucially, such systems even allow for the successful quantum engineering of targeted \nmany-body systems by means of coherent periodic driving. The essential properties of \nthese Floquet systems encompass two main aspects: fast driving facilitates the simulation \nof effective static systems, and interactions lead to unique heating effects as energy is only \nconserved modulo the driving frequency. Within this thesis we theoretically study both \nof these aspects in respective model systems. \nIn part I of this thesis, we investigate the dynamics of excitations of a bosonic Mott \ninsulator in a designed one-dimensional Floquet system. Here, periodic driving in combination \nwith breaking all mirror symmetries of the system can induce directed motion of \nparticles. In the limit of small excitation densities, the effectively non-interacting quantum \nratchet determines the motion of holes and doublons in the Mott insulator and can in fact \nbe used to manipulate the dynamics of such. This little quantum machine can also be \nused to drive particles against an external force, where transport is possible but requires \nthe fulfilment of a commensurability condition for long times. \nIn part II, we discuss the role of interactions for periodically driven systems by means \nof a Floquet version of the Boltzmann equation. Starting from the Keldysh approach, \nwe develop this semiclassical formalism based on a clear separation of time scales. The \nresult is a description of the dynamics and the scattering of Floquet quasiparticles in \nsuch systems. Here, the property of discrete energy violation is naturally encoded in our \nformalism predicting the heating of interacting Floquet systems to infinite temperatures in \nthe long-time limit. As a first application of this approach, we investigate a cold atom setup \nrealising the Haldane model by means of periodic shaking. While homogeneous systems \nheat up globally, a confining potential evokes thermoelectric transport effects resulting \nfrom spatially dependent heating characteristics. Moreover, we show that the interplay \nof intrinsic heating, macroscopic diffusion and non-trivial topological properties of the \nHaldane model lead to an anomalous Floquet-Nernst effect, which describes anomalous \nparticle transport as the result of developing temperature gradients. \nIn part III, we elaborate on the quantum simulator aspect of ultracold atoms by providing \na theoretical framework for a possible simulation of a topological edge state in a \none-dimensional optical lattice. In this case, the one-dimensional Dirac equation with \nspatially varying mass is important, which captures the topological properties of a corresponding \nsystem of the BDI symmetry class. We analytically discuss such system and \ninvestigate the role of mean-field interaction effects. We also identify the emergence of \ndynamical instabilities in a realisation with bosonic atoms.
Abstract We consider the Hubbard model at half filling, driven by an external, stationary laser field. This stationary, but periodic in time, electromagnetic field couples to the charge current, i.e. it induces an extra contribution to the hopping amplitude in the Hubbard Hamiltonian (photo‐induced hopping). We generalize the dynamical mean‐field theory (DMFT) for nonequilibrium with periodic‐in‐time external fields, using a Floquet mode representation and the Keldysh formalism. We calculate the non‐equilibrium electron distribution function, the density of states and the optical DC conductivity in the presence of the external laser field for laser frequencies above and below the Mott‐Hubbard gap. The results demonstrate that the system exhibits an insulator‐metal transition as the frequency of the external field is increased and exceeds the Mott‐Hubbard gap. This corresponds to photo‐induced excitations into the upper Hubbard band.
We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a noninteracting system with or without a staggered on-site potential, and we find that periodic driving can generate states localized completely or partially near the ends of a finite-sized system. Depending on the system parameters, such states have Floquet eigenvalues lying either outside or inside the continuum of eigenvalues of the bulk states. In the former case, we find that these states are completely localized at the ends and are true edge states, while in the latter case, the states are not completely localized at the ends although the localization can be made almost perfect by tuning the driving parameters. We then consider a system of two bosonic particles which have an on-site Hubbard interaction and show that a periodically driven electric field can generate two-particle states which are localized at the ends of the system. We show that many of these effects can be understood using a Floquet perturbation theory which is valid in the limit of a large staggered potential or large interaction strength. Some of these effects can also be understood qualitatively by considering time-independent Hamiltonians which have a potential at the sites at the edges; Hamiltonians of these kinds effectively appear in a Floquet-Magnus analysis of the driven problem. Finally, we discuss how the edge states produced by periodic driving of a noninteracting system of fermions can be detected by measuring the differential conductance of the system.
The Floquet theorem allows one to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density-functional theory as well, one could reduce in such cases time-dependent density-functional theory to a time-independent Floquet density-functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical ab initio solutions of the interacting time-dependent Schr\"odinger equation with time-periodic external potentials we show that the exact effective potential in the corresponding Kohn-Sham equation is not unconditionally periodic. Whenever several Floquet states in the interacting system are involved in a physical process the corresponding Hartree-exchange-correlation potential is not periodic with the external frequency only. Using an analytically solvable example we demonstrate that, in general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be restored by choosing a different initial state. Only if the external periodic potential is sufficiently weak such that the initial state of the interacting system evolves adiabatically to a single, field-dressed state, the resulting Kohn-Sham system admits the application of the Floquet theorem.