6 research outputs found
Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
No full textWe investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) of one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient scaling features of localization, even though it provides only an upper bound to the von Neumann entropy. First, we numerically show that the OPDM entropy of the eigenstates obeys an area law. Second, like the von Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well toward the transition into the ergodic phase. We discuss prospects for calculating the OPDM entropy using approximate numerical methods and for its measurement in quantum gas experiments
Molecular junctions and molecular motors : Including Coulomb repulsion in electronic friction using nonequilibrium Green's functions
No full textWe present a theory of molecular motors based on the Ehrenfest dynamics for nuclear coordinates and the adiabatic limit of the Kadanoff-Baym equations for current-induced forces. Electron-electron interactions can be systematically included through many-body perturbation theory, making the nonequilibrium Green's function formulation suitable for first-principles treatments of realistic junctions. The method is benchmarked against simulations via real-time Kadanoff-Baym equations, finding an excellent agreement. Results on a paradigmatic model of a molecular motor show that correlations can change dramatically the physical scenario by, e.g., introducing a sizable damping in self-sustained van der Pol oscillations
Löwdin's symmetry dilemma within Green functions theory for the one-dimensional Hubbard model
No full textThe energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the “symmetry dilemma” introduced by Löwdin for Hartree–Fock wave function calculations
Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
No full textWe benchmark a set of quantum-chemistry methods, including multitrajectory
Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest
dynamics, against exact quantum-many-body techniques by studying real-time
dynamics in the Holstein model. This is a paradigmatic model in condensed
matter theory incorporating a local coupling of electrons to Einstein phonons.
For the two-site and three-site Holstein model, we discuss the exact and
quantum-chemistry methods in terms of the Born-Huang formalism, covering
different initial states, which either start on a single Born-Oppenheimer
surface, or with the electron localized to a single site. For extended systems
with up to 51 sites, we address both the physics of single Holstein polarons
and the dynamics of charge-density waves at finite electron densities. For
these extended systems, we compare the quantum-chemistry methods to exact
dynamics obtained from time-dependent density matrix renormalization group
calculations with local basis optimization (DMRG-LBO). We observe that the
multitrajectory Ehrenfest method, in general, only captures the ultrashort time
dynamics accurately. In contrast, the surface-hopping method with suitable
corrections provides a much better description of the long-time behavior but
struggles with the short-time description of coherences between different
Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method
yields a significant improvement over the multitrajectory Ehrenfest method and
can be converged to the exact results in small systems with moderate
computational efforts. We further observe that for extended systems, this
convergence is slower with respect to the number of configurations. Our
benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the
quality of the quantum-chemistry methods.Comment: 44 pages, 34 figures. Minor revision due to reviewer comments. The
data that support the findings of this study are openly available at
https://doi.org/10.25625/YDU1XT, G\"ottingen Research Online / Dat
Probing Strongly Correlated Materials in Non-equilibrium: Basic Concepts and Possible Future Trends in First Principle Approaches
No full textTime-resolved spectroscopy has an emerging role among modern material-characterization techniques. Two powerful theoretical formalisms for systems out of equilibrium (and thus for time-resolved spectroscopy) are Non-Equilibrium Green’s Functions (NEGF) and Time-Dependent Density Functional Theory (TDDFT). In this chapter, we offer a perspective (with more emphasis on the NEGF) on their current capability to deal with the case of strongly correlated materials. To this end, the NEGF technique is briefly presented, and its use in time-resolved spectroscopy highlighted. We then show how a linear response description is recovered from NEGF real-time dynamics. This is followed by a review of a recent ab initio NEGF treatment and by a short introduction to TDDFT. With these background notions, we turn to the problem of describing strong correlation effects by NEGF and TDDFT. This is done in terms of model Hamiltonians: using simple lattice systems as benchmarks, we illustrate to what extent NEGF and TDDFT can presently describe complex materials out of equilibrium and with strong electronic correlations. Finally, an outlook is given on future trends in NEGF and TDDFT research of interest to time-resolved spectroscopy
Merging Features from Green's Functions and Time Dependent Density Functional Theory : A Route to the Description of Correlated Materials out of Equilibrium?
No full textWe propose a description of nonequilibrium systems via a simple protocol that combines exchangecorrelation
potentials from density functional theory with self-energies of many-body perturbation theory.
The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbardtype
systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system
dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent
density functional theory or second Born nonequilibrium Green’s function approximations. We briefly
discuss the reasons for the residual discrepancies, and directions for future work.peerReviewe
