A Green's function decoupling scheme for the Edwards fermion-boson model

Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular exact diagonalization and density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n=0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained by DMRG and dynamical DMRG and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.Comment: 19 pages, 7 figures, final version with updated reference

Collapse-revival dynamics and atom-field entanglement in the non-resonant Dicke model

We consider the dynamics of atomic and field coherent states in the non-resonant Dicke model. At weak coupling an initial product state evolves into a superposition of multiple field coherent states that are correlated with the atomic configuration. This process is accompanied by the buildup and decay of atom-field entanglement and leads to the periodic collapse and revival of Rabi oscillations. We provide a perturbative derivation of the underlying dynamical mechanism that complements the rotating wave approximation at resonance. The identification of two different time scales explains how the dynamical signatures depend on the sign of detuning between the atomic and field frequency, and predicts the generation of either atomic or field cat states in the two opposite cases. We finally discuss the restrictions that the buildup of atom-field entanglement during the collapse of Rabi oscillations imposes on the validity of semi-classical approximations that neglect entanglement.Comment: 9 pages, 10 figures. Published versio

Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation-dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fullfills a generalized Gallavotti-Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.Comment: 21 page

Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system

In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.Comment: final version, minor correction

Correlation-induced metal insulator transition in a two-channel fermion-boson model

We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing groundstate and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.Comment: 4 pages, 4 figures, 1 table, revised version accepted for publication in Phys. Rev. Let

Putting "space" on the agenda of sociocultural research in education

The global rescaling of the world, culture, and education has influenced how people experience their situationality, meaning-making, and learning in relation to the Other. This article explores the implications of spatial analysis for rethinking education in new conditions of cultural complexity. The experience of living and learning with difference is conceptualized as an open journey in which the very act of movement across spatial boundaries unlocks the fixity of meanings and identities and, hence, problematizes the spatial logic of bounded learning places. Explicating the tension between fixity and mobility, boundedness and flows, this article deploys the concepts of cultural-semiotic space, scale, and boundary to theorize locations of learning and meaning-making in new times. <br /

Spectral signatures of the Luttinger liquid to charge-density-wave transition

Electron- and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition.Comment: 5 pages, 4 figures; final version, accepted for publication in Physical Review

Chebyshev approach to quantum systems coupled to a bath

We propose a new concept for the dynamics of a quantum bath, the Chebyshev space, and a new method based on this concept, the Chebyshev space method. The Chebyshev space is an abstract vector space that exactly represents the fermionic or bosonic bath degrees of freedom, without a discretization of the bath density of states. Relying on Chebyshev expansions the Chebyshev space representation of a bath has very favorable properties with respect to extremely precise and efficient calculations of groundstate properties, static and dynamical correlations, and time-evolution for a great variety of quantum systems. The aim of the present work is to introduce the Chebyshev space in detail and to demonstrate the capabilities of the Chebyshev space method. Although the central idea is derived in full generality the focus is on model systems coupled to fermionic baths. In particular we address quantum impurity problems, such as an impurity in a host or a bosonic impurity with a static barrier, and the motion of a wave packet on a chain coupled to leads. For the bosonic impurity, the phase transition from a delocalized electron to a localized polaron in arbitrary dimension is detected. For the wave packet on a chain, we show how the Chebyshev space method implements different boundary conditions, including transparent boundary conditions replacing infinite leads. Furthermore the self-consistent solution of the Holstein model in infinite dimension is calculated. With the examples we demonstrate how highly accurate results for system energies, correlation and spectral functions, and time-dependence of observables are obtained with modest computational effort.Comment: 18 pages, 13 figures, to appear in Phys. Rev.

Carrier-density effects in many-polaron systems

Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the one-dimensional spinless Holstein model considered here. In this work, previous results obtained using numerical as well as analytical approaches are reviewed from a unified perspective, focussing on spectral properties which reveal the nature of the quasiparticles in the system. In the adiabatic regime and for intermediate electron-phonon coupling, a carrier-density driven crossover from a polaronic to a rather metallic system takes place. Further insight into the effects due to changes in density is gained by calculating the phonon spectral function, and the fermion-fermion and fermion-lattice correlation functions. Finally, we provide strong evidence against the possibility of phase separation.Comment: 13 pages, 6 figures, accepted for publication in J. Phys.: Condens. Matter; final versio

Optical absorption and activated transport in polaronic systems

We present exact results for the optical response in the one-dimensional Holstein model. In particular, by means of a refined kernel polynomial method, we calculate the ac and dc electrical conductivities at finite temperatures for a wide parameter range of electron phonon interaction. We analyze the deviations from the results of standard small polaron theory in the intermediate coupling regime and discuss non-adiabaticity effects in detail.Comment: 7 pages, 8 figure