Quantum adiabatic polarons by translationally invariant perturbation theory

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency omega0, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/omega0>1 for g/omega0~(t/omega0)^{1/4} when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/omega0)^{1/2}>g/omega0>(t/omega0)^{1/4}>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset.Comment: 10 pages, 5 figure

Polarons by translationally invariant diagrammatic perturbation theory

The structure of the translationally-invariant diagrammatic perturbation theory for one polaron is examined on the 1D discrete lattice described by the Holstein Hamiltonian. The latter is characterized by the electron hopping t, the phonon frequency ω_0 and the electron-phonon coupling g. It is shown that the polaron localization (and translation) properties are contained in the electron propagator of one electron, intermittently added to the lattice, and/or in the phonon correlation function with one electron permanently present in the lattice. The order by order analysis in g/ω_0 shows that the expansion of the irreducible electron self-energy corresponds to the expansion of the phonon correlation function, rather than of the irreducible phonon self-energy. The range of polaronic correlations is determined in this way. For small t/ω_0 and already to the second order g/ω_0 small, the electron-lattice correlation becomes very short ranged, i.e. the polaron is already localized to one site, although the overall translational symmetry remains unbroken. For large t/ω0, the second order result is meaningful up to large g/ω_0 ≈ (t/ω_0)^\frac14, where it becomes degenerate with the results for the large adiabatic Holstein polaron. This suggests that the translationally invariant perturbation theory crosses then over smoothly, without symmetry breaking, into the adiabatic, continuous quantum limit, as rigorously demonstrated in the companion paper. Thus the quantum theory of the large adiabatic Holstein polaron provides a simple, instructive example of the quantum crossover which replaces the behavior in the quantum critical point

Translacijski invarijantna dijagramska teorija smetnje za polarone

The structure of the translationally-invariant diagrammatic perturbation theory for one polaron is examined on the 1D discrete lattice described by the Holstein Hamiltonian. The latter is characterized by the electron hopping t, the phonon frequency ω0 and the electron-phonon coupling g. It is shown that the polaron localization (and translation) properties are contained in the electron propagator of one electron, intermittently added to the lattice, and/or in the phonon correlation function with one electron permanently present in the lattice. The order by order analysis in g/ω0 shows that the expansion of the irreducible electron self-energy corresponds to the expansion of the phonon correlation function, rather than of the irreducible phonon self-energy. The range of polaronic correlations is determined in this way. For small t/ω0 and already to the second order g/ω0 small, the electron-lattice correlation becomes very short ranged, i.e. the polaron is already localized to one site, although the overall translational symmetry remains unbroken. For large t/ω0, the second order result is meaningful up to large g/ω0 ≈ (t/ω0) 1 4 , where it becomes degenerate with the results for the large adiabatic Holstein polaron. This suggests that the translationally invariant perturbation theory crosses then over smoothly, without symmetry breaking, into the adiabatic, continuous quantum limit, as rigorously demonstrated in the companion paper. Thus the quantum theory of the large adiabatic Holstein polaron provides a simple, instructive example of the quantum crossover which replaces the behavior in the quantum critical point.Istraživali smo strukturu translacijski invarijantne dijagramske perturbacijske teorije jednog polarona na 1D diskretnoj rešetki opisanoj Holsteinovim hamiltonijanom. Taj je hamiltonijan karakteriziran elektronskim preskokom t, fononskom frekvencijom ω0, i elektron-fononskim vezanjem g. Pokazali smo da su lokalizacijska (i translacijska) svojstva polarona sadržana u propagatoru jednog elektrona, privremeno dodanog rešetki, i/ili u fononskoj korelacijskoj funkciji s jednim elektronom stalno prisutnim u rešetki. Analiza po potencijama od g/ω0 pokazuje da razvoj elektronske ireducibilne vlastite energije odgovara razvoju fononske korelacijske funkcije, a ne razvoju fononske ireducibilne vlastite energije. Na taj je način određen doseg polaronskih korelacija. Za mali t/ω0, već u drugom redu po g/ω0 elektronreetka korelacija postaje vrlo kratkodosena, odnosno polaron je lokaliziran na jedno čvorište rešetke, iako opća translacijska simetrija ostaje sačuvana. Za veliki t/ω0 rezultat računa u drugom redu ostaje primjenjiv do velikih g/ω0 ≈ (t/ω0) 1/4 , gdje postaje degeneriran s rezultatom za veliki, adijabatski Holsteinov polaron. To naznačuje da translacijski invarijantna perturbacijska teorija tada prelazi glatko, bez loma simetrije, u adijabatsku kontinuiranu kvantnu granicu, što e biti rigorozno dokazano u članku-pratitelju. Kvantna teorija velikog adijabatskog Holsteinovog polarona, dakle, predstavlja jednostavan i poučan primjer kvantnog križanja koje zamjenjuje ponašanje u kvantnoj kritičnoj točki

Conductivity in a disordered one-dimensional system of interacting fermions

Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing d.c. transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the d.c. conductivity sigma0 scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase of the effective localization length with the interaction.Comment: 4 pages, 5 figures, submitted to PR

Thermal transport in a spin-1/2 Heisenberg chain coupled to a (non) magnetic impurity

We explore the effect of a (non) magnetic impurity on the thermal transport of the spin-1/2 Heisenberg chain model. This unique system allows to probe Kondo-type phenomena in a prototype strongly correlated system. Using numerical diagonalization techniques we study the scaling of the frequency dependent thermal conductivity with system size and host-impurity coupling strength as well as the dependence on temperature. We focus in particular on the analysis of cutting-healing of weak links or a magnetic impurity by the host chain via Kondo-like screening as the temperature is lowered.Comment: 7 pages, 12 figure