Variational wave functions for spin-phonon models

Eugene P. Gross

Francesco Ferrari, Roser Valentí, Federico Becca

We introduce variational wave functions to evaluate the ground-state properties of spin-phonon coupled systems described by the Su-Schrieffer-Heeger model. Quantum spins and phonons are treated on equal footing within a Monte Carlo sampling, and different regimes are investigated. We show that the proposed variational Ansatz yields good agreement with previous density-matrix renormalization group results in one dimension and is able to accurately describe the spin-Peierls transition. This variational approach is constrained neither by the magnetoelastic-coupling strength nor by the dimensionality of the systems considered, thus allowing future investigations in more general cases, which are relevant to spin-liquid and topological phases in two spatial dimensions.

S.M. Weber-Milbrodt

Paolo Barone, Roberto Raimondi, Massimo Capone +2 more

We analyze the ground-state properties of strongly correlated electrons coupled with phonons by means of a generalized Gutzwiller wave function, which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wave function in describing the various transitions and crossovers that occur as a function of the parameters. Previous variational attempts are recovered as particular choices of the wave function, while keeping all the variational freedom allows to access regions of the phase diagram, otherwise inaccessible within previous variational approaches.

Paolo Barone, Roberto Raimondi, Massimo Capone +2 more

We introduce a new type of Gutzwiller variational wave function for correlated electrons coupled to phonons, able to treat on equal footing electronic and lattice degrees of freedom. We benchmark the wave function in the infinite- U Hubbard-Holstein model away from half-filling on a Bethe lattice, where we can directly compare with exact results by the Dynamical Mean-Field Theory. For this model, we find that variational results agree perfectly well with the exact ones. In particular the wave function correctly describes the crossover to a heavy polaron gas upon increasing the electron-phonon coupling.

Zoran M. Ivić, Dragan Kostić, D. Kapor