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arXiv:2208.07205 · Physical review. B./Physical review. B

Full configuration interaction quantum Monte Carlo for coupled electron-boson systems and infinite spaces

Robert J. Anderson, Charles J. C. Scott, George H. Booth

Published Oct 31, 2022• 4 citations
arXivHTMLPDF

Abstract

When electrons interact not only with themselves, but also with bosons (phonons or other bosonic quasiparticles), what was previously a ``curse of dimensionality'' for its computational solution now becomes one of infinite size. To deal with this, the authors adapt here a recent method for its stochastic solution, without requiring truncation of the bosonic occupations, and which allows systematic improvability to exact solutions. They apply this to the paradigmatic Hubbard-Holstein model of local phonons, finding a state-of-the-art solution in the thermodynamic limit, as well as to a novel approach in which long-range collective electronic fluctuations are mapped to bosonic quasiparticles to tackle even long-range interacting problems of purely electronic form.

DOI
10.1103/physrevb.106.155158

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When electrons interact not only with themselves, but also with bosons (phonons or other bosonic quasiparticles), what was previously a ``curse of dimensionality'' for its computational solution now becomes one of infinite size. To deal with this, the authors adapt here a recent method for its stochastic solution, without requiring truncation of the bosonic occupations, and which allows systematic improvability to exact solutions. They apply this to the paradigmatic Hubbard-Holstein model of local phonons, finding a state-of-the-art solution in the thermodynamic limit, as well as to a novel approach in which long-range collective electronic fluctuations are mapped to bosonic quasiparticles to tackle even long-range interacting problems of purely electronic form.
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Recent studies of pairing and charge order in materials such as FeSe, SrTiO3_33​, and 2H-NbSe2_22​ have suggested that momentum dependence of the electron-phonon coupling plays an important role in their properties. Initial attempts to study Hamiltonians which either do not include or else truncate the range of Coulomb repulsion have noted that the resulting spatial non-locality of the electron-phonon interaction leads to a dominant tendency to phase separation. Here we present Quantum Monte Carlo results for such models in which we incorporate both on-site and intersite electron-electron interactions. We show that these can stabilize phases in which the density is homogeneous and determine the associated phase boundaries. As a consequence, the physics of momentum dependent electron-phonon coupling can be determined outside of the trivial phase separated regime.
Monte Carlo simulations are performed to examine superconductivity and charge-density-wave fluctuations in the infinite-dimensional electron-phonon Holstein model. The electron-phonon system interpolates between an attractive, static, Falicov-Kimball model that always exhibits charge-density-wave order and an attractive, instantaneous, Hubbard model that always superconducts as a function of phonon frequency. The maximum charge-density-wave transition temperature at half-filling is an order of magnitude smaller than the effective electronic bandwidth and is virtually independent of the phonon frequency. The maximum superconducting transition temperature depends strongly on phonon frequency and is bounded from above by the maximum charge-density-wave transition temperature. The exact solution is compared to both weak-coupling expansions and strong-coupling expansions. The effective phonon potential becomes anharmonic and develops a double-well structure that deepens as the electron-phonon interaction increases.
This work deals with the development and application of novel quantum Monte Carlo methods to simulate fermion-boson models. Our developments are based on the path-integral formalism, where the bosonic degrees of freedom are integrated out exactly to obtain a retarded fermionic interaction. We give an overview of three methods that can be used to simulate retarded interactions. In particular, we develop a novel quantum Monte Carlo method with global directed-loop updates that solves the autocorrelation problem of previous approaches and scales linearly with system size. We demonstrate its efficiency for the Peierls transition in the Holstein model and discuss extensions to other fermion-boson models as well as spin-boson models. Furthermore, we show how with the help of generating functionals bosonic observables can be recovered directly from the Monte Carlo configurations. This includes estimators for the boson propagator, the fidelity susceptibility, and the specific heat of the Holstein model. The algorithmic developments of this work allow us to study the specific heat of the spinless Holstein model covering its entire parameter range. Its key features are explained from the single-particle spectral functions of electrons and phonons. In the adiabatic limit, the spectral properties are calculated exactly as a function of temperature using a classical Monte Carlo method and compared to results for the Su-Schrieffer-Heeger model.