Abstract
We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wavefunction that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wavefunction exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.
Highlights
Correlated systems pose important theoretical questions about the nature of interacting systems at intermediate and strong coupling
The benchmarks with exact solutions obtained from determinant QMC (DQMC) and extreme limits in the Holstein model demonstrate that the non-Gaussian exact diagonalization (NGSED) method can adequately evaluate the coupling to phonons, though both the non-Gaussian transformation and phonon states are restricted to a variational subspace of the entire Hilbert space
We have presented NGSED, a wave-function-based method used to treat systems with both e-e and e-ph interactions, taking advantage of both variational non-Gaussian transformations and exact diagonalization
Summary
Correlated systems pose important theoretical questions about the nature of interacting systems at intermediate and strong coupling. The inclusion of the full electronic Hilbert space and many-body wave function addresses the fluctuation issue of pure variational approaches, reducing the bias incurred by a mean-field treatment of the correlated electronic state. A natural extension is the embedding of a variational phonon wave function and polaron transformation into an exact numerical technique: this forms the intuition of our NGSED method. We identify a region between AFM and chargedensity-wave (CDW) states in which both charge and spin orders are absent This region can further be divided: one subregion has enhanced charge susceptibility and considerable binding energy, possibly corresponding to a two-dimensional (2D) analog of the Luther-Emery liquid observed in the onedimensional (1D) Hubbard-Holstein model [36]; the other subregion exhibits superconductivity at the weak-coupling side but gradually becomes metallic for stronger coupling. IV, together with the outlook of this method for other systems
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