Phonon-Mediated Electron–Phonon Interaction in Hubbard–Holstein Model

Nath, S.; Ghosh, N. K.

doi:10.1007/s10909-015-1346-2

Cited by 12 publications

(2 citation statements)

References 43 publications

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“…Perhaps the most important opportunity enabled by CPT+DQMC is the possibility to study models that are not well suited to ED. For instance, strongly electronphonon coupled system involves huge Hilbert space and cannot be solved by pure ED [36][37][38][39][40]. However, both the Hilbert-space issue and the fermion-sign issue are absent for DQMC in the electron-phonon systems.…”

Section: The Spectral Function Is Extracted From the Relationmentioning

confidence: 99%

Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory

Huang¹,

Wang²

2021

Preprint

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Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings, CPT provides access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce Determinantal Quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study of temperature dependence, and enables large-scale simulations of a greater set of models. We discuss the implementation of the DQMC solver for CPT and benchmark the CPT+DQMC method for the attractive and repulsive Hubbard models, showcasing its advantages over standard DQMC and CPT+ED simulations.

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Section: The Spectral Function Is Extracted From the Relationmentioning

confidence: 99%

Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory

Huang¹,

Wang²

2021

Preprint

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“…These studies were followed by ED studies at zero temperature. However, due to the infinite Hilbert-space dimensions, these ED studies of HH model was restricted to a one-phonon truncation at small clusters 57,58 or single-phonon-mode simplification [59][60][61] . These calculations, though also exact, are highly restricted by the coupling strength and fillings due to the model simplification.…”

Section: Equilibrium Properties Of the Hubbard-holstein Modelmentioning

confidence: 99%

Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study

Wang,

Esterlis,

Shi

et al. 2019

Preprint

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We propose a novel numerical method which embeds the variational non-Gaussian wavefunction approach with 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 CDW-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.

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