Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons

Abstract

We present an extension of constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) for the treatment of correlated electronic systems coupled to phonons. The algorithm follows the standard CP-AFQMC approach for description of the electronic degrees of freedom while phonons are described in first quantization and propagated via a diffusion Monte Carlo approach. Our method is tested on the one-and two-dimensional Holstein and Hubbard-Holstein models. With a simple semiclassical trial wavefunction, our approach is remarkably accurate for ω/(2dtλ) < 1 for all parameters in the Holstein model considered in this study. In addition, we empirically show that the autocorrelation time scales as 1/ω for ω/t 1, which is an improvement over the 1/ω 2 scaling of the conventional determinant quantum Monte Carlo algorithm. In the Hubbard-Holstein model, the accuracy of our algorithm is found to be consistent with that of standard CP-AFQMC for the Hubbard model when the Hubbard U term dominates the physics of the model, and is nearly exact when the ground state is dominated by the electron-phonon coupling scale λ. The approach developed in this work should be valuable for understanding the complex physics arising from the interplay between electrons and phonons in both model lattice problems and ab-initio systems.

Spectral Functions from Auxiliary-Field Quantum Monte Carlo without Analytic Continuation: The Extended Koopmans’ Theorem Approach

“…Next, the extension of the EKT framework for finite-temperature coupled electronphonon problems would provide a way to compute temperature-dependent vibronic spectra directly from AFQMC. 101,108 We also leave the comparison of these EKT-based spectral functions to analytically continued spectral functions for a future study.…”

Antiferromagnetism induced by electron-phonon-coupling

“…Since unconventional SC is often closely related to antiferromagnetism [18][19][20][21][22][23], it is natural to ask whether EPC can play any essential role in driving AF ordering. Although various previous works have studied the competition between AF order dominantly induced by the Hubbard interactions and other types of orders such as CDW induced by EPC [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70], whether AF ordering can be induced dominantly by EPC remains elusive.…”