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Register a new userA coupled cluster framework for electrons and phonons
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We describe a coupled cluster framework for coupled systems of electrons and phonons. Neutral and charged excitations are accessed via the equation-of-motion version of the theory. Benchmarks on the Hubbard-Holstein model allow us to assess the strengths and weaknesses of different coupled cluster approximations which generally perform well for weak to moderate coupling. Finally, we report progress towards an implementation for {it ab initio} calculations on solids, and present some preliminary results on finite-size models of diamond. We also report the implementation of electron-phonon coupling matrix elements from crystalline Gaussian type orbitals (cGTO) within the PySCF program package.
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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 $omega/(2text{d}tlambda) < 1$ for all parameters in the Holstein model considered in this study. In addition, we empirically show that the autocorrelation time scales as $1/omega$ for $omega/t lesssim 1$, which is an improvement over the $1/omega^2$ 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 $lambda$. 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.
We use coupled-cluster quantum chemical methods to calculate the energetics of molecular clusters cut out of periodic molecular hydrogen structures that model observed phases of solid hydrogen. The hydrogen structures are obtained from Kohn-Sham density functional theory (DFT) calculations at pressures of 150, 250 and 350 GPa, which are within the pressure range in which phases II, III and IV are found to be stable. The calculated deviations in the DFT energies from the coupled-cluster data are reported for different functionals, and optimized functionals are generated which provide reduced errors. We give recommendations for semi-local and hybrid density functionals that are expected to accurately describe hydrogen at high pressures.
First-principles calculations combining density functional theory and many-body perturbation theory can provide microscopic insight into the dynamics of electrons and phonons in materials. We review this theoretical and computational framework, focusing on perturbative treatments of scattering, dynamics and transport of coupled electrons and phonons. We discuss application of these first-principles calculations to electronics, lighting, spectroscopy and renewable energy.
We present a rigorous and efficient approach to the calculation of classical lattice-dynamical quantities from simulations that do not require an explicit solution of the time evolution. We focus on the temperature-dependent vibrational spectrum. We start from the moment expansion of the relevant time-correlation function for a many-body system, and show that it can be conveniently rewritten by using a basis in which the low-order moments are diagonal. This allows us to compute the main spectral features (e.g., position and width of the phonon peaks) from thermal averages available from any statistical simulation. We successfully apply our method to a model system that presents a structural transition and strongly temperature-dependent phonons. Our theory clarifies the status of previous heuristic schemes to estimate phonon frequencies.
Coupled cluster (CC) has established itself as a powerful theory to study correlated quantum many-body systems. Finite temperature generalizations of CC theory have attracted considerable interest and have been shown to work as well as the ground-sate theory. However, most of these recent developments address only fermionic or bosonic systems. The distinct structure of the $su(2)$ algebra requires the development of a similar thermal CC theory for spin degrees of freedom. In this paper, we provide a formulation of our thermofield-inspired thermal CC for SU(2) systems. We apply the thermal CC to the Lipkin-Meshkov-Glick system as well as the one-dimensional transverse field Ising model as benchmark applications to highlight the accuracy of thermal CC in the study of finite-temperature phase diagram in SU(2) systems.
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