اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConstrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
285
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization err
ors, and is particularly useful as impurity solver in large cluster dynamical mean field theory (DMFT) calculations.
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 stren
gths 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.
We introduce a new numerical technique -- bosonic auxiliary-field Monte Carlo (bAFMC) -- which allows to calculate the thermal properties of large lattice-boson systems within a systematically improvable semiclassical approach, and which is virtually
applicable to any bosonic model. Our method amounts to a decomposition of the lattice into clusters, and to an Ansatz for the density matrix of the system in the form of a cluster-separable state -- with non-entangled, yet classically correlated clusters. This approximation eliminates any sign problem, and can be systematically improved upon by using clusters of growing size. Extrapolation in the cluster size allows to reproduce numerically exact results for the superfluid transition of hardcore bosons on the square lattice, and to provide a solid quantitative prediction for the superfluid and chiral transition of hardcore bosons on the frustrated triangular lattice.
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N -body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonst
rate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the en
ergy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques implemented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences shows a quantitative connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
