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Title: Self-learning quantum Monte Carlo method in interacting fermion systems

Authors:
; ; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1371802
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 4; Related Information: CHORUS Timestamp: 2017-07-18 22:13:36; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Xu, Xiao Yan, Qi, Yang, Liu, Junwei, Fu, Liang, and Meng, Zi Yang. Self-learning quantum Monte Carlo method in interacting fermion systems. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.041119.
Xu, Xiao Yan, Qi, Yang, Liu, Junwei, Fu, Liang, & Meng, Zi Yang. Self-learning quantum Monte Carlo method in interacting fermion systems. United States. doi:10.1103/PhysRevB.96.041119.
Xu, Xiao Yan, Qi, Yang, Liu, Junwei, Fu, Liang, and Meng, Zi Yang. 2017. "Self-learning quantum Monte Carlo method in interacting fermion systems". United States. doi:10.1103/PhysRevB.96.041119.
@article{osti_1371802,
title = {Self-learning quantum Monte Carlo method in interacting fermion systems},
author = {Xu, Xiao Yan and Qi, Yang and Liu, Junwei and Fu, Liang and Meng, Zi Yang},
abstractNote = {},
doi = {10.1103/PhysRevB.96.041119},
journal = {Physical Review B},
number = 4,
volume = 96,
place = {United States},
year = 2017,
month = 7
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 18, 2018
Publisher's Accepted Manuscript

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  • We study the single-particle spectral function of resonantly interacting fermions in the unitary regime, as described by the three-dimensional attractive Hubbard model in the dilute limit. Our approach, based on the dynamical cluster approximation and the maximum entropy method, shows the emergence of a gap with decreasing temperature, as reported in recent cold-atom photoemission experiments, for coupling values that span the BEC-BCS crossover. By comparing the behavior of the spectral function to that of the imaginary time dynamical pairing susceptibility, we attribute the development of the gap to the formation of local bound atom pairs.
  • Cited by 7
  • We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed node ground state wave function and (ii) to define a cost function that relates the interacting-ground-state-fixed-node and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wavemore » function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multi-determinant expansions of the trial wave function. The method can be generalized to other wave function forms such as pfaffians. We test the method in a model system where benchmark configuration interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77 245110 (2008)]. Tests of the method are extended to a model system with a conventional Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.« less