Elective-momentum ultrasize quantum Monte Carlo method

Zi Hong Liu, Xiao Yan Xu, Yang Qi, Kai Sun, and Zi Yang Meng
Phys. Rev. B 99, 085114 – Published 11 February 2019

Abstract

One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions, the best methodology at hand still scales with βN3 where β is the inverse temperature and N is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated electron models at (2+1)D, let alone (3+1)D. To reduce the computational complexity, we develop a new QMC method with inhomogeneous momentum-space mesh, dubbed elective-momentum ultrasize quantum Monte Carlo (EQMC) method. Instead of treating all fermionic excitations on an equal footing as in conventional QMC methods, by converting the fermion determinant into the momentum space, our method focuses on fermion modes that are directly associated with low-energy (IR) physics in the vicinity of the so-called hot spots, while other fermion modes irrelevant for universal properties are ignored. As shown in the paper, for any cutoff-independent quantities, e.g., scaling exponents, this method can achieve the same level of accuracy with orders of magnitude increase in computational efficiency. We demonstrate this method with a model of antiferromagnetic itinerant quantum critical point, realized via coupling itinerant fermions with a frustrated transverse-field Ising model on a triangle lattice. The system size of 48×48×32 (L×L×β, almost 3 times of previous investigations) are comfortably accessed with EQMC. With much larger system sizes, the scaling exponents are unveiled with unprecedentedly high accuracy, and this result sheds new light on the open debate about the nature and the universality class of itinerant quantum critical points.

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  • Received 3 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.085114

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zi Hong Liu1,2,*, Xiao Yan Xu3,*, Yang Qi4,5,6,†, Kai Sun7, and Zi Yang Meng1,8,9,‡

  • 1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
  • 3Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
  • 4Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China
  • 5State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
  • 6Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
  • 7Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 8CAS Center of Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
  • 9Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

  • *These authors have contributed equally to this work.
  • qiyang@fudan.edu.cn
  • zymeng@iphy.ac.cn

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Issue

Vol. 99, Iss. 8 — 15 February 2019

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