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Title: Interlaced coarse-graining for the dynamic cluster approximation

Journal Article · · Physical Review. B
 [1];  [2];  [2];  [2];  [3]
  1. IBM Research–Zurich (Switzerland)
  2. Eidgenoessische Technische Hochschule, Zurich (Switzerland)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
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The dynamical cluster approximation (DCA) and its DCA+ extension use coarse-graining of the momentum space to reduce the complexity of quantum many-body problems, thereby mapping the bulk lattice to a cluster embedded in a dynamical mean-field host. In this work, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. While it gives a more localized self-energy for a given cluster size, we show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which converge to the results obtained from the standard coarse-graining with increasing cluster size. Most importantly, the new coarse-graining reduces the severity of the fermionic sign problem of the underlying quantum Monte Carlo cluster solver and thus allows for calculations on larger clusters. This enables the treatment of correlations longer ranged than those accessible with the standard coarse-graining and thus can allow for the evaluation of the exact infinite cluster size result via finite size scaling. As a demonstration, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the extended DCA+ algorithm permits the determination of the superconducting Tc on cluster sizes for which the results can be fit with a Kosterlitz-Thouless scaling law.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF) and Center for Nanophase Materials Science (CNMS)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1565496
Alternate ID(s):
OSTI ID: 1249932
Journal Information:
Physical Review. B, Vol. 93, Issue 16; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

References (15)

Fictive impurity models: An alternative formulation of the cluster dynamical mean-field method journal November 2003
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Structure of the Pairing Interaction in the Two-Dimensional Hubbard Model journal February 2006
Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model journal October 2010
Dynamical cluster approximation with continuous lattice self-energy journal September 2013
Nonlocal dynamical correlations of strongly interacting electron systems journal September 1998
Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the two-dimensional Hubbard model journal May 2014
Sign problem in the numerical simulation of many-electron systems journal May 1990
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations journal May 2005
Monte Carlo calculations of coupled boson-fermion systems. I journal October 1981
Continuous-time auxiliary-field Monte Carlo for quantum impurity models journal May 2008
Quantum cluster theories journal October 2005
Quantum Monte Carlo algorithm for nonlocal corrections to the dynamical mean-field approximation journal October 2001
Submatrix updates for the continuous-time auxiliary-field algorithm journal February 2011
Momentum space anisotropy and pseudogaps: a comparative cluster dynamical mean field analysis of the doping-driven metal-insulator transition in the two dimensional Hubbard model text January 2010

Cited By (1)

Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t ′ journal September 2019

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