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Strongly Correlated Systems pp 271–302Cite as

Dynamical Cluster Approximation

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 171))

Abstract

The dynamical cluster approximation (DCA) is a method which systematically incorporates nonlocal corrections to the dynamical mean-field approximation. Here we present a pedagogical discussion of the DCA by describing it as a Φ-derivable coarse-graining approximation in k-space, which maps an infinite lattice problem onto a periodic finite-sized cluster embedded in a self-consistently determined effective medium. We demonstrate the method by applying it to the two-dimensional Hubbard model. From this application, we show evidences of the presence of a quantum critical point (QCP) at a finite doping underneath the superconducting dome. The QCP is associated with the second-order terminus of a line of first order phase separation transitions. This critical point is driven to zero temperature by varying the band parameters, generating the QCP. The effect of the proximity of the QCP to the superconducting dome is also discussed.

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Acknowledgments

We would like to thank S. Kivelson, Michael Ma, A. Macridin, P. Phillips, E. W. Plummer, D. J. Scalapino, C. Sen, J.-H. She, A. M. Tremblay, C. Varma, I. Vekhter, N. S. Vidhyadhiraja, M. Vojta, and J. Zaanen for useful conversations. This research was supported by NSF DMR-0312680, DMR-0706379, NSF OISE-0952300, DOE CMSN DE-FG02-04ER46129, and by the DOE SciDAC grant DE-FC02-06ER25792. This research used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803, USA

    H. Fotso, S. Yang, K. Chen, S. Pathak, J. Moreno & M. Jarrell

  2. Department of Physics, Georgetown University, Washington, DC, 20057, USA

    K. Mikelsons & E. Khatami

  3. Division of Physics and Applied Physics, Nanyang Technological University of Singapore, 21 Nanyang Link, Singapore, Singapore, 637371

    D. Galanakis

Authors
  1. H. Fotso
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  2. S. Yang
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  3. K. Chen
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  4. S. Pathak
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  6. M. Jarrell
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  7. K. Mikelsons
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  8. E. Khatami
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  9. D. Galanakis
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Correspondence to H. Fotso .

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Editors and Affiliations

  1. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Adolfo Avella

  2. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Ferdinando Mancini

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Fotso, H. et al. (2012). Dynamical Cluster Approximation. In: Avella, A., Mancini, F. (eds) Strongly Correlated Systems. Springer Series in Solid-State Sciences, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21831-6_9

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  • DOI: https://doi.org/10.1007/978-3-642-21831-6_9

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