Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] aeol_v1_0.tar.gz(20071 Kbytes)
Manuscript Title: Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
Authors: Hartmut Hafermann, Philipp Werner, Emanuel Gull
Program title: ct-hyb
Catalogue identifier: AEOL_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)1280
Programming language: C++/Python.
Computer: Desktop PC, high-performance computers.
Operating system: Unix, Linux, OSX, Windows.
Has the code been vectorised or parallelized?: Yes, MPI parallelized.
RAM: 1 GB
Keywords: DMFT, CT-QMC, CT-HYB.
Classification: 7.3.

External routines: ALPS [1, 2, 3], BLAS [4, 5], LAPACK [6], HDF5 [7]

Nature of problem:
Quantum impurity models were originally introduced to describe a magnetic transition metal ion in a nonmagnetic host metal. They are widely used today. In nanoscience they serve as representations of quantum dots and molecular conductors. In condensed matter physics, they are playing an increasingly important role in the description of strongly correlated electron materials, where the complicated many-body problem is mapped onto an auxiliary quantum impurity model in the context of dynamical mean-field theory and its cluster and diagrammatic extensions.
The quantum impurity model still constitutes a nontrivial many-body problem, which takes into account the (possibly retarded) interaction between electrons occupying the impurity site. Electrons are allowed to dynamically hop on and off the impurity site, which is described by a time-dependent hybridization function.

Solution method:
The quantum impurity model is solved using a continuous-time quantum Monte Carlo algorithm which is based on a perturbation expansion of the partition function in the impurity-bath hybridization. Monte Carlo configurations are represented as segments on the imagery time interval and individual terms correspond to Feynman diagrams which are stochastically sampled to all orders using a Metropolis algorithm. For a detailed review on the method we refer the reader to [8].

Running time:
1h - 8h

References:
[1] B. Bauer, L. D. Carr, H. G. Evertz, A. Feiguin, J. Freire, S. Fuchs, L. Gamper, J. Gukelberger, E. Gull, S. Guertler, A. Hehn, R. Igarashi, S. V. Isakov, D. Koop, P. N. Ma, P. Mates, H. Matsuo, O. Parcollet, G. Pawlowski, J. D. Picon, L. Pollet, E. Santos, V. W. Scarola, U. Schollwöck, C. Silva, B. Surer, S. Todo, S. Trebst, M. Troyer, M. L. Wall, P. Werner and S.Wessel, Journal of Statistical Mechanics: Theory and Experiment 2011, P05001 (2011).
[2] F. Alet, P. Dayal, A. Grzesik, A. Honecker, M. Körner, A. Läuchli, S. R. Manmana, I. P. McCulloch, F. Michel, R. M. Noack, G. Schmid, U. Schollwöck, F. Stöckli, S. Todo, S. Trebst, M. Troyer, P. Werner, and S. W. collaboration, J. Phys. Soc. Jpn. 74S, 30 (2005).
[3] A. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S. Gürtler, A. Honecker, R. Igarashi, M. Körner, A. Kozhevnikov, A. Läuchli, S. Manmana, M. Matsumoto, I. McCulloch, F. Michel, R. Noack, G. Pawlowski, L. Pollet, T. Pruschke, U. Schollwöck, S. Todo, S. Trebst, M. Troyer, P. Werner and S. Wessel, J. Magn. Magn. Mater. 310, 1187 (2007), proceedings of the 17th International Conference on Magnetism { The International Conference on Magnetism.
[4] C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh, ACM Transactions on Mathematical Software 5, 324 (1979).
[5] L. S. Blackford, J. Demmel, I. Du, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, and R. C. Whaley, ACM Trans. Math. Softw. 28, 135 (2002).
[6] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999).
[7] The HDF Group, \Hierarchical data format version 5," http://www.hdfgroup.org/HDF5 (2000-2010).
[8] E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer and P. Werner, Rev. Mod. Phys. 83, 349 (2011).