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Code and Method References

Code and Method References

The following list contains additional references for individual libraries, applications, and the implemented numerical methods:

ALPS codesNumerical Methods
  • The scheduler library
    • M. Troyer, Beat Ammon and Elmar Heeb, Parallel object oriented Monte Carlo Simulations, Lect. Notes Comput. Sci. 1505, 191 (1998).
    • The looper code
      • S. Todo and K. Kato, Cluster Algorithms for General-S Quantum Spin Systems, Phys. Rev. Lett. 87, 047203 (2001).
      • Clusters and Loops
        • The idea of cluster updates for quantum systems
          • H. G. Evertz, G. Lana, and M. Marcu, Cluster algorithm for vertex models, Phys. Rev. Lett. 70, 875 (1993).
        • The extension to continuous time
          • B. B. Beard and U.-J. Wiese, Simulations of Discrete Quantum Systems in Continuous Euclidean time, Phys. Rev. Lett. 77, 5130 (1996).
        • review/overview paper
          • H. G. Evertz, The loop algorithm, Adv. Phys. 52, 1 (2003).
      • The Directed Loop code in SSE representation
        • The code is mainly based on this paper
          • Fabien Alet, Stefan Wessel, and Matthias Troyer, Generalized directed loop method for quantum Monte Carlo simulations, Phys. Rev. E 71, 036706 (2005).
        • The paper introducing the operator loops (also implemented)
          • A. W. Sandvik, Stochastic series expansion method with operator-loop update, Phys. Rev. B 59, 14157 (1999).
        • and also these updates are implemented
          • L. Pollet, S. M. A. Rombouts, K. Van Houcke, and K. Heyde, Optimal Monte Carlo updating, Phys. Rev. E 70, 056705 (2004).
      • Stochastic Series Expansion (SSE)
        • The following two papers use local updates in the SSE framework
          • A. W. Sandvik and J. Kurkijärvi, Quantum Monte Carlo simulation method for spin systems, Phys. Rev. B 43, 5950 (1991).
          • A. W. Sandvik, A generalization of Handscomb’s quantum Monte Carlo scheme-application to the 1D Hubbard model, J. Phys. A 25, 3667 (1992).
        • The paper introducing the directed loops
          • O.F. Syljuåsen and A.W. Sandvik, Quantum Monte Carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
      • The worm algorithm
        • N.V. Prokof’ev, B.V. Svistunov, I.S. Tupitsyn, Exact, Complete and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems, Phys. Lett. A 238, 253 (1998), Sov. Phys. - JETP 87,310 (1998), cond-mat/9703200.
      • Non-local Updates
        • M. Troyer, F. Alet, S. Trebst, S. Wessel, Non-local Updates for Quantum Monte Carlo Simulations, AIP Conference Proceedings 690, 400 (2003).
      • Quantum Wang-Landau code
        • M. Troyer, S. Wessel, and F. Alet, Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy, Phys. Rev. Lett. 90, 120201 (2003).
      • The Density Matrix Renormalization Group (DMRG)
        • S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
        • S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
        • U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005).
        • Karen Hallberg, New Trends in Density Matrix Renormalization, Adv. Phys. 55, 477 (2006).
      • Continuous-Time quantum Monte Carlo impurity solver programs and the DMFT framework
        • E. Gull, P. Werner, S. Fuchs, B. Surer, T. Pruschke, and M. Troyer, Continuous-Time Quantum Monte Carlo Impurity Solvers, Computer Physics Communications 182, 1078 (2011).
      • Continous-time Monte Carlo methods for quantum impurity models
        • E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer and P. Werner, Continuous-time Monte Carlo methods for quantum impurity models, Rev. Mod. Phys. 83, 349–404 (2011)
      • Matrix product state applications and the MPS framework
        • M. Dolfi, B. Bauer, S. Keller, A. Kosenkov, T. Ewart, A. Kantian, T. Giamarchi, M. Troyer, Matrix product state applications for the ALPS project, Computer Physics Communications 185, 3430 (2014).
      • Density Matrix Renormalization Group (DMRG)
        • S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
        • Time evolution algorithms
          • G. Vidal, Efficient Simulation of One-Dimensional Quantum Many-Body Systems, Phys. Rev. Lett. 93, 040502 (2004).
          • S. R. White and A. E. Feiguin, Real-Time Evolution Using the Density Matrix Renormalization Group, Phys. Rev. Lett. 93, 076401 (2004).
          • A. J. Dale, C. Kollath, U. Schollwöck, G. Vidal, Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces, J. Stat. Mech.-Theory E. 2004, P04005 (2004).
        • Matrix Product State (MPS) formalism (a review)
          • U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (N.Y.) 326, 96 (2011).
      Papers