Code and Method References

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

ALPS codes	Numerical 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 Citations