実装論文とアルゴリズム論文
以下に、個々の ALPS アプリケーションの実装論文と、それらの基礎となっている元のアルゴリズム論文を示します。
並列モンテカルロスケジューラ
実装論文
M. Troyer, B. Ammon, and E. Heeb, Parallel object oriented Monte Carlo Simulations, Lect. Notes Comput. Sci. 1505, 191 (1998).
厳密対角化と完全対角化 — sparsediag と fulldiag
ソース：applications/diag/sparsediag/, fulldiag/
実装論文
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. Pawłowski, 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, The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. 2011, P05001 (2011).
アルゴリズム論文
C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Natl. Bur. Stand. 45, 255-282 (1950).
スピンモデルのための古典モンテカルロ — spinmc
アルゴリズム論文
R. H. Swendsen and J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58, 86 (1987).
U. Wolff, Collective Monte Carlo updating for spin systems, Phys. Rev. Lett. 62, 361 (1989).
ループアルゴリズム QMC — looper
実装論文
S. Todo and K. Kato, Cluster Algorithms for General-S Quantum Spin Systems, Phys. Rev. Lett. 87, 047203 (2001).
アルゴリズム論文
H. G. Evertz, G. Lana, and M. Marcu, Cluster algorithm for vertex models, Phys. Rev. Lett. 70, 875 (1993).
B. B. Beard and U.-J. Wiese, Simulations of Discrete Quantum Systems in Continuous Euclidean Time, Phys. Rev. Lett. 77, 5130 (1996).
H. G. Evertz, The loop algorithm, Adv. Phys. 52, 1 (2003).
SSE 表示によるディレクテッドループコード — dirloop_sse
ソース：applications/qmc/sse/, sse2/, sse4/
実装論文
F. Alet, S. Wessel, and M. Troyer, Generalized directed loop method for quantum Monte Carlo simulations, Phys. Rev. E 71, 036706 (2005).
アルゴリズム論文
A. W. Sandvik, Stochastic series expansion method with operator-loop update, Phys. Rev. B 59, R14157 (1999).
O. F. Syljuåsen and A. W. Sandvik, Quantum Monte Carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
ワームコード — worms
アルゴリズム論文
N. V. Prokof’ev, B. V. Svistunov, and I. S. Tupitsyn, “Worm” algorithm in quantum Monte Carlo simulations, Phys. Lett. A 238, 253 (1998).
量子 Wang-Landau フラットヒストグラム QMC — qwl
実装論文
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).
DMFT：CT-QMC 不純物ソルバーと動的平均場理論 — dmft、interaction、hybridization
実装論文
E. Gull, P. Werner, S. Fuchs, B. Surer, T. Pruschke, and M. Troyer, Continuous-Time Quantum Monte Carlo Impurity Solvers, Comput. Phys. Commun. 182, 1078 (2011).
アルゴリズム論文
A. N. Rubtsov, V. V. Savkin, and A. I. Lichtenstein, Continuous-time quantum Monte Carlo method for fermions, Phys. Rev. B 72, 035122 (2005).
P. Werner, A. Comanac, L. de’ Medici, M. Troyer, and A. J. Millis, Continuous-Time Solver for Quantum Impurity Models, Phys. Rev. Lett. 97, 076405 (2006).
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 (2011).
DMRG — dmrg
実装論文
A. E. Feiguin, The Density Matrix Renormalization Group. In: A. Avella and F. Mancini (eds.), Strongly Correlated Systems, Springer Series in Solid-State Sciences 176, 31–65 (2013).
アルゴリズム論文
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).
K. Hallberg, New Trends in Density Matrix Renormalization, Adv. Phys. 55, 477 (2006).