实现论文与算法论文
下面列出了各个 ALPS 应用程序的实现论文，以及它们所依据的原始算法论文。
如果 ALPS 对您发表的研究有所贡献，请引用下列相关的算法、实现和框架论文。 这是对学术贡献的引用请求，与 MIT 许可证条款无关。
- 算法: 请引用与计算相关的原始算法。
- 实现: 请引用计算中使用的 ALPS 实现和基础设施。
- 框架: 请引用最新的 ALPS 发布论文（即 CITATION.cff 中的 preferred-citation）。
ALPS 框架
框架论文
F. Alet, T. Chen, A. Feiguin, E. Gull, S. Iskakov, J. P. F. LeBlanc, F. Lin, A. Mirmira, G. Möller, L. Pollet, M. Rosales, V. W. Scarola, H. Shinaoka, H. Terletska, S. Todo, M. Troyer, M. Wallerberger, P. Werner, and T. M. R. Wolf, The ALPS project release 3.0: open source software for strongly correlated systems, arXiv:2610.03884 (2026).
ALPS 并行蒙特卡洛调度器 — scheduler
源代码: src/alps/scheduler
实现论文
M. Troyer, B. Ammon, and E. Heeb, Parallel Object Oriented Monte Carlo Simulations, in Computing in Object-Oriented Parallel Environments, Lecture Notes in Computer Science 1505, 191–198 (Springer, 1998).
ALPS 稀疏对角化 — sparsediag
实现论文
F. Alet, T. Chen, A. Feiguin, E. Gull, S. Iskakov, J. P. F. LeBlanc, F. Lin, A. Mirmira, G. Möller, L. Pollet, M. Rosales, V. W. Scarola, H. Shinaoka, H. Terletska, S. Todo, M. Troyer, M. Wallerberger, P. Werner, and T. M. R. Wolf, The ALPS project release 3.0: open source software for strongly correlated systems, arXiv:2610.03884 (2026).
算法论文
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 (1950).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 完全对角化 — fulldiag
实现论文
F. Alet, T. Chen, A. Feiguin, E. Gull, S. Iskakov, J. P. F. LeBlanc, F. Lin, A. Mirmira, G. Möller, L. Pollet, M. Rosales, V. W. Scarola, H. Shinaoka, H. Terletska, S. Todo, M. Troyer, M. Wallerberger, P. Werner, and T. M. R. Wolf, The ALPS project release 3.0: open source software for strongly correlated systems, arXiv:2610.03884 (2026).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 经典蒙特卡洛 — spinmc
源代码: src/apps/mc/spins
实现论文
F. Alet, T. Chen, A. Feiguin, E. Gull, S. Iskakov, J. P. F. LeBlanc, F. Lin, A. Mirmira, G. Möller, L. Pollet, M. Rosales, V. W. Scarola, H. Shinaoka, H. Terletska, S. Todo, M. Troyer, M. Wallerberger, P. Werner, and T. M. R. Wolf, The ALPS project release 3.0: open source software for strongly correlated systems, arXiv:2610.03884 (2026).
算法论文
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).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 圈算法量子蒙特卡洛 — looper
源代码: src/apps/qmc/looper
实现论文
S. Todo and K. Kato, Cluster Algorithms for General-S Quantum Spin Systems, Phys. Rev. Lett. 87, 047203 (2001).
算法论文
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).
ALPS 有向圈随机级数展开 — dirloop_sse
源代码: src/apps/qmc/sse, src/apps/qmc/sse2, src/apps/qmc/sse4
实现论文
F. Alet, S. Wessel, and M. Troyer, Generalized Directed Loop Method for Quantum Monte Carlo Simulations, Phys. Rev. E 71, 036706 (2005).
算法论文
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).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 蠕虫算法量子蒙特卡洛 — worm
源代码: src/apps/qmc/worms
实现论文
F. Alet, T. Chen, A. Feiguin, E. Gull, S. Iskakov, J. P. F. LeBlanc, F. Lin, A. Mirmira, G. Möller, L. Pollet, M. Rosales, V. W. Scarola, H. Shinaoka, H. Terletska, S. Todo, M. Troyer, M. Wallerberger, P. Werner, and T. M. R. Wolf, The ALPS project release 3.0: open source software for strongly correlated systems, arXiv:2610.03884 (2026).
算法论文
N. V. Prokof'ev, B. V. Svistunov, and I. S. Tupitsyn, “Worm” Algorithm in Quantum Monte Carlo Simulations, Phys. Lett. A 238, 253 (1998).
N. V. Prokof'ev, B. V. Svistunov, and I. S. Tupitsyn, Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems, J. Exp. Theor. Phys. 87, 310 (1998).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 量子 Wang-Landau — qwl
源代码: src/apps/qmc/qwl
实现论文
F. Alet, T. Chen, A. Feiguin, E. Gull, S. Iskakov, J. P. F. LeBlanc, F. Lin, A. Mirmira, G. Möller, L. Pollet, M. Rosales, V. W. Scarola, H. Shinaoka, H. Terletska, S. Todo, M. Troyer, M. Wallerberger, P. Werner, and T. M. R. Wolf, The ALPS project release 3.0: open source software for strongly correlated systems, arXiv:2610.03884 (2026).
算法论文
F. Wang and D. P. Landau, Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States, Phys. Rev. Lett. 86, 2050 (2001).
F. Wang and D. P. Landau, Determining the Density of States for Classical Statistical Models: A Random Walk Algorithm to Produce a Flat Histogram, Phys. Rev. E 64, 056101 (2001).
M. Troyer, S. Wessel, and F. Alet, Flat-Histogram Methods for Quantum Systems: Algorithms to Overcome Tunneling Problems and Calculate the Free Energy, Phys. Rev. Lett. 90, 120201 (2003).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 密度矩阵重整化群 — dmrg
源代码: src/apps/dmrg/dmrg
实现论文
A. E. Feiguin, The Density Matrix Renormalization Group, in Strongly Correlated Systems: Numerical Methods, edited by A. Avella and F. Mancini, Springer Series in Solid-State Sciences 176, 31–65 (Springer, 2013).
算法论文
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. A. Hallberg, New Trends in Density Matrix Renormalization, Adv. Phys. 55, 477 (2006).
另请引用: ALPS 并行蒙特卡洛调度器
ALPS 动力学平均场框架 — dmft
源代码: src/apps/dmft
实现论文
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).
算法论文
W. Metzner and D. Vollhardt, Correlated Lattice Fermions in d=∞ Dimensions, Phys. Rev. Lett. 62, 324 (1989).
A. Georges and G. Kotliar, Hubbard model in infinite dimensions, Phys. Rev. B 45, 6479 (1992).
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical Mean-Field Theory of Strongly Correlated Fermion Systems and the Limit of Infinite Dimensions, Rev. Mod. Phys. 68, 13 (1996).
注: 通过 DMFT 驱动程序使用杂质求解器时，也请引用相应求解器的文献。
ALPS CT-INT 杂质求解器 — interaction
源代码: src/apps/dmft/qmc/interaction_expansion, src/apps/dmft/qmc/interaction_expansion2
实现论文
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).
算法论文
A. N. Rubtsov, V. V. Savkin, and A. I. Lichtenstein, Continuous-Time Quantum Monte Carlo Method for Fermions, Phys. Rev. B 72, 035122 (2005).
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).
ALPS CT-HYB 杂质求解器 — hybridization
源代码: src/apps/dmft/qmc/hybridization
实现论文
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).
H. Hafermann, P. Werner, and E. Gull, Efficient implementation of the continuous-time hybridization expansion quantum impurity solver, Comput. Phys. Commun. 184, 1280 (2013).
算法论文
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).
ALPS Hirsch-Fye 杂质求解器 — hirschfye
源代码: src/apps/dmft/qmc/hirschfyesim.C
实现论文
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).
算法论文
J. E. Hirsch and R. M. Fye, Monte Carlo Method for Magnetic Impurities in Metals, Phys. Rev. Lett. 56, 2521 (1986).
ALPS maximum entropy analytic continuation (CQMP/Maxent) — maxent
实现论文
R. Levy, J. P. F. LeBlanc, and E. Gull, Implementation of the maximum entropy method for analytic continuation, Comput. Phys. Commun. 215, 149 (2017).
算法论文
R. K. Bryan, Maximum entropy analysis of oversampled data problems, European Biophysics Journal 18, 165 (1990).
M. Jarrell and J. E. Gubernatis, Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data, Physics Reports 269, 133 (1996).