Implementation and Algorithm Papers

The following lists the implementation papers for individual ALPS applications and the original algorithm papers on which they are based.

If ALPS contributes to published research, please cite the relevant algorithm, implementation, and framework papers below. This is a request for scientific credit, separate from the MIT license terms.

• Algorithms: Credit the original algorithms relevant to the calculation.
• Implementations: Credit the ALPS implementations and infrastructure used in the calculation.
• Framework: Cite the most recent ALPS release paper, recorded as preferred-citation in CITATION.cff.

ALPS framework

Framework paper

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 parallel Monte Carlo scheduler — scheduler

Source: src/alps/scheduler

Implementation papers

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 sparse diagonalization — sparsediag

Source: src/apps/diag/sparsediag

Implementation papers

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).

Algorithm papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS full diagonalization — fulldiag

Source: src/apps/diag/fulldiag

Implementation papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS classical Monte Carlo — spinmc

Source: src/apps/mc/spins

Implementation papers

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).

Algorithm papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS loop-cluster quantum Monte Carlo — looper

Source: src/apps/qmc/looper

Implementation papers

S. Todo and K. Kato, Cluster Algorithms for General-S Quantum Spin Systems, Phys. Rev. Lett. 87, 047203 (2001).

Algorithm papers

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 directed-loop stochastic series expansion — dirloop_sse

Source: src/apps/qmc/sse, src/apps/qmc/sse2, src/apps/qmc/sse4

Implementation papers

F. Alet, S. Wessel, and M. Troyer, Generalized Directed Loop Method for Quantum Monte Carlo Simulations, Phys. Rev. E 71, 036706 (2005).

Algorithm papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS worm-algorithm quantum Monte Carlo — worm

Source: src/apps/qmc/worms

Implementation papers

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).

Algorithm papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS quantum Wang-Landau — qwl

Source: src/apps/qmc/qwl

Implementation papers

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).

Algorithm papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS density matrix renormalization group — dmrg

Source: src/apps/dmrg/dmrg

Implementation papers

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).

Algorithm papers

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).

Also cite: ALPS parallel Monte Carlo scheduler

ALPS dynamical mean-field framework — dmft

Source: src/apps/dmft

Implementation papers

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).

Algorithm papers

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).

Note: Cite the relevant impurity-solver references as well when using a solver through the DMFT driver.

ALPS CT-INT impurity solver — interaction

Source: src/apps/dmft/qmc/interaction_expansion, src/apps/dmft/qmc/interaction_expansion2

Implementation papers

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).

Algorithm papers

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 impurity solver — hybridization

Source: src/apps/dmft/qmc/hybridization

Implementation papers

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).

Algorithm papers

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 impurity solver — hirschfye

Source: src/apps/dmft/qmc/hirschfyesim.C

Implementation papers

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).

Algorithm papers

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

Implementation papers

R. Levy, J. P. F. LeBlanc, and E. Gull, Implementation of the maximum entropy method for analytic continuation, Comput. Phys. Commun. 215, 149 (2017).

Algorithm papers

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).