From ALPS Algorithms and Libraries for Physics Simulations

Contents 1 Papers and Talks 1.1 ALPS references 1.2 Code and method references 1.3 Talks 1.4 Papers citing the ALPS project 1.5 Textbook references to the ALPS project

[edit] Papers and Talks

[edit] ALPS references

The ALPS project has been outlined in a series of manuscripts which now serve as the standard reference for the ALPS project. For the current release (1.3) and higher please cite the manuscript:

F. Albuquerque et al. (ALPS collaboration)

The ALPS project release 1.3: open source software for strongly correlated systems

Journal of Magnetism and Magnetic Materials 310, 1187 (2007).

For earlier versions please give a reference to:

F. Alet et al. (ALPS collaboration)

The ALPS project: open source software for strongly correlated systems

J. Phys. Soc. Jpn. Suppl. 74, 30 (2005).

[edit] 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 1) 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) 2) A. W. Sandvik Stochastic series expansion method with operator-loop update Phys. Rev. B 59, 14157 (1999). and also these updates are implemented 3) 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 code	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).	Extended ensemble simulations
The DMRG code	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).

[edit] Talks

The following is a collection of talks on the ALPS project and talks from the user and developer workshops.

• Talks from the user workshop in Lugano

• Talks from the tutorial at PSI (Sep. 2006)
• ALPS Overview (M. Troyer)
• Introduction to ALPS XML [PDF] [Keynote] (S. Todo)
• Exact Diagonalization (M. Troyer)
• The ALPS project : talk in Taipei(PDF) (L. Pollet)
• Introduction to Monte Carlo at PSI [PDF] (L. Pollet)
• Quantum Monte Carlo [PDF] (F. Alet)

[edit] Papers citing the ALPS project

search recent citations

85) A. Fabricio Albuquerque, Chris J. Hamer, Jaan Oitmaa
Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy
arXiv: 0811.0646

84) Philipp Werner, Takashi Oka, Andrew J. Millis
Diagrammatic Monte Carlo simulation of non-equilibrium systems
arXiv: 0810.2345

83) C. Gils, E. Ardonne, S. Trebst, A. W. W. Ludwig, M. Troyer, Z. Wang
Topological stability of anyonic quantum spin chains and formation of new topological liquids
arXiv:0810.2277

82) Keisuke Matsuda, Shin Miyahara, and Nobuo Furukawa
Projection Method for Exact Diagonalization in the Strong Coupling Limit for Frustrated Models with Highly Degenerate Ground States
J. Phys. Soc. Jpn. 77, 085002 (2008).

81) Stefan Wessel
Mixed columnar-plaquette phase of hard-core bosons and its quantum melting
Phys. Rev. B 78, 075112 (2008).

80) Sandro Wenzel and Wolfhard Janke
Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
Phys. Rev. B 78, 064402 (2008).

79) O. Zaharko, et al.
New structural and magnetic aspects of the nanotube system Na2V3O7
arXiv:0809.1248

78) B. Thielemann, et al.
Transition from a Spin Luttinger-Liquid to a Bose-Einstein Condensate of Magnons in the Quantum Spin Ladder (C5H12N)2CuBr4
arXiv:0809.0440

77) Ping Nang Ma, Kai Yu Yang, Lode Pollet, J. V. Porto, Matthias Troyer, and Fu Chun Zhang
Influence of the trap shape on the detection of the superfluid—Mott-insulator transition
Phys. Rev. A 78, 023605 (2008).

76) Zi Yang Meng and Stefan Wessel
Phases and magnetization process of an anisotropic Shastry-Sutherland model
arXiv:0808.3104

75) V.W. Scarola, K.B. Whaley, M. Troyer
Thermal Canting of Spin-Bond Order
arXiv:0808.1748

74) Daisuke Yamamoto, Synge Todo, Susumu Kurihara
Green's function theory for spin-1/2 ferromagnets with an easy-plane exchange anisotropy
arXiv:0802.0559

73) G. Roux, S. Capponi, P. Lecheminant, P. Azaria
Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and effect of the trap
arXiv:0807.0412

72) Synge Todo and Akira Shibasaki
Improved chain mean-field theory for quasi-one-dimensional quantum magnets
arXiv:0805.3097

71) A. Fabricio Albuquerque, Matthias Troyer, Jaan Oitmaa
Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions
Phys. Rev. B 78, 132402 (2008)

70) J.-D. Picon, A. F. Albuquerque, K. P. Schmidt, N. Laflorencie, M. Troyer, F. Mila
Mechanisms for Spin-Supersolidity in S=1/2 Spin-Dimer Antiferromagnets
Phys. Rev. B 78, 184418 (2008)

69) G. Pawlowski
Quantum spin system with on-site exchange in a magnetic field
Materials Science-Poland 25, 565 (2007).

68) Philipp Werner, Emanuel Gull, Matthias Troyer, Andrew J. Millis
Spin freezing transition in a 3-orbital model: non-Fermi-liquid self energy and possible implications for the optical conductivity of SrRuO3
Phys. Rev. Lett. 101, 166405 (2008).

67) Gang Chen and Leon Balents
Spin-orbit effects in Na₄Ir₃O₈, a hyper-kagome lattice antiferromagnet
Phys. Rev. B 78, 094403 (2008).

66) D. Charrier, F. Alet, P. Pujol
Gauge theory picture of an ordering transition in a dimer model
Phys. Rev. Lett. 101, 167205 (2008)

65) Emanuel Gull, Philipp Werner, Matthias Troyer, A. J. Millis
Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation
EPL 84, 37009 (2008).

64) Matthias Troyer, Simon Trebst, Kirill Shtengel, and Chetan Nayak
Local interactions and non-Abelian quantum loop gases
Phys. Rev. Lett. 101, 230401 (2008)

63) K.P. Schmidt, J. Dorier, and A.M. Läuchli
Solids and supersolids of three-body interacting polar molecules in an optical lattice
Phys. Rev. Lett. 101, 150405 (2008).

62) D. N. Sheng, Olexei I. Motrunich, Simon Trebst, Emanuel Gull, and Matthew P.A. Fisher
Strong-Coupling Phases of Frustrated Bosons on a 2-leg Ladder with Ring Exchange
Phys. Rev. B 78, 054520 (2008).

61) Gregoire Misguich, Vincent Pasquier, and Fabien Alet
Correlations and order parameter at a Coulomb-crystal phase transition
Phys. Rev. B 78, 100402(R) (2008).

60) G.J. Nielsen, H.M. Ronnow, A.M. Läuchli, F.P.A. Fabbiani, J. Sanchez-Benitez, K.V. Kamenev, and A. Harrison
A new realisation of the S=1/2 frustrated chain antiferromagnet
Chem. Mater. 20, 8 (2008).

59) Emanuel Gull, Philipp Werner, Olivier Parcollet, and Matthias Troyer
Continuous-time auxiliary field Monte Carlo for quantum impurity models
EPL 82, 57003 (2008).

58) Kouki Fukui and Synge Todo
Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
arXiv:0802.0272

57) Austen Lamacraft and Paul Fendley
Order parameter statistics in the critical quantum Ising chain
Phys. Rev. Lett. 100, 165706 (2008).

56) S. Trebst, E. Ardonne, A. Feiguin, D. A. Huse, A. W. W. Ludwig, M. Troyer
Collective States of Interacting Fibonacci Anyons
Phys. Rev. Lett. 101, 050401 (2008).

55) A.N. Rudenko, V.V. Mazurenko, V.I. Anisimov, and A.I. Lichtenstein
Weak ferromagnetism in Mn nanochains on the CuN surface
arXiv:0801.2857

54) Andreas Honecker and Josef Schüle
OpenMP Implementation of the Householder Reduction for Large Complex Hermitian Eigenvalue Problems
pp. 271-278 in NIC Series Volume 38: C. Bischof et al. (Eds.) (2007).

53) S. Demeshko, G. Leibeling, S. Dechert, S. Fuchs, T. Pruschke, and F. Meyer
Alternating Spin Chains: Controlled Assembly from Bimetallic Building Blocks and QMC Simulation of Spin Correlation
ChemPhysChem 8, 405 (2007).

52) Siegfried Guertler, Matthias Troyer, and Fu-Chun Zhang
Quantum Monte Carlo study of a two-species bosonic Hubbard model
Phys. Rev. B 77, 184505 (2008).

51) Andreas Läuchli, Sylvain Capponi, and Fakher F. Assaad
Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points
J. Stat. Mech. P01010 (2008).

50) Ping Nang Ma, Lode Pollet, Matthias Troyer, Fu Chun Zhang
A classical picture of the role of vacancies and interstitials in Helium-4
J. Low Temp. Phys. 152, 156 (2008).

49) S. Wessel, N. Stoop, E. Gull, S. Trebst, M. Troyer
Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems
J. Stat. Mech. P12005 (2007).

48) D.V.Dmitriev and V.Ya.Krivnov
Weakly anisotropic frustrated zigzag spin chain
Phys. Rev. B 77, 024401 (2008).

47) Simon Anders, Hans J. Briegel, Wolfgang Dür
A variational method based on weighted graph states
New J. Phys. 9, 361 (2007).

46) A. Fabricio Albuquerque, Helmut G. Katzgraber, Matthias Troyer, and Gianni Blatter
Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models
Phys. Rev. B 78, 014503 (2008).

45) Franz Michel and Hans-Gerd Evertz
Lattice dynamics of the Heisenberg chain coupled to finite frequency bond phonons
arXiv:0705.0799

44) C. Brünger, F. F. Assaad, S. Capponi, F. Alet, D. N. Aristov, and M. N. Kiselev
Spin Gap and String Order Parameter in the Ferromagnetic Spiral Staircase Heisenberg Ladder: A Quantum Monte Carlo Study
Phys. Rev. Lett. 100, 017202 (2008).

43) K.P. Schmidt, J. Dorier, A.M. Läuchli, and F. Mila
Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets
Phys. Rev. Lett. 100, 090401 (2008).

42) Steven R. White and A.L. Chernyshev
Neel order in square and triangular lattice Heisenberg models
Phys. Rev. Lett. 99, 127004 (2007).

41) Stefan Wessel
Phase Diagram of Interacting Bosons on the Honeycomb Lattice
Phys. Rev. B 75, 174301 (2007).

40) S. Henning, F. Koermann, J. Kienert, S. Schwieger and W. Nolting
Green function theory versus Quantum Monte Carlo calculations for thin magnetic films
Phys. Rev. B 75, 214401 (2007).

39) Fa Wang, Ashvin Vishwanath, and Yong Baek Kim
Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite
Phys. Rev. B 76, 094421 (2007).

38) Philipp Werner and Andrew J. Millis
High-spin to low-spin and orbital polarization transitions in multiorbital Mott systems
Phys. Rev. Lett. 99, 126405 (2007).

37) Yoshitaka Maeda, Chisa Hotta, Masaki Oshikawa
Universal temperature dependence of the magnetization of gapped spin chains
Phys. Rev. Lett. 99, 057205 (2007).

36) Sergei L. Lukyanov and Philipp Werner
Resistively shunted Josephson junctions: QFT predictions versus MC results
J. Stat. Mech. P06002 (2007).

35) Fabien Alet, Sylvain Capponi, Nicolas Laflorencie, and Matthieu Mambrini
Valence Bond Entanglement Entropy
Phys. Rev. Lett. 99, 117204 (2007).

34) Philipp Werner and Andrew J. Millis
Efficient DMFT-simulation of the Holstein-Hubbard Model
Phys. Rev. Lett. 99, 146404 (2007).

33) Vassilis Tangoulis
Monte Carlo Studies of a Mn^II Molecular System with a 2D trellis layer coupled-ladder configuration
Chem. Phys. 332, 271 (2007).

32) A. Feiguin, S. Trebst, A. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. Freedman
Interacting anyons in topological quantum liquids: The golden chain
Phys. Rev. Lett. 98, 160409 (2007).

31) Doron Bergman, Jason Alicea, Emanuel Gull, Simon Trebst, Leon Balents
Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
Nature Physics 3, 487 (2007).

30) Zengo Tsuboi
A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain
Physica A 377, 95 (2007).

29) Philipp Werner and Andrew J. Millis
Doping-driven Mott transition in the one-band Hubbard model
Phys. Rev. B 75, 085108 (2007).

28) Emanuel Gull, Philipp Werner, Andrew J. Millis, and Matthias Troyer
Performance analysis of continuous-time solvers for quantum impurity models
Phys. Rev. B 76, 235123 (2007).

27) Karen Hallberg
New Trends in Density Matrix Renormalization
Adv. Phys. 55, 477 (2006).

26) Simon Trebst, Philipp Werner, Matthias Troyer, Kirill Shtengel, and Chetan Nayak
Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
Phys. Rev. Lett. 98, 070602 (2007).

25) Fabien Alet, Yacine Ikhlef, Jesper Lykke Jacobsen, Gregoire Misguich, and Vincent Pasquier
Classical dimers with aligning interactions on the square lattice
Phys. Rev. E 74, 041124 (2006).

24) K.P. Schmidt, J. Dorier, A. Läuchli, and F. Mila
Single-particle versus pair condensation of hard-core bosons with correlated hopping
Phys. Rev. B 74, 174508 (2006).

23) Corinna Kollath, Andreas Läuchli, and Ehud Altman
Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
Phys. Rev. Lett. 98, 180601 (2007).

22) Philipp Werner and Andrew J. Millis
Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
Phys. Rev. B 74, 155107 (2006).

21) M. Lewenstein et al.
Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond
Advances in Physics 56, 243 (2007).

20) Synge Todo
Universal Reduction of Effective Coordination Number in the Quasi-One-Dimensional Ising Model
Phys. Rev. B 74, 104415 (2006).

19) Sergei L. Lukyanov and Philipp Werner
Universal scaling behavior of the single electron box in the strong tunneling limit
J. Stat. Mech. P11002 (2006).

18) B. Pedrini, S. Wessel, J.L. Gavilano, H.R. Ott, S.M. Kazakov and J. Karpinski
Quenching of the Haldane gap in LiVSi₂O₆ and related compounds
Eur. Phys. J. B 55, 219 (2007).

17) Gunnar Moller and R. Moessner
Artificial square ice and related dipolar nanoarrays
Phys. Rev. Lett. 96, 237202 (2006).

16) J. Wehr et al.
Disorder versus the Mermin-Wagner-Hohenberg Effect: From Classical Spin Systems to Ultracold Atomic Gases
Phys. Rev. B 74, 224448 (2006).

15) Fabien Alet et al.
Unconventional continuous phase transition in a three dimensional dimer model
Phys. Rev. Lett. 97, 030403 (2006).

14) O. Gygi et al.
Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps
Phys. Rev. A 73, 063606 (2006).

13) Mohamad Al Hajj et al.
Parity law of the singlet-triplet gap in graphitic ribbons
Eur. Phys. J. B 51, 517 (2006).

12) Philipp Werner, Armin Comanac, Luca de’ Medici, Matthias Troyer, and Andrew J. Millis
A continuous-time solver for quantum impurity models
Phys. Rev. Lett. 97, 076405 (2006).

11) Reinhard M. Noack and Salvatore R. Manmana
Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems
AIP Conf. Proc. 789, 93 (2005).

10) Philipp Werner, Gil Rafael, and Matthias Troyer
Simulation results for an interacting pair of resistively shunted Josephson junctions
J. Stat. Mech. P12003 (2005).

9) Simon Trebst et al.
d-wave resonating valence bond states of fermionic atoms in optical lattices
Phys. Rev. Lett. 96, 250402 (2006).

8) Zengo Tsuboi and Masahiro Shiroishi
High temperature expansion of emptiness formation probability for isotropic Heisenberg chain
J. Phys. A 38, L363 (2005).

7) Salvatore R. Manmana, Alejandro Muramatsu, and Reinhard M. Noack
Time evolution of one-dimensional Quantum Many Body Systems
AIP Conf. Proc. 789, 269 (2005).

6) Fabien Alet et al.
Interacting classical dimers on the square lattice
Phys. Rev. Lett. 94, 235702 (2005).

5) Johannes Richter, Jörg Schulenburg, and Andreas Honecker
Quantum Magnetism in Two Dimensions: From Semi-classical Néel Order to Magnetic Disorder
Lect. Notes Phys. 645, 85 (2004).

4) Omid Nohadani, Stefan Wessel, and Stephan Haas
Quantum Phase Transitions in Coupled Dimer Compounds
Phys. Rev. B 72, 024440 (2005).

3) Philipp Werner and Matthias Troyer
Effective charging energy of the single electron box
J. Stat. Mech. P01003 (2005).

2) Philipp Werner and Matthias Troyer
A cluster algorithm for resistively shunted Josephson junctions
Phys. Rev. Lett. 95, 060201 (2005).

1) Fabien Alet, Stefan Wessel, and Matthias Troyer
Generalized Directed Loop Method for Quantum Monte Carlo Simulations
Phys. Rev. E 71, 036706 (2005).

0) Subir Sachdev, Philipp Werner, and Matthias Troyer
Universal conductance of nanowires near the superconductor-metal quantum transition
Phys. Rev. Lett. 92, 237003 (2004).

[edit] Textbook references to the ALPS project

H. Gould, J. Tobochnik, and W. Christian
An Introduction to Computer Simulation Methods: Applications to Physical Systems,
Third Edition, Pearson/Addison-Wesley, San Francisco (2007).
(see page 718)