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

0.2 MB·English

by  A. F. Albuquerque

Journal ofMagnetism andMagnetic Materials 0(2008) 1–0
www.elsevier.com/locate/jmmm
The ALPSproject release1.3:
8 opensourcesoftwareforstronglycorrelatedsystems
0
0
2 A.F.Albuquerquea, F.Aletb, P.Corboza, P.Dayala,c, A.Feiguind, S.Fuchse, L.Gampera
, E. Gulla, S.Gu¨rtlerf,g, A.Honeckere, R.Igarashih, M. K¨ornera, A.Kozhevnikovi, A.L¨auchlij
n
a , S.R.Manmanak,ℓ, M.Matsumotoa, I.P. McCullochm, F.Micheln, R.M.Noackk, G.Paw lowskio
J , L.Polleta, T.Pruschkee, U.Schollw¨ockm, S.Todop, S. Trebstd, M. Troyera,∗, P.Wernerq
1
, S.Wesselℓ
1
(for theALPS collaboration)

]
l aTheoretische Physik, ETH Zu¨rich, 8093 Zu¨rich, Switzerland
e
- bLaboratoire de Physique Th´eorique, UMRCNRS5152, Universit´e Paul Sabatier, 31062 Toulouse, France
r cUniversityof Minnesota, Department of Computer Scienceand Engineering, 200 UnionStreet S.E. Minneapolis, MN55455, USA
st dMicrosoft Research, StationQ, Universityof California, SantaBarbara, CA 93106, USA
. eInstitut fu¨rTheoretische Physik, Universit¨atG¨ottingen,D-37077 G¨ottingen,Germany
t
a fCentrefor Theoretical & Computational Physics, The Universityof Hong Kong, Hong Kong, China
m gDepartment of Physics, The Universityof Hong Kong, Hong Kong, China
hDepartment of Physics, Universityof Tokyo, 113-0033 Tokyo, Japan
-
d iInstitute of MetalPhysics, Russian Academy of Sciences–Ural Division, 620219 Ekaterinburg GSP-170, Russia
n jInstitutRomand de Recherche Num´erique enPhysique desMat´eriaux (IRRMA), CH-1015 Lausanne, Switzerland
o kAGVielteilchennumerik, FachbereichPhysik, Philipps-Universit¨at Marburg, D-35032 Marburg, Germany
c ℓInstitutfu¨rTheoretische Physik III, Universit¨at Stuttgart,Pfaffenwaldring 57, D-70550 Stuttgart,Germany
[ m Institutfu¨rTheoretische Physik C, RWTH Aachen, D-52056 Aachen, Germany
n Institutfu¨rTheoretische Physik, Technische Universita¨tGraz, Petersgasse 16, A-8010 Graz, Austria
1 oInstituteof Physics, A.MickiewiczUniversity,ul. Umultowska 85, 61-614 Poznan, Poland
v pDepartment of Applied Physics, Universityof Tokyo,113-8656 Tokyo,Japan
5 qDepartment of Physics, Columbia University,538 West 120th Street, NewYork,NY 10027, USA
6
Received 2February 2008
7
1
.
1
Abstract
0
8
We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source
0
software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models
:
v such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML
i and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The
X
programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important
r
a algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble
simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the
newreleaseincludeaDMRGprogramforinteractingmodels,supportfortranslationsymmetriesinthediagonalization programs,
the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps.
Thesoftware isavailable from ourweb serverat http://alps.comp-phys.org/.
(cid:13)c 2008 Elsevier B.V. Allrightsreserved.
PACS: 02.70.-c;75.40.Mg
Keywords: quantum latticemodel;opensourcesoftware;C++,MonteCarlo;quantum MonteCarlo;densitymatrixrenormalizationgroup;
DMRG;exact diagonalization
0304-8853/08/$-see frontmatter (cid:13)c 2008 ElsevierB.V.Allrights reserved.
A.F. Albuquerque etal./Journal of Magnetismand MagneticMaterials 0(2008) 1–0 2
1. Introduction searchersboth about the algorithms and the use of the
applications.
Inthispaperwepresentrelease1.3oftheALPSproject – improved reproducibility of numerical results by
(Algorithms and Libraries for Physics Simulations), an publishingsourcecodesusedtoobtainpublishedresults.
opensourcesoftwaredevelopmentprojectforstronglycor- – anarchive forsimulationresults.
relatedlatticemodels.Wewillpresentashortoverviewand
The ready-to-use applications are useful both for theo-
focus on new features compared to the previous releases
reticianswhowanttotesttheoreticalideasaboutquantum
[1,2].
lattice models and to explore their properties, as well as
Quantum fluctuations and competing interactions in
forexperimentaliststryingtofitexperimentaldatatotheo-
quantummanybodysystemsleadtounusualandexciting
reticalmodelstoobtaininformationaboutthemicroscopic
properties of strongly correlated materials such as quan-
propertiesofmaterials.
tum magnetism [3], high temperature superconductivity
In the following, we present a quick review of these as-
[4], heavy fermion behavior [5], and topological quantum
pects ofthe ALPSproject,focusing onnew featuresin re-
order [6]. The same strong interactionsmake accurate an-
lease1.3.
alytical treatments hard and direct numerical simulations
are essential to increase our understanding of the unusual
2. Fileformats
propertiesofthesesystems.
Thelastdecadehasseentremendousprogressinthede-
ThemostbasicpartoftheALPSprojectisthedefinition
velopmentofalgorithms.Speedupsofmanyordersofmag-
of common standardized file formats suitable for a wide
nitudehavebeenachieved[7,8,9,10,11,12].Theseadvances
rangeofapplications.Standardizedfileformatsenablethe
comeatthecostofsubstantiallyincreasedalgorithmiccom-
exchangeof data between applications,allow the develop-
plexity andchallengethe currentmodel ofprogramdevel-
mentofcommonevaluationtools,simplifytheapplication
opmentinthis researchfield.Incontrasttootherresearch
of more than one algorithm to a given model, and are a
areas, in which large “community codes” are being used,
prerequisite for the storage of simulation data in a com-
thefieldofstronglycorrelatedsystemshassofarbeenbased
mon archive. The ISO standard XML [13] was chosen for
mostlyonsinglecodesdevelopedbyindividualresearchers
thespecificationoftheseformatsbecauseithasbecomethe
for particular projects. While the simple algorithms used
main text-based data format on the internet and because
a decade ago could be easily programmed by a beginning
itissupportedby alargeandgrowingnumber oftools.
graduate student in a matter of weeks, it now takes sub-
We have designed a number of XML schemas [14] to
stantially longer to master and implement the new algo-
describe
rithms. Thus,their use has increasinglybecome restricted
to asmallnumberofexperts. – the inputofsimulationparameters,
TheALPSprojectaimstoovercometheproblemsposed – the lattices,
by the growing complexity of algorithms and the special- – quantumlattice models,
ization of researchers onto single algorithms through an – andthe output ofresults.
open-sourcesoftwaredevelopmentinitiative.Inrelease1.3 Adetailedspecificationoftheformatsisgivenonourweb
newfeaturesdesiredbyALPSusers,especiallyexperimen- pages [2,14]. As examples we show a lattice and a model
talists, have been added, as well as a DMRG program for definitioninfigures1and2.AnyoftheALPSapplications
interactingproblems. can be run by providing an input file, specifying the sim-
To quote from the previous publication [1], the goals of ulation parameters, together with lattice and model defi-
the ALPSprojectaretoprovide: nitions (figures 1 and 2) to that application (provided the
applicationsupportsthattypeofmodel).Standardizedfor-
– standardized file formats to simplify exchange, dis-
matsthatextendacrossallapplicationsreducethelearning
tribution and archiving of simulation results and to
curveforusingtheapplicationsandallowcommontoolsto
achieveinteroperabilitybetweencodes.
be usedtoanalyzethe data.
– genericandoptimizedlibrariesforcommonaspects
of simulations of quantum and classical lattice models,
2.1. Newfeatures
to simplify code development.
– asetofapplicationscoveringthe majoralgorithms.
2.1.1. Latticedefinitions
– license conditions that encourage researchers to con-
New features in the lattice definitions in release 1.3 in-
tribute to the ALPSprojectby gaining scientific credit
clude the possibility to specify inhomogeneity and deple-
foruse oftheir work.
tion. While in a regular lattice, the model Hamiltonian is
– outreach through a web page [2], mailing lists and
the same for all bonds or sites with the same type, in an
workshops to distribute the results and to educate re-
inhomogeneous lattice the couplings in the model can be
differentforeachbondorsite.Examplesaredisorderedsys-
∗ tems,withrandomlychosencouplingssuchasspinglasses,
Corresponding author.
Email address: [e-mail] (M. Troyer).
A.F. Albuquerque etal./Journal of Magnetismand MagneticMaterials 0(2008) 1–0 3
<LATTICEGRAPH name ="depleted inhomogeneous square lattice"> <BASIS name="boson">
<FINITELATTICE> <SITEBASIS>
<LATTICE dimension="2"/> <PARAMETER name="Nmax" default="infinity"/>
<EXTENT dimension="1" size="L"/> <QUANTUMNUMBER name="N" min="0" max="Nmax"/>
<EXTENT dimension="2" size="L"/> <OPERATOR name="bdag" matrixelement="sqrt(N+1)">
<BOUNDARY type="periodic"/> <CHANGE quantumnumber="N" change="1"/>
</FINITELATTICE> </OPERATOR>
<UNITCELL> <OPERATOR name="b" matrixelement="sqrt(N)">
<VERTEX/> <CHANGE quantumnumber="N" change="-1"/>
<EDGE> </OPERATOR>
<SOURCE vertex="1" offset="0 0"/> <OPERATOR name="n" matrixelement="N"/>
<TARGET vertex="1" offset="0 1"/> </SITEBASIS>
</EDGE> </BASIS>
<EDGE>
<SOURCE vertex="1" offset="0 0"/> <SITEOPERATOR name="double_occupancy" site="x">
<TARGET vertex="1" offset="1 0"/> n(x)*(n(x)-1)/2
</EDGE> </SITEOPERATOR>
</UNITCELL>
<INHOMOGENEOUS><VERTEX/></INHOMOGENEOUS>} <BONDOPERATOR name="boson_hop" source="x" target="y">
<DEPLETION> bdag(x)*b(y)+bdag(y)*b(x)
<VERTEX probability="DEPLETION" seed="DEPLETION_SEED"/> </BONDOPERATOR>
</DEPLETION>
</LATTICEGRAPH> <HAMILTONIAN name="trapped boson Hubbard">
<PARAMETER name="mu" default="0"/>
Fig. 1. The definition of a square lattice with one site (vertex) per <PARAMETER name="t" default="1"/>
unit cell and bonds (edges) only to nearest neighbors. First the <PARAMETER name="U" default="0"/>
dimension, extent, and boundary conditions of the Bravais lattice <PARAMETER name="K" default="0"/>
are described in the <FINITELATTICE> element, then the unit cell <BASIS ref="boson"/>
includingthebondsinthelatticeisdefined.Newfeaturesinrelease <SITETERM site="i">
1.3. includeinhomogeneity and depletion. -mu*n(i)+U*double_occupancy(i)+K/2*((x-L/2)^2+(y-L/2)^2)
</SITETERM>
orsystemsinspatiallyvaryingtrappingpotentials,suchas <BONDTERM source="i" target="j">
opticallattices in harmonic traps.Inhomogeneitiescan be -t*boson_hop(i,j)
</BONDTERM>
specified for vertices (sites) and edges (bonds), either for
</HAMILTONIAN>
all(suchasforallverticesinfigure1),oronlyforonetype
ofvertexoredge. Fig. 2. The definition of a bosonic Hubbard Hamiltonian (1) in a
The other new feature is depletion of a lattice, where harmonic trap. After describing the local basis for each site and
operatorsactingonit,thefirstnewfeatureinrelease1.3istheability
a fraction of sites or bonds is randomly removed from a
to define composite site and bond operators, such as the double
lattice. Currently only site depletion is implemented, but
occupancy and bosonic hopping terms, which are then used in the
additional types of depletion can be added easily if the definition ofthe Hamiltonian.
need arises [15]. In the example in figure 1,the fractionof
depleted sites is specified to be passed in the DEPLETION
geneous lattice, to use site-dependent couplings, such as
input parameter, and the random number generator seed
theharmonictrappingpotentialK whichdependsonthex
DEPLETION SEED can be changed to give different random
andycoordinatesofthesite.Thisfeaturehasbeenusedfor
realizationsofthe depletionpattern.
thesimulationofcoldbosonicgasesinopticallattices[16].
2.1.2. Model definitions
2.2. Futureplans
Figure 2 shows the definition of the Hamiltonian of a
bosonicHubbardmodelinaharmonictrap
The immediate goalfor release1.4will be to addmulti-
U site interaction terms and measurements, such as ring ex-
H=−µ n + n (n −1) (1)
X i 2 X i i changeterms.
i i Withtheexperiencegainedinusingcommonfileformats
K
−t b†b +b†b + (x2+y2). forseveralyearsacrossa number ofdifferent applications,
X(cid:16) i j j i(cid:17) 2 X i i wenextplantodesignmorewidelyusedcommonformats,
hi,ji i
suchas standardformats for results of Monte Carlo simu-
Thefirstnewfeatureofrelease1.3,showninthisexample, lationsthathavebeendefinedataworkshopinSeptember
istheabilitytospecifycompositesiteandbondoperators, 2006.
suchasthedouble occupancysitetermortheboson hop
bond term. These site and bond operators can be used in 3. Libraries
the specificationofthe modelandofmeasurements.
Theothernewfeature,alsoshownintheexample,isthe The ALPS libraries are the foundation of all the ALPS
ability,inconjunctionwiththespecificationofaninhomo- applications, providing functionality common to all of
A.F. Albuquerque etal./Journal of Magnetismand MagneticMaterials 0(2008) 1–0 4
them, such as file I/O, expression evaluation, parallel job 4.1. Exact diagonalization
scheduling,orthe statisticalanalysisofMonteCarlomea-
surements.Theselibrariesmakefulluseofobject-oriented The existing exact diagonalization [19,11] programs
and generic programming techniques [18], which allows sparsediag and fulldiag have been substantially im-
them to be very flexible without losing any performance proved. sparsediag calculates the ground state and low
comparedtoFORTRANprograms. lying excited states of quantum lattice models using the
Lanczos [20] algorithm, while fulldiag calculates the
3.1. Newfeatures complete spectrum of quantum lattice models and fromit
allthermodynamic properties.
The new library features are mainly hidden from the The first major improvement is the use of translation
application users, providing support for the new features symmetry to reduce the Hilbert space dimension. This
in the input files, discussed above, or providing support speedsup the calculationsandallowslargersystems tobe
for new features in the applications, such as translational calculated. In addition, by calculating the energy eigen-
symmetries in the diagonalization codes, and the ability values separately for each momentum, the momentum-
to define custom measurements, which will be discussed resolvedexcitationspectrumcanbe calculated.
below. The second new feature is the possibility to define cus-
One new feature that should be mentioned explic- tommeasurementsof averagedor localsite- andbondop-
itly is the inclusion of random number generators in the erators, as well as arbitrary 2-point correlation functions.
expression library. Expressions for couplings and other As an example, for the inhomogeneous bosonic Hubbard
parameters can make use of new functions random(), model of figure 2, one can specify the measurement of the
normal random(), and integer random(n) to obtain average double occupancy, local density, density correla-
uniform random numbers in the interval [0,1), normally tions,andGreen’sfunctionbydefiningthefollowinginput
distributed random numbers or integer random numbers parameters,whichuse the definitions ofsite andbondop-
between0andn.Thisfeatureismostusefulinconjunction eratorsprovidedwith the model:
withinhomogeneouslattices to define disorderedmodels. MEASURE_AVERAGE[Double]=double_occupancy
Another change to be mentioned is that since the pars- MEASURE_LOCAL[Localdensity]= n
ingofcommandlineoptionstotheapplicationisnowhan- MEASURE_CORRELATION[Densitycorrelation]= n
dledbytheBoostprogramoptionslibrary[17],multi-letter MEASURE_CORRELATION[Greenfunction]= "bdag:b"
commandlineoptionsnowneedtobeprecededbytwohy- MEASURE_STRUCTURE_FACTOR[SpinStrFact]=Sz
phens asin--Tmin,insteadofthe previoususage-Tmin. Inthefutureweplantosupportpointgroupsymmetries
and to add the calculation of dynamical correlation func-
3.2. Futureplans tions.
Code fromthe ALPSlibrarieshas recentlybeenusedin 4.2. Classical MonteCarlo
the development of Boost [17] libraries. These include op-
timizationstotheBoost.Serializationlibrary,newfeatures TheMonteCarloprogramforclassicalmagnetsemploy-
for the Boost.Random library, a proposed Boost.MPI li- ing local and cluster updates [21] has been extended ac-
braryanda Boost.Accumulatorlibraryfor statisticalesti- cording to wishes of several users. The most notable new
mates.Onceacceptedinthepeerreviewprocess,andpub- featuresarethepossibilitytospecifysingleionanisotropies
lished in a future Boost release, the ALPS codes will be andanisotropicinteractions.
changed to use these Boost libraries. The ALPS libraries
willthencontainlessgeneralpurposecodes(whichwillhave 4.3. QuantumMonteCarlo
beenmovedtoBoost)andwillbemorefocusedondomain-
specific librariesfor the simulationofquantummodels. ThequantumMonteCarloprogramshavealsobeenup-
datedinrelease1.3.
4. Applications The “looper” program using the loop cluster algorithm
[7,22]inastochasticseriesexpansion[23](SSE)andpath-
In addition to common libraries, the ALPS project in- integral representation for quantum magnets has been re-
cludes a number of ready to use applications implement- placed with a new version,offering 40-80%speed increase
ing the most important unbiased algorithms for quantum andsupportinglongitudinalandtransversemagneticfields
many body systems. The applications all share the same aswellassingle ionanisotropies.
file formats, simplifying their use, reducing the learning The directed loop QMC program [24] in an SSE repre-
curve,andenablingtheeasyinvestigationofamodelwith sentationforbosonicandmagneticquantumlatticemodels
more than one method. Tutorials on the use of the appli- hasbeenextendedtoofferalsothe“Locallyoptimalworm
cationsareincludedwiththesourcesthatcanbefoundon algorithm”(LOWA)[25]updates.
the ALPSwebpage[2]. The worm algorithm [26] programhas been updated to
allownonlocalinteractions[27].
A.F. Albuquerque etal./Journal of Magnetismand MagneticMaterials 0(2008) 1–0 5
AllQMCprogramhavebeenextendedbynewmeasure- jointhe mailinglistandparticipateinthe workshops.
ments, including correlation functions, structure factors,
and stiffness or superfluid density. In addition, the same 7. Future plans
custom measurements as discussed above for exact diago-
nalization can be used in these codes, as long as the mea- 7.1. Newapplication
surementsarediagonalinthechosenbasis.Thelooperpro-
gramadditionallymeasureslocalsusceptibilitiesandtrans- The following new applications are planned for future
versemagnetization. releases:
– A series expansion [35] code for both perturbation
4.4. DensityMatrix Renormalization Group
seriesandhightemperatureseriesinrelease1.4
– Also in release 1.4, the addition of generalized sam-
In addition to the DMRG [9,10,11] program for nonin-
pling algorithms, such as the quantum version [8] of
teracting particles (an adaptation of the program in Refs.
the Wang-Landau algorithm [36] and optimized en-
[28,29] to the ALPS libraries), release 1.3 contains a new
semble methods [37] to the quantum Monte Carlo
DMRG programfor interacting many body systems, with
algorithmsto obtainthermodynamic quantities over
the ability to calculate local quantities and two-pointcor-
largetemperatureranges.
relationfunctions.
– Implementationofparalleltempering[38]fortheclas-
sicalandquantumMonteCarloalgorithmsincluding
4.5. Tools
feedback-optimizedtemperaturesets [39].
– AQMCalgorithminthevalencebondrepresentation
Release1.3addsadatabasetool,toarchiveacollectionof
for quantumspinsystems [40]
simulationresults,andtoallowfastandefficientextraction
– A continuum QMC programfor bosons, implement-
andevaluationofresults.Thetool,basedontheSQlite[30]
ing the continuousspacewormalgorithm[41].
databaseiseasytouse,basedonasimpleflatfiledatabase
and does not require to set up a complex database appli-
7.2. Realisticmodel: interface toband structurecodes
cation.
Also planned for release 1.4 is an interface of the ALPS
5. License
applications to band structure codes. Instead of running
simulationsonphenomenologicaltoymodels,suchasasim-
The ALPS software is distributed under the ALPS li-
ple Heisenberg model with only a few different couplings,
brary [31] and application [32] licenses, which have re-
itwillbe possibletorunthe ALPSapplicationsonacom-
mained unchanged. The use of the codes is free for non-
plex, realistic model obtained from ab-initio band struc-
commercialapplicationsbutcarriesacitationrequirement
ture calculations. In the past this was done manually, e.g.
to publications, such as the current one, describing the li-
in reference[42],the exchangecouplings determined in an
brariesandcodes.Inaddition,besidestherequiredcitation
LDA+Ucalculation[43]usingtheLichtensteinmethod[44]
of the publication describing the ALPS application, users
were used to manually prepare input files for QMC simu-
areencouragedtocite thepublicationdescribingthe algo-
lationsusingthe loopalgorithm[7].
rithmusedinthe applications.
Release1.4ofALPSwillcontaintoolstoautomatesuch
calculations, based on a standard XML I/O format for
6. Distribution,outreach development
band structure codes developed by T. Schulthess and M.
SummersattheOakRidgeNationalLaboratory.Asanex-
TheALPSwebpage[2]isthecentralinformationreposi-
ampleofsuchanautomatedcalculationusinga prototype
toryoftheALPScollaboration.Itmakessourcecodesofthe
tool by A. Kozhevnikov, we show in figure 3 a compari-
ALPS libraries and applications available, provides access
sonofexperimentalmeasurementsonthespinladdercom-
to the documentation, and distributes information about
poundSrCu2O3 [45]withautomatedab-initio simulations
the mailing lists,new releases,andworkshops.
(“LDA+U+ALPS”).
For this release we have replaced the static web page
bya Wikisystem[33],whichenablesdevelopersandusers
7.3. Dynamical mean fieldtheory (DMFT) solvers
to easily and quickly add new contents and improve the
instructionsandtutorialsonthe webpage.
Inafurtherstage,weplantoexpandtheALPSprojectto
AnothernewfeatureiscdALPS[34]byG.Pawlowski,a
includedynamicalmeanfieldtheory(DMFT) [46]solvers.
bootableKnoppixLinuxALPSCD,whichallowstorunthe
We have designed a DMFT framework for QMC solvers
ALPS tutorials and simple ALPS codes on a PC without
and implemented the standard Hirsch-Fye solver [47], as
installingthe fullALPSsoftware.
well as two new continuous time solvers [48,12]. The first
Development of the ALPS libraries and applications is
application of the framework, a careful comparison of the
coordinated through both mailing lists and semi-annual
performanceofthethreesolvers[47,48,12]isinpreparation
developer workshops.Interested researchersare invited to
A.F. Albuquerque etal./Journal of Magnetismand MagneticMaterials 0(2008) 1–0 6
0.0001 [7] For a review see M. Troyer et al., AIP Conf. Proc. 690 (2003),
p. 156; H.G. Evertz, Adv. inPhysics52 (2003), p. 1.
[8] M. Troyer, S. Wessel, and F. Alet, Phys. Rev. Lett. 90 (2003),
8 10-5 p. 120201.
[9] S.R. White, Phys. Rev. Lett. 69 (1992), p. 2863; Phys. Rev. B
48 (1993), p. 10345.
[10]for a review see: U. Schollwo¨ck, Rev. Mod. Phys. 77 (2005), p.
mol] 6 10-5 259.
u / [11]for a review see R.M. Noack and S.R. Manmana, AIP Conf.
m Proc. 789 (2005), p.93.
[e! 4 10-5 Experiment [[1132]]Pht.tWp:e/r/nwewrwe.twa3l..o,rPgh/yXsM.LR/ev. Lett.97(2006), p.076405.
[14]http://xml.comp-phys.org/
LDA+U+ALPS
[15]Please contact the authors if youneed this or another feature.
2 10-5 [16]S.Wesseletal.,Phys.Rev.A70(2004),p.053615;S.Wesselet
al., J. Phys. Soc. Jpn. Suppl. 74 (2005), p. 10; O. Gygi et al.,
Phys. Rev. A 73(2006), p. 063606.
0 [17]http://www.boost.org/
0 100 200 300 400 500 600 [18]K. Czarnecki and U.W. Eisenecker: Generative Programming,
T (K) (Addison Wesley, 2000).
[19]for a review see N. Laflorencie and D. Poilblanc, Lect. Notes
Fig. 3. Comparison of experimental measurements on the spin lad- Phys. 645 (2004), p.227.
der compound SrCu2O3 [45] with automated ab-initio simulations [20]C. Lanczos, J. Res. Natl. Bur. Stand. 45(1950), p.225.
using “LDA+U+ALPS”. The deviation at low temperature is due [21]R.H. Swendsen and J-S. Wang, Phys. Rev. Lett. 58 (1987), p.
to impurities in the experimental sample, causing a Curie-Weiss 86; U. Wolff, Phys. Rev. Lett.62(1989), p.361.
like divergence at low temperatures. The dominant couplings are [22]S. Todo and K. Kato, Rev. Lett. 87 (2001), p. 047203;
an intra-chain coupling J = 162meV and an inter-chain coupling http://wistaria.comp-phys.org/alps-looper/
J⊥=76meV [23]A.W. Sandvik and J. Kurkija¨rvi, Phys. Rev. B 43 (1991), p.
5950; A.W.Sandvik, Phys. Rev. B59(1999), p. R14157.
[49]. Work is in progress to expand the framework to in- [24]F. Alet, S. Wessel, and M. Troyer, Phys. Rev. E 71 (2005), p.
036706.
cludeEDandDMRGbasedsolvers,andweexpectapublic
[25]L. Polletetal., cond-mat/0508462.
open-source release of the first codes soon. Interested re- [26]N.V. Prokof’ev, B.V. Svistunov, and I.S. Tupitsyn, Sov. Phys.
searcherscancontactustoparticipateinthe development JETP 87 (1998), p. 310.
orto obtainpre-releaseversionsofthe codes. [27]Thepreviousversionrequiredacompilerswitchtoturnonthis
feature.
[28]I.Pescheletal.(Ed.):DensityMatrixRenormalization-ANew
8. Conclusions
Numerical Method inPhysics, (Springer Verlag,Berlin,1999).
[29]M.A. Martin-Delgado, G. Sierra, and R. M. Noack, J. Phys. A
TheALPSprojectiscontinuouslyevolving.Researchers 32 (1999), p. 6079; andchapter 2 ofRef. [28].
[30]http://www.sqlite.org/
interested in announcements of new releases, information
[31]http://alps.comp-phys.org/software/ALPS/LICENSE.txt
about workshops, or in contributing to the ALPS project
[32]http://alps.comp-phys.org/software/applications/
are encouraged to sign up to the mailing lists on our web LICENSE.txt
page[2]. [33]http://en.wikipedia.org/wiki/Wiki
We acknowledge support by the Swiss National Science [34]http://hoth.amu.edu.pl/~netma/
[35]M. P. Gelfand and R. R. P. Singh, Advances in Physics 49
Foundation, the KavliInstitute for TheoreticalPhysicsat
(2000), p.93.
the University of California at Santa Barbara, the Aspen [36]F.WangandD.P.Landau,Phys.Rev.Lett.86(2001), p.2050;
CenterforPhysics,CNPq(Brazil),theNetworkforInterna- Phys. Rev. E64 (2001), p. 056101.
tional Development and Cooperation (NIDECO) at ETH [37]S. Trebst, D. Huse, and M. Troyer, Phys. Rev. E 70 (2004), p.
046701.
Zu¨rich, the RGC grant of Hong Kong, and the Deutsche
[38]K. Hukushima and K. Nemoto, J. Phys. Soc. Japan 65 (1996),
ForschungsgemeinschaftthroughSFB 602.
p. 1604.
[39]H.G. Katzgraber et al., J. Stat. Mech. (2006), p. P03018.
[40]A.W. Sandvik, Phys. Rev. Lett.95 (2005), p. 207203.
References [41]M.Boninsegni,N.Prokof’ev,andB.Svistunov,Phys.Rev.Lett.
96 (2006), p. 070601.
[42]M.A. Korotinetal., Phys. Rev. Lett. 83(1999), p. 1387.
[1] F.Aletet al., J. Phys. Soc. Jpn. Suppl. 74 (2005), p. 30. [43]V. I. Anisimov et al., Phys. Rev. B 44 (1991), p. 943; V. I.
[2] http://alps.comp-phys.org/ Anisimovetal., J. Phys. Condens. Matter9(1997), p. 767.
[3] U.Schollwo¨cketal.(Eds.),Quantummagnetism,LectureNotes [44]A. I. Lichtenstein et al., J. Magn. Magn. Mater. 67 (1987), p.
inPhysics 645 (Springer Verlag, Berlin,2004). 65; A. I. Lichtenstein et al., Phys. Rev. B52(1995), p.R5467.
[4] J.G. Bednorz and K.A.Mu¨ller,Z.Phys. B 64(1986), p.189. [45]M.Azuma etal., Phys. Rev. Lett.73 (1994), p. 3463.
[5] for a review see P. Thalmeier, G. Zwicknagl, O. Stockert, G. [46]A.Georgesetal.,Rev.Mod.Phys68(1996),p.13;T.Pruschke,
Sparn,andF.Steglich,p.109in“FrontiersinSuperconducting M.Jarrell,and J.K.Freericks,Adv. Phys. 42(1995), p.187.
Materials”,A.V.Narlikar(Ed.), (Springer, 2005). [47]J.E.HirschandR.M.Fye,Phys.Rev.Lett.56(1986),p.,2521.
[6] for a review see X.G. Wen: Quantum Field Theory Of Many- [48]A.N.Rubtsov,V.V.SavkinandA.I.Lichtenstein,Phys.Rev.B
body Systems: From The Origin Of Sound To An Origin Of 72 (2005), p. 035122.
LightAndElectrons (OxfordUniversityPress,2004) [49]E. Gullet al., inpreparation.