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Reduction of the sign problem using the meron-cluster approach
KTH, Superseded Departments, Physics.
KTH, Superseded Departments, Physics.ORCID iD: 0000-0003-3228-2826
KTH, Superseded Departments, Physics.ORCID iD: 0000-0002-2076-5911
2003 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 68, 016122-1-016122-8 p.Article in journal (Refereed) Published
Abstract [en]

The sign problem in quantum Monte Carlo calculations is analyzed using the meron-cluster solution. A meron is a loop that alters the sign of the configuration, and the concept of merons can be used to solve the sign problem for a limited class of models. Here we show that the method can be used to reduce the sign problem in a wider class of models. We investigate how the meron solution evolves between a point in parameter space where it eliminates the sign problem and a point where it does not affect the sign problem at all. In this intermediate regime, the merons can be used to reduce the sign problem. The average sign still decreases exponentially with system size and inverse temperature, but with a different prefactor. The sign exhibits the slowest decrease in the vicinity of points where the meron-cluster solution eliminates the sign problem. We have used stochastic series expansion quantum Monte Carlo combined with the concept of directed loops.

Place, publisher, year, edition, pages
2003. Vol. 68, 016122-1-016122-8 p.
Keyword [en]
QUANTUM MONTE-CARLO; SPIN SYSTEMS; SIMULATIONS; MODELS
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-6796DOI: 10.1103/PhysRevE.68.016122ISI: 000184582500032OAI: oai:DiVA.org:kth-6796DiVA: diva2:11607
Note
QC 20100628Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2012-01-19Bibliographically approved
In thesis
1. Numerical studies of spin chains and cold atoms in optical lattices
Open this publication in new window or tab >>Numerical studies of spin chains and cold atoms in optical lattices
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

An important, but also difficult, research field in condensed matter physics is that of strongly correlated systems. This thesis considers two topics in this field.

The first topic is disorder and frustration in spin models. The introduction of disorder into quantum spin chains creates a complex problem. The ground state of the random-bond spin-1 Heisenberg chain is studied by means of stochastic series expansion quantum Monte Carlo simulation, applying the concept of directed loops. It is found that this system undergoes a phase transition to the random-singlet phase if the bond disorder is strong enough. Further a frustrated spin system is investigated. The frustration is introduced by having spins positioned on a triangular lattice. Performing a quantum Monte Carlo simulation for such a frustrated lattice leads to the occurrence of the infamous sign problem. This problem is investigated and it is shown that it is possible to use a meron cluster approach to reduce its effect for some specific models.

The second topic concerns atomic condensates in optical lattices. A system of trapped bosonic atoms in such a lattice is described by a Bose-Hubbard model with an external confining potential. Using quantum Monte Carlo simulations it is demonstrated that the local density approximation that relates the observables of the unconfined and the confined models yields quantitatively correct results in most of the interesting parameter range of the model. Further, the same model with the addition that the atoms carry spin-1 is analyzed using density matrix renormalization group calculations. The anticipated phase diagram, with Mott insulating regions of dimerized spin-1 chains for odd particle density, and on-site singlets for even density is confirmed. Also an ultracold gas of bosonic atoms in an anisotropic two dimensional optical lattice is studied. It is found that if the system is finite in one direction it exhibits a quantum phase transition. The Monte Carlo simulations performed show that the transition is of Kosterlitz-Thouless type.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007
Series
Trita-FYS, ISSN 0280-316X ; 2007:01
Keyword
Teoretisk Fysik, Kondenserade materiens teori
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-4281 (URN)978-91-7178-562-6 (ISBN)
Public defence
2007-02-23, Oskar Kleins Auditorium, AlbaNova, Roslagstullsbacken 21, Stockholm, 13:30
Opponent
Supervisors
Note
QC 20100628Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2012-03-19Bibliographically approved

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Henelius, PatrikRosengren, Anders

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