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Ground state of the random-bond spin-1 Heisenberg chain
KTH, Superseded Departments, Physics.
KTH, Superseded Departments, Physics.ORCID iD: 0000-0003-3228-2826
KTH, Superseded Departments, Physics.ORCID iD: 0000-0002-2076-5911
2002 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 66, 134407-1-134407-9 p.Article in journal (Refereed) Published
Abstract [en]

Stochastic series expansion quantum Monte Carlo is used to study the ground state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder. Typical spin- and string-correlation functions behave in accordance with real-space renormalization group predictions for the random-singlet phase. The average string-correlation function decays algebraically with an exponent of -0.378(6), in very good agreement with the prediction of -(3-root5)/2similar or equal to-0.382, while the average spin-correlation function is found to decay with an exponent of about -1, quite different from the expected value of -2. By implementing the concept of directed loops for the spin-1 chain we show that autocorrelation times can be reduced by up to two orders of magnitude.

Place, publisher, year, edition, pages
2002. Vol. 66, 134407-1-134407-9 p.
Keyword [en]
MATRIX RENORMALIZATION-GROUP; QUANTUM MONTE-CARLO; MODEL; PHASE; FIELD
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-6795DOI: 10.1103/PhysRevB.66.134407ISI: 000179067900072OAI: oai:DiVA.org:kth-6795DiVA: diva2:11606
Note
QC 20100628Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2017-12-14Bibliographically 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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