Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Numerical studies of spin chains and cold atoms in optical lattices
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
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 [en]
Teoretisk Fysik, Kondenserade materiens teori
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-4281ISBN: 978-91-7178-562-6 (print)OAI: oai:DiVA.org:kth-4281DiVA: diva2:11611
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
List of papers
1. Ground state of the random-bond spin-1 Heisenberg chain
Open this publication in new window or tab >>Ground state of the random-bond spin-1 Heisenberg chain
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.

Keyword
MATRIX RENORMALIZATION-GROUP; QUANTUM MONTE-CARLO; MODEL; PHASE; FIELD
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6795 (URN)10.1103/PhysRevB.66.134407 (DOI)000179067900072 ()
Note
QC 20100628Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2017-12-14Bibliographically approved
2. Reduction of the sign problem using the meron-cluster approach
Open this publication in new window or tab >>Reduction of the sign problem using the meron-cluster approach
2003 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 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.

Keyword
QUANTUM MONTE-CARLO; SPIN SYSTEMS; SIMULATIONS; MODELS
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6796 (URN)10.1103/PhysRevE.68.016122 (DOI)000184582500032 ()
Note
QC 20100628Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2017-12-14Bibliographically approved
3. Local-density approximation for confined bosons in an optical lattice
Open this publication in new window or tab >>Local-density approximation for confined bosons in an optical lattice
2004 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 70, 053601-1-053601-7 p.Article in journal (Refereed) Published
Abstract [en]

We investigate local and global properties of the one-dimensional Bose-Hubbard model with an external confining potential, describing an atomic condensate in an optical lattice. Using quantum Monte Carlo techniques we demonstrate that a local-density approximation, which relates the unconfined and the confined model, yields quantitatively correct results in most of the interesting parameter range. We also examine claims of universal behavior in the confined system, and demonstrate the origin of a previously calculated fine structure in the experimentally accessible momentum distribution.

Keyword
ATOMS, MODEL
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6797 (URN)10.1103/PhysRevA.70.053601 (DOI)000225479000105 ()
Note
QC 20100628 QC 20110915Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2017-12-14Bibliographically approved
4. Spinful bosons in an optical lattice
Open this publication in new window or tab >>Spinful bosons in an optical lattice
2006 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 74, no 5, 053419-1-053419-8 p.Article in journal (Refereed) Published
Abstract [en]

We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized S=1 chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.

Keyword
QUANTUM RENORMALIZATION-GROUPS; DIMERIZATION; TRANSITION; SUPERFLUID; INSULATOR; SPECTRUM; CHAINS; STATES; ATOMS; ORDER
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6798 (URN)10.1103/PhysRevA.74.053419 (DOI)000242408900114 ()
Note
QC 20100628Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2017-12-14Bibliographically approved
5. Transition from a two-dimensional superfluid to a one-dimensional mott insulator
Open this publication in new window or tab >>Transition from a two-dimensional superfluid to a one-dimensional mott insulator
Show others...
2007 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 99, no 11, 110401-1-110401-5 p.Article in journal (Refereed) Published
Abstract [en]

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.

Keyword
OPTICAL LATTICES; ATOMS; MODEL
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-6799 (URN)10.1103/PhysRevLett.99.110401 (DOI)000249474700001 ()2-s2.0-34548803504 (Scopus ID)
Note

QC 20100628

Available from: 2007-02-20 Created: 2007-02-20 Last updated: 2017-06-14Bibliographically approved

Open Access in DiVA

fulltext(458 kB)1468 downloads
File information
File name FULLTEXT01.pdfFile size 458 kBChecksum MD5
810cf1bedc0bcf33bac75424ed3d22d483e4ba8e48372a8335bda466ca92a5382766e906
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Bergkvist Sylvan, Sara
By organisation
Theoretical Physics
Condensed Matter Physics

Search outside of DiVA

GoogleGoogle Scholar
Total: 1468 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 592 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf