J{sub 1}-J{sub 2} Heisenberg model at and close to its z=4 quantum critical point

Sirker, J; Krivnov, V Y; Dmitriev, D V; Herzog, A; Janson, O; Nishimoto, S; Drechsler, S -L; Richter, J

doi:10.1103/PHYSREVB.84.144403

Title: J{sub 1}-J{sub 2} Heisenberg model at and close to its z=4 quantum critical point

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Abstract

We study the frustrated J{sub 1}-J{sub 2} Heisenberg model with ferromagnetic nearest-neighbor coupling J{sub 1}<0 and antiferromagnetic next-nearest-neighbor coupling J{sub 2}>0 at and close to the z=4 quantum critical point (QCP) at J{sub 1}/J{sub 2}=-4. The J{sub 1}-J{sub 2} model plays an important role for recently synthesized chain cuprates as well as in supersymmetric Yang-Mills theories. We study the thermodynamic properties using field theory, a modified spin-wave theory, as well as numerical density-matrix renormalization group calculations. Furthermore, we compare with results for the classical model obtained by analytical methods and Monte Carlo simulations. As one of our main results, we present numerical evidence that the susceptibility at the QCP seems to diverge with temperature T as {chi}{approx}T{sup -1.2} in the quantum case, in contrast to the classical model where {chi}{approx}T{sup -4/3}.

Authors:

Sirker, J ^[1]; Krivnov, V Y; Dmitriev, D V ^[2]; Herzog, A ^[1]; Janson, O ^[3]; Nishimoto, S; Drechsler, S -L ^[4]; Richter, J ^[5]

Department of Physics, Technical University Kaiserslautern, D-67663 Kaiserslautern (Germany)
Joint Institution of Chemical Physics of RAS, Kosygin Strasse 4, 119334 Moscow (Russian Federation)
Max Planck Institute for Chemical Physics of Solids, Noethnitzer Str. 40, D-01187 Dresden (Germany)
IFW Dresden, P.O. Box 270116, D-01171 Dresden (Germany)
Institut fuer Theoretische Physik, Universitaet Magdeburg, P.O. Box 4120, D-39016 Magdeburg (Germany)

Publication Date:: Sat Oct 01 00:00:00 EDT 2011

OSTI Identifier:: 21596896

Resource Type:: Journal Article

Journal Name:: Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:: Journal Volume: 84; Journal Issue: 14; Other Information: DOI: 10.1103/PhysRevB.84.144403; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANTIFERROMAGNETISM; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; COUPLING; CUPRATES; DENSITY MATRIX; FIELD THEORIES; HEISENBERG MODEL; MONTE CARLO METHOD; RENORMALIZATION; SPIN WAVES; SUPERSYMMETRY; THERMODYNAMIC PROPERTIES; YANG-MILLS THEORY; CALCULATION METHODS; COPPER COMPOUNDS; CRYSTAL MODELS; EVALUATION; MAGNETISM; MATHEMATICAL MODELS; MATRICES; OXYGEN COMPOUNDS; PHYSICAL PROPERTIES; SIMULATION; SYMMETRY; TRANSITION ELEMENT COMPOUNDS

Citation Formats


                    Sirker, J, Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern, Krivnov, V Y, Dmitriev, D V, Herzog, A, Janson, O, Nishimoto, S, Drechsler, S -L, and Richter, J. J{sub 1}-J{sub 2} Heisenberg model at and close to its z=4 quantum critical point.  United States: N. p., 2011. 
        Web.  doi:10.1103/PHYSREVB.84.144403.

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                    Sirker, J, Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern, Krivnov, V Y, Dmitriev, D V, Herzog, A, Janson, O, Nishimoto, S, Drechsler, S -L, & Richter, J. J{sub 1}-J{sub 2} Heisenberg model at and close to its z=4 quantum critical point.  United States.  https://doi.org/10.1103/PHYSREVB.84.144403

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                    Sirker, J, Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern, Krivnov, V Y, Dmitriev, D V, Herzog, A, Janson, O, Nishimoto, S, Drechsler, S -L, and Richter, J. 2011.  
        "J{sub 1}-J{sub 2} Heisenberg model at and close to its z=4 quantum critical point".  United States.  https://doi.org/10.1103/PHYSREVB.84.144403.

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@article{osti_21596896,

  title        = {J{sub 1}-J{sub 2} Heisenberg model at and close to its z=4 quantum critical point},

  author       = {Sirker, J and Research Center OPTIMAS, Technical University Kaiserslautern, D-67663 Kaiserslautern and Krivnov, V Y and Dmitriev, D V and Herzog, A and Janson, O and Nishimoto, S and Drechsler, S -L and Richter, J},

  abstractNote = {We study the frustrated J{sub 1}-J{sub 2} Heisenberg model with ferromagnetic nearest-neighbor coupling J{sub 1}<0 and antiferromagnetic next-nearest-neighbor coupling J{sub 2}>0 at and close to the z=4 quantum critical point (QCP) at J{sub 1}/J{sub 2}=-4. The J{sub 1}-J{sub 2} model plays an important role for recently synthesized chain cuprates as well as in supersymmetric Yang-Mills theories. We study the thermodynamic properties using field theory, a modified spin-wave theory, as well as numerical density-matrix renormalization group calculations. Furthermore, we compare with results for the classical model obtained by analytical methods and Monte Carlo simulations. As one of our main results, we present numerical evidence that the susceptibility at the QCP seems to diverge with temperature T as {chi}{approx}T{sup -1.2} in the quantum case, in contrast to the classical model where {chi}{approx}T{sup -4/3}.},

  doi          = {10.1103/PHYSREVB.84.144403},

  url          = {https://www.osti.gov/biblio/21596896},
  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  issn         = {1098-0121},

  number       = 14,

  volume       = 84,

  place        = {United States},

  year         = {Sat Oct 01 00:00:00 EDT 2011},

  month        = {Sat Oct 01 00:00:00 EDT 2011}

}

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