Heisenberg necklace model in a magnetic field

Tsvelik, A. M.; Zaliznyak, I. A.

doi:10.1103/PhysRevB.94.075152

Title: Heisenberg necklace model in a magnetic field

Abstract

Here, we study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO₂ and Sr₂CuO₃ cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J. We also consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I=3/2) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ~J^1/3(γI)^2/3, at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. Furthermore, this energy scale is insensitive to a magnetic field B. For _μBB>Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, 2√+1.

Authors:

Tsvelik, A. M. ^[1]; Zaliznyak, I. A. ^[1]

Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Division

Publication Date:: Fri Aug 26 00:00:00 EDT 2016

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1336113

Alternate Identifier(s):: OSTI ID: 1307794

Report Number(s):: BNL-112559-2016-JA
Journal ID: ISSN 2469-9950; PRBMDO; R&D Project: PO015; PO010; KC0202030; KC0201060

Grant/Contract Number:: SC00112704; AC02-98CH10886

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 94; Journal Issue: 7; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Tsvelik, A. M., and Zaliznyak, I. A. Heisenberg necklace model in a magnetic field.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevB.94.075152.

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                    Tsvelik, A. M., & Zaliznyak, I. A. Heisenberg necklace model in a magnetic field.  United States.  https://doi.org/10.1103/PhysRevB.94.075152

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                    Tsvelik, A. M., and Zaliznyak, I. A. Fri .  
"Heisenberg necklace model in a magnetic field".  United States.  https://doi.org/10.1103/PhysRevB.94.075152.  https://www.osti.gov/servlets/purl/1336113.

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@article{osti_1336113,

  title        = {Heisenberg necklace model in a magnetic field},

  author       = {Tsvelik, A. M. and Zaliznyak, I. A.},

  abstractNote = {Here, we study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J. We also consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I=3/2) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ~J1/3(γI)2/3, at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. Furthermore, this energy scale is insensitive to a magnetic field B. For μBB>Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, 2√+1.},

  doi          = {10.1103/PhysRevB.94.075152},

  journal      = {Physical Review B},

  number       = 7,

  volume       = 94,

  place        = {United States},

  year         = {Fri Aug 26 00:00:00 EDT 2016},

  month        = {Fri Aug 26 00:00:00 EDT 2016}

}

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Similar Records

Title: Heisenberg necklace model in a magnetic field

Abstract

Citation Formats

Asymmetric spin- 1 2 two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations journal, November 2010

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models journal, August 1979

Anisotropic Spin Freezing in the S = 1 / 2 Zigzag Chain Compound SrCuO 2 journal, December 1999

Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State journal, April 1983

Investigation of a gap in the AFMR spectrum in the quasi-one-dimensional hexagonal antiferromagnet CsMnBr3 journal, September 1996

Impurities in S = 1 / 2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift journal, July 1995

Spinons in the Strongly Correlated Copper Oxide Chains in S r C u O 2 journal, August 2004

Magnetic ordering, spin waves, and Haldane-gap excitations in ( Nd x Y 1 − x ) 2 BaNiO 5 linear-chain mixed-spin antiferromagnets journal, December 1998

Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains journal, November 1992

Magnetic ordering of Nd in (Nd,Ce ) 2 CuO 4 journal, February 1990

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional Antiferromagnets Sr 2 CuO 3 and Ca 2 CuO 3 journal, March 1997

Quantum Field Theory in Condensed Matter Physics book, January 2010

Nuclear magnetic resonance of 55Mn in the antiferromagnet CsMnBr3 in a variable longitudinal magnetic field journal, June 1999

Critical theory of quantum spin chains journal, October 1987

Quantum Impurity in a Nearly Critical Two-Dimensional Antiferromagnet journal, December 1999

Relation between the Anderson and Kondo Hamiltonians journal, September 1966

The Kondo lattice and weak antiferromagnetism journal, July 1977

Quantum Phase Transition of a Magnet in a Spin Bath journal, April 2005

Exact solution of the O(3) nonlinear σ-model journal, March 1985

Quantum impurity in an antiferromagnet: Nonlinear sigma model theory journal, August 2003

Theory of nonabelian goldstone bosons in two dimensions journal, November 1983

Experimental Measurement of the Staggered Magnetization Curve for a Haldane Spin Chain journal, April 1998

Luttinger liquid coupled to quantum spins: Flow equation approach to the Kondo necklace model journal, September 2007

Quantum Phase Transitions book, January 2011

Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds journal, October 2009

Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model journal, February 1983

Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors journal, June 2000

Massless factorized scattering and sigma models with topological terms journal, July 1992

Spin gap in chains with hidden symmetries journal, March 2005

Asymmetric spin- $\frac{1}{2}$ two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations
journal, November 2010

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
journal, August 1979

Anisotropic Spin Freezing in the $S = 1 / 2$ Zigzag Chain Compound ${SrCuO}_{2}$
journal, December 1999

Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
journal, April 1983

Investigation of a gap in the AFMR spectrum in the quasi-one-dimensional hexagonal antiferromagnet CsMnBr3
journal, September 1996

Impurities in $S = 1 / 2$ Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift
journal, July 1995

Spinons in the Strongly Correlated Copper Oxide Chains in ${S r C u O}_{2}$
journal, August 2004

Magnetic ordering, spin waves, and Haldane-gap excitations in $({Nd}_{x} Y_{1 - x})_{2} {BaNiO}_{5}$ linear-chain mixed-spin antiferromagnets
journal, December 1998

Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains
journal, November 1992

Magnetic ordering of Nd in (Nd,Ce $)_{2}$ ${CuO}_{4}$
journal, February 1990

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional Antiferromagnets ${Sr}_{2} {CuO}_{3}$ and ${Ca}_{2} {CuO}_{3}$
journal, March 1997

Quantum Field Theory in Condensed Matter Physics
book, January 2010

Nuclear magnetic resonance of 55Mn in the antiferromagnet CsMnBr3 in a variable longitudinal magnetic field
journal, June 1999

Critical theory of quantum spin chains
journal, October 1987

Quantum Impurity in a Nearly Critical Two-Dimensional Antiferromagnet
journal, December 1999

Relation between the Anderson and Kondo Hamiltonians
journal, September 1966

The Kondo lattice and weak antiferromagnetism
journal, July 1977

Quantum Phase Transition of a Magnet in a Spin Bath
journal, April 2005

Exact solution of the O(3) nonlinear σ-model
journal, March 1985

Quantum impurity in an antiferromagnet: Nonlinear sigma model theory
journal, August 2003

Theory of nonabelian goldstone bosons in two dimensions
journal, November 1983

Experimental Measurement of the Staggered Magnetization Curve for a Haldane Spin Chain
journal, April 1998

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journal, September 2007

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book, January 2011

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journal, October 2009

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journal, February 1983

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