A holographic two-impurity Kondo model

被引:17
|
作者
O'Bannon, Andy [1 ]
Papadimitriou, Ioannis [2 ,3 ]
Probst, Jonas [4 ]
机构
[1] Univ Southampton, STAG Res Ctr, Phys & Astron, Southampton SO17 1BJ, Hants, England
[2] SISSA, Via Bonomea 265, I-34136 Trieste, Italy
[3] Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy
[4] Univ Oxford, Rudolf Peierls Ctr Theoret Phys, 1 Keble Rd, Oxford OX1 3NP, England
来源
JOURNAL OF HIGH ENERGY PHYSICS | 2016年 / 01期
基金
欧洲研究理事会;
关键词
Holography and condensed matter physics (AdS/CMT); Gauge-gravity correspondence; AdS-CFT Correspondence; CONFORMAL-FIELD-THEORY; RENORMALIZATION-GROUP APPROACH; DILUTE MAGNETIC-ALLOYS; ANDERSON MODEL; QUANTUM CRITICALITY; STATIC PROPERTIES; CRITICAL-POINT; FERMI LIQUIDS; GAUGE-THEORY; PHASE;
D O I
10.1007/JHEP01(2016)103
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We propose a model of a strongly-interacting two-impurity Kondo system based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. In a Landau Fermi Liquid, the single-impurity Kondo effect is the screening of an impurity spin at low temperature T. The two-impurity Kondo model then describes the competition between the Kondo interaction and the Heisenberg interaction between two impurity spins, also called the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For spin-1/2 impurities, that competition leads to a quantum phase transition from a Kondo-screened phase to a phase in which the two impurity spins screen one another. Our holographic model is based on a (1 + 1)-dimensional CFT description of the two-impurity Kondo model, reliable for two impurities with negligible separation in space. We consider only impurity spins in a totally anti-symmetric representation of an SU(N) spin symmetry. We employ a large-N limit, in which both Kondo and RKKY couplings are double-trace, and both Kondo and inter-impurity screening appear as condensation of single-trace operators at the impurities' location. We perform the holographic renormalization of our model, which allows us to identify the Kondo and RKKY couplings as boundary conditions on fields in AdS. We numerically compute the phase diagram of our model in the plane of RKKY coupling versus T, finding evidence for a quantum phase transition from a trivial phase, with neither Kondo nor inter-impurity screening, to a non-trivial phase, with both Kondo and anti-ferromagnetic inter-impurity screening. More generally we show, just using SU(N) representation theory, that ferromagnetic correlations must be absent at leading order in the large-N limit. Our holographic model may be useful for studying many open problems involving strongly-interacting quantum impurities, including for example the Kondo lattice, relevant for describing the heavy fermion compounds.
引用
收藏
页码:1 / 62
页数:62
相关论文
共 50 条
  • [1] A holographic two-impurity Kondo model
    Andy O’Bannon
    Ioannis Papadimitriou
    Jonas Probst
    Journal of High Energy Physics, 2016
  • [2] Integrable two-impurity Kondo model
    Schlottmann, P
    PHYSICAL REVIEW LETTERS, 1998, 80 (22) : 4975 - 4978
  • [3] Thermodynamics for the two-impurity Kondo model
    Campo, VL
    Oliveira, LN
    PHYSICAL REVIEW B, 2004, 70 (15) : 153401 - 1
  • [4] Quantum entanglement in the two-impurity Kondo model
    Cho, SY
    McKenzie, RH
    PHYSICAL REVIEW A, 2006, 73 (01):
  • [5] A two-impurity model for the underscreened Kondo problem
    LeHur, K
    Coqblin, B
    PHYSICA B, 1997, 230 : 454 - 456
  • [6] Two-impurity model for the underscreened Kondo problem
    Le Hur, K.
    Coqblin, B.
    Physica B: Condensed Matter, 230-232 : 454 - 456
  • [7] Absence of two energy scales in the two-impurity Kondo model
    Fischer, K
    PHYSICAL REVIEW B, 1998, 57 (12) : R6771 - R6774
  • [8] Two-impurity Kondo model with spin-orbit interactions
    Mross, David F.
    Johannesson, Henrik
    PHYSICAL REVIEW B, 2009, 80 (15)
  • [9] Two-Channel Kondo Physics in Two-Impurity Kondo Models
    Mitchell, Andrew K.
    Sela, Eran
    Logan, David E.
    PHYSICAL REVIEW LETTERS, 2012, 108 (08)
  • [10] Particle-hole asymmetry in the two-impurity Kondo model
    Silva, JB
    Lima, WLC
    Oliveira, WC
    Mello, JLN
    Oliveira, LN
    Wilkins, JW
    PHYSICAL REVIEW LETTERS, 1996, 76 (02) : 275 - 278