Numerical renormalization group method for quantum impurity systems

被引:1217
作者
Bulla, Ralf [1 ,2 ]
Costi, Theo A. [3 ]
Pruschke, Thomas [4 ]
机构
[1] Univ Augsburg, Inst Phys, D-86135 Augsburg, Germany
[2] Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany
[3] Forschungszentrum Julich, D-52425 Julich, Germany
[4] Univ Gottingen, Inst Theoret Phys, D-37077 Gottingen, Germany
关键词
D O I
10.1103/RevModPhys.80.395
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.
引用
收藏
页码:395 / 450
页数:56
相关论文
共 324 条
[1]  
AFFLECK I, 1992, PHYS REV B, V45, P7918, DOI 10.1103/PhysRevB.45.7918
[2]   EXACT CRITICAL-THEORY OF THE 2-IMPURITY KONDO MODEL [J].
AFFLECK, I ;
LUDWIG, AWW .
PHYSICAL REVIEW LETTERS, 1992, 68 (07) :1046-1049
[3]   CONFORMAL-FIELD-THEORY APPROACH TO THE 2-IMPURITY KONDO PROBLEM - COMPARISON WITH NUMERICAL RENORMALIZATION-GROUP RESULTS [J].
AFFLECK, I ;
LUDWIG, AWW ;
JONES, BA .
PHYSICAL REVIEW B, 1995, 52 (13) :9528-9546
[4]   EFFECT OF COULOMB REPULSION BETWEEN LOCALIZED AND EXTENDED STATES IN THE ANDERSON MODEL [J].
ALASCIO, B ;
ALLUB, R ;
BALSEIRO, CA .
PHYSICAL REVIEW B, 1986, 34 (07) :4786-4789
[5]   GROUND-STATE AND MAGNETIC-SUSCEPTIBILITY OF INTERMEDIATE-VALENCE TM IMPURITIES [J].
ALLUB, R ;
ALIGIA, AA .
PHYSICAL REVIEW B, 1995, 52 (11) :7987-7993
[6]   Phase coherence of conduction electrons below the Kondo temperature [J].
Alzoubi, Gassem M. ;
Birge, Norman O. .
PHYSICAL REVIEW LETTERS, 2006, 97 (22)
[7]   Can competition between the crystal field and the Kondo effect cause non-fermi-liquid-like behavior? [J].
Anders, FB ;
Pruschke, T .
PHYSICAL REVIEW LETTERS, 2006, 96 (08) :1-4
[8]   Coulomb blockade and non-Fermi-liquid behavior in quantum dots [J].
Anders, FB ;
Lebanon, E ;
Schiller, A .
PHYSICAL REVIEW B, 2004, 70 (20) :201306-1
[9]   Renormalization-group approach to spectral properties of the two-channel Anderson impurity model [J].
Anders, FB .
PHYSICAL REVIEW B, 2005, 71 (12)
[10]   X-ray singularities in the f-electron spectral function of the Falicov-Kimball model -: art. no. 125101 [J].
Anders, FB ;
Czycholl, G .
PHYSICAL REVIEW B, 2005, 71 (12)