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The renormalization group: Critical phenomena and the Kondo problem
Abstract
This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in detail. See Secs. VII-IX. "Block spin" methods, applied to the two dimensional Ising model, are explained in Sec. VI. The first three sections give a relatively short review of basic renormalization group ideas, mainly in the context of critical phenomena. The relationship of the modern renormalization group to the older problems of divergences in statistical mechanics and field theory and field theoretic renormalization is discussed in Sec. IV. In Sec. V the special case of "marginal variables" is discussed in detail, along with the relationship of the modern renormalization group to its original formulation by Gell-Mann and Low and others.
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White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
Georges, A., Kotliar, G., Krauth, W., & Rozenberg, M. J. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.13 · Cited by 6,901
Dynamics of the dissipative two-state system
Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., & Zwerger, W. (1987) · Reviews of Modern Physics · doi:10.1103/revmodphys.59.1 · Cited by 5,109
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
Density-matrix algorithms for quantum renormalization groups
White, S. R. (1993) · Physical Review B · doi:10.1103/physrevb.48.10345 · Cited by 3,244
Vicsek, T., & Zafeiris, A. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.03.004 · Cited by 2,923
Colloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Entanglement renormalization and holography
Swingle, B. (2012) · Physical Review D · doi:10.1103/physrevd.86.065007 · Cited by 915
Matrix product states represent ground states faithfully
Verstraete, F., & Cirac, J. I. (2006) · Physical Review B · doi:10.1103/physrevb.73.094423 · Cited by 730
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Chan, G. K.-L., & Head-Gordon, M. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1449459 · Cited by 554
Tensor product methods and entanglement optimization for ab initio quantum chemistry
Szalay, S., Pfeffer, M., Murg, V., Barcza, G., Verstraete, F., Schneider, R., & Legeza, Ö. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24898 · Cited by 314
Baiardi, A., & Reiher, M. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5129672 · Cited by 306
Legeza, Ö., Röder, J., & Hess, B. A. (2003) · Physical Review B · doi:10.1103/physrevb.67.125114 · Cited by 263
Tagliacozzo, L., Evenbly, G., & Vidal, G. (2009) · Physical Review B · doi:10.1103/physrevb.80.235127 · Cited by 261
Simulating strongly correlated quantum systems with tree tensor networks
Murg, V., Verstraete, F., Legeza, Ö., & Noack, R. M. (2010) · Physical Review B · doi:10.1103/physrevb.82.205105 · Cited by 245
Mapping local Hamiltonians of fermions to local Hamiltonians of spins
Verstraete, F., & Cirac, J. I. (2005) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2005/09/p09012 · Cited by 196
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Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture Notes in Physics · doi:10.1007/978-3-030-34489-4 · Cited by 176
Quantum circuits for strongly correlated quantum systems
Verstraete, F., Cirac, J. I., & Latorre, J. I. (2009) · Physical Review A · doi:10.1103/physreva.79.032316 · Cited by 158
Quantum Hamiltonian Complexity
Gharibian, S., Huang, Y., Landau, Z., & Shin, S. W. (2015) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000066 · Cited by 144
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Li, S.-H., & Wang, L. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.260601 · Cited by 140
Entanglement, Quantum Phase Transitions, and Density Matrix Renormalization
Osborne, T. J., & Nielsen, M. A. (2002) · Quantum Information Processing · doi:10.1023/a:1019601218492 · Cited by 95
Rams, M. M., Czarnik, P., & Cincio, L. (2018) · Physical Review X · doi:10.1103/physrevx.8.041033 · Cited by 81
Transfer matrices and excitations with matrix product states
Zauner, V, Draxler, D., Vanderstraeten, L., Degroote, M., Haegeman, J., Rams, M. M., Stojevic, V, Schuch, N., & Verstraete, F. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/5/053002 · Cited by 80
Applying the Variational Principle to (1+1)-Dimensional Quantum Field Theories
Haegeman, J., Cirac, J. I., Osborne, T. J., Verschelde, H., & Verstraete, F. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.251601 · Cited by 59
Quantum algorithms for classical lattice models
De las Cuevas, G., Dür, W., Van den Nest, M., & Martin-Delgado, M. A. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/9/093021 · Cited by 40
The quartic oscillator: a non-perturbative study by continuous unitary transformations
Dusuel, S., & Uhrig, G. S. (2004) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/37/39/014 · Cited by 38
Relevance in the Renormalization Group and in Information Theory
Gordon, A., Banerjee, A., Koch-Janusz, M., & Ringel, Z. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.240601 · Cited by 18
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Metadata
- Authors
- Wilson, K. G.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1975-10-01
- Volume
- 47
- Issue
- 4
- Pages
- 773-840
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2052810501
- Cited by
- 4,522
- References
- 0
- FWCI
- 33.66
- Type
- journal article
- Language
- en
- Open access
- closed
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