1
|
Abstract
It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.
Collapse
|
2
|
Evangelou SN, Katsanos DE. Spectral statistics in chiral-orthogonal disordered systems. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/12/322] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
3
|
Plerou V, Gopikrishnan P, Rosenow B, Amaral LAN, Guhr T, Stanley HE. Random matrix approach to cross correlations in financial data. PHYSICAL REVIEW E 2002; 65:066126. [PMID: 12188802 DOI: 10.1103/physreve.65.066126] [Citation(s) in RCA: 170] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2001] [Indexed: 11/07/2022]
Abstract
We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"--a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [lambda(-),lambda(+)] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these "deviating eigenvectors" are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.
Collapse
Affiliation(s)
- Vasiliki Plerou
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
| | | | | | | | | | | |
Collapse
|
4
|
|
5
|
Oppermann R, Jungling K. Determination of universality classes for spin-dependent ensembles with time-reversal invariance. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/14/26/011] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
6
|
Oppermann R. Critical localisation behaviour of spin-dependent ensembles with broken time-reversal invariance. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/14/26/012] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
7
|
|
8
|
Kopp T. A diagrammatic two-particle locator theory for disordered systems. II. Self-consistent treatment of the Anderson transition and the role of hopping processes. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/17/11/012] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
9
|
Castellani C, Castro CD, Forgacs G, Tabet E. Gauge invariance and the multiplicative renormalisation group in the Anderson transition. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/16/1/018] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
10
|
Evangelou SN. Spectral singularities and localisation in one- and quasi-one-dimensional systems with off-diagonal disorder. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/19/22/015] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
11
|
Evangelou SN. Universal scaling near the band edge for one-dimensional disordered systems. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/20/8/001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
12
|
|
13
|
Nakhmedov EP, Kumru M, Oppermann R. Density of states of disordered two-dimensional crystals with half-filled band. PHYSICAL REVIEW LETTERS 2000; 84:3930-3933. [PMID: 11019242 DOI: 10.1103/physrevlett.84.3930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/1999] [Indexed: 05/23/2023]
Abstract
A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P0 = +/-pi / a,pi / a for a half-filled electronic band. The density of electronic states (DoS) is shown to have nontrivial quantum corrections due to both nesting and elastic impurity scattering processes, and as a result the Van Hove singularity is preserved in the center of the band. However, the energy dependence of the DoS is significantly changed. A small offset from the middle of the band gives rise to the disappearance of quantum corrections to the DoS.
Collapse
Affiliation(s)
- EP Nakhmedov
- Institut fur Theoretische Physik, Universitat Wurzburg, D-97074 Wurzburg, Germany and Institute of Physics, Azerbaijan Academy of Sciences, H. Cavid Street 33, Baku, Azerbaijan
| | | | | |
Collapse
|
14
|
Lee DK, Kim DH, Lee PA. Degenerate Bose liquid in a fluctuating gauge field. PHYSICAL REVIEW LETTERS 1996; 76:4801-4804. [PMID: 10061384 DOI: 10.1103/physrevlett.76.4801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
15
|
Taniguchi N, Simons BD, Altshuler BL. Spectral correlation and response functions in quantum dots. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:R7618-R7621. [PMID: 9982281 DOI: 10.1103/physrevb.53.r7618] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
16
|
Girko VL. A Matrix Equation for Resolvents of Random Matrices with Independent Blocks. THEORY OF PROBABILITY AND ITS APPLICATIONS 1996. [DOI: 10.1137/1140073] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
17
|
Magalhães SG, Theumann A. Magnetoconductivity of a disordered electron system with N orbitals per site. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:5691-5694. [PMID: 10011529 DOI: 10.1103/physrevb.49.5691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
18
|
Inui M, Trugman SA, Abrahams E. Unusual properties of midband states in systems with off-diagonal disorder. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:3190-3196. [PMID: 10011177 DOI: 10.1103/physrevb.49.3190] [Citation(s) in RCA: 78] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
19
|
Sugiyama T, Nagaosa N. Localization in a random magnetic field in 2D. PHYSICAL REVIEW LETTERS 1993; 70:1980-1983. [PMID: 10053435 DOI: 10.1103/physrevlett.70.1980] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
20
|
VOLLHARDT DIETER, WÖLFLE PETER. Self-Consistent Theory of Anderson Localization. MODERN PROBLEMS IN CONDENSED MATTER SCIENCES 1992. [DOI: 10.1016/b978-0-444-88885-3.50006-8] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
|
21
|
Khurana A. Spectrum of the correlation matrix in short-range Ising spin glasses. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:9279-9282. [PMID: 9991417 DOI: 10.1103/physrevb.40.9279] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
22
|
Ando T. Numerical study of symmetry effects on localization in two dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:5325-5339. [PMID: 9992560 DOI: 10.1103/physrevb.40.5325] [Citation(s) in RCA: 111] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
23
|
Bickers NE, Cox DL, Wilkins JW. Self-consistent large-N expansion for normal-state properties of dilute magnetic alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:2036-2079. [PMID: 9943050 DOI: 10.1103/physrevb.36.2036] [Citation(s) in RCA: 258] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
24
|
Singh A, Fradkin E. Localization and correlation effects in itinerant ferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:6894-6901. [PMID: 9940947 DOI: 10.1103/physrevb.35.6894] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
25
|
Kirkpatrick TR, Belitz D. Critical behavior of transverse sound attenuation at a mobility edge. PHYSICAL REVIEW. B, CONDENSED MATTER 1986; 34:9008-9011. [PMID: 9939643 DOI: 10.1103/physrevb.34.9008] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
26
|
Mazenko GF. Simple model for the inflationary expansion of the early Universe. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1986; 34:2223-2240. [PMID: 9957409 DOI: 10.1103/physrevd.34.2223] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
27
|
Belitz D, Kirkpatrick TR. Universal coefficients of perturbation expansion for the Anderson localization problem. PHYSICAL REVIEW. B, CONDENSED MATTER 1986; 33:7332-7335. [PMID: 9938085 DOI: 10.1103/physrevb.33.7332] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
28
|
Kim Y, Harris AB. Density of states of the random-hopping model on a Cayley tree. PHYSICAL REVIEW. B, CONDENSED MATTER 1985; 31:7393-7407. [PMID: 9935663 DOI: 10.1103/physrevb.31.7393] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
29
|
Schreiber M. Fractal character of eigenstates in weakly disordered three-dimensional systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1985; 31:6146-6149. [PMID: 9936631 DOI: 10.1103/physrevb.31.6146] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
30
|
The Scaling Theory of Localisation. ACTA ACUST UNITED AC 1985. [DOI: 10.1007/978-3-642-82516-3_9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
31
|
Oppermann R. Magnetic field induced crossover in weakly localized regimes and scaling of the conductivity. ACTA ACUST UNITED AC 1984. [DOI: 10.1051/jphyslet:0198400450240116100] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
|
32
|
|
33
|
Schäfer L, Wegner F. Disordered system withn orbitals per site: Lagrange formulation, hyperbolic symmetry, and goldstone modes. ACTA ACUST UNITED AC 1980. [DOI: 10.1007/bf01598751] [Citation(s) in RCA: 301] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
34
|
Effects of spin interactions in disordered electronic systems: Loop expansions and exact relations among local gauge invariant models. ACTA ACUST UNITED AC 1980. [DOI: 10.1007/bf01598749] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
35
|
|
36
|
|