Journal ArticleDOI
Characteristic numbers of U1-valued lattice gauge fields
TLDR
In this paper, a U1-valued latice gauge field u defined on a periodic, 2-dimensional lattice satisfies the generic continuity condition uuuu ≠ − 1, it can be used to construct a principal U 1-bundle over the torus and in that bundle a connection such that parallel transport along bonds is given by u. The characteristic classes and numbers of this bundle can then be calculated from u in a straightforward way.About:
This article is published in Annals of Physics.The article was published on 1985-05-01. It has received 40 citations till now. The article focuses on the topics: Frame bundle & Parallel transport.read more
Citations
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Journal ArticleDOI
Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
TL;DR: A manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions.
Journal ArticleDOI
Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb
Takahiro Fukui,Yasuhiro Hatsugai +1 more
TL;DR: In this article, an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect is derived in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions.
Journal ArticleDOI
Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and edge versus bulk quantum numbers
TL;DR: In this article, the authors studied the topological quantum Hall effect (QHE) on a honeycomb lattice and found that the massless Dirac QHE around the center of the tight-binding band crossed over to the ordinary finite-mass fermion QHE at the band edges.
Journal ArticleDOI
Lattice gauge fields, principal bundles and the calculation of topological charge
Anthony Phillips,David A. Stone +1 more
TL;DR: In this article, the SU2-valued lattice gauge fields are studied on a 4-dimensional simplicial lattice, and an algorithm is explicitly given which associates an integer to everyu off a certain set of measure zero, which only involves evaluation of 4×4 determinants and the solution of quadratic equations.
Journal ArticleDOI
Remnants of the index theorem on the lattice
Jan Smit,Jeroen C. Vink +1 more
TL;DR: In this paper, the spectrum of lattice Dirac operators in two dimensions in external U(1) gauge fields was investigated and the properties and renormalization of the quantity m Tr γ 5 /(¶ + m) which provided a definition of topological charge based on axial-vector divergence relations.
References
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Journal ArticleDOI
Confinement of Quarks
TL;DR: In this paper, it is shown how to quantize a gauge field theory on a discrete lattice in Euclidean space-time, preserving exact gauge invariance and treating the gauge fields as angular variables.
Journal ArticleDOI
Gravitation, Gauge Theories and Differential Geometry
TL;DR: In this article, the Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois, USA Peter B. GILKEY Fine Hall, Box 37.
Journal ArticleDOI
Phase transitions in Abelian lattice gauge theories
TL;DR: In this paper, the Euclidean partition function of Abelian lattice (gauge) theories in various dimensions was studied using generalizations of mathematical methods developed recently to study the XY model in two dimensions and physical pictures of the phases of these more complicated theories.
Book ChapterDOI
Differential characters and geometric invariants
Jeff Cheeger,James Simons +1 more
TL;DR: A collection of lecture notes which were distributed at the A.M.S. Summer Institute on Differential Geometry, held at Stanford in 1973, has been made available in their original form as discussed by the authors.
Journal ArticleDOI
Topology of lattice gauge fields
TL;DR: In this article, non-Abelian gauge fields on a four-dimensional hypercubic lattice with small action density were shown to carry an integer topological charge, which is invariant under continuous deformations of the field.