Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

If light of a frequency which corresponds to an energy greater than the ionisation potential falls on an atom, an electron may be ejected and energy absorbed. To calculate the absorption coefficient, or the rate of absorption of energy per unit intensity of incident radiation for a given frequency, one must first choose a model for the atom. If we confine ourselves to the inner K electrons there will be two electrons in this shell for the heavier atoms, and a fairly good model of the atom is obtained by considering each electron to be moving independently in a central field of force due to the charged nucleus: i.e. we neglect electronic interaction and assume that the wave functions for the system are hydrogenic. Some writers make a partial correction for this neglect of interaction by modifying the central charge through the introduction of a screening factor which is so chosen that the minimum calculated energy required to remove one of the K electrons will agree with the experimental value provided by the K absorption edge. In general, however, the approximation is fairly good, and this is particularly so in the interior of a star where the atoms are highly ionised. It is not so good when the atom is bound as in a metal, and, of course, most of the laboratory work has been carried out on atoms in this bound state.

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Wave functions of bosonic symmetry protected topological phases

Physical Review B ◽

10.1103/physrevb.87.174412 ◽

2013 ◽

Vol 87 (17) ◽

Cited By ~ 62

Author(s):

Cenke Xu ◽

T. Senthil

Keyword(s):

Wave Functions ◽

Topological Phases ◽

Symmetry Protected

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The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

Nuclear Physics B ◽

10.1016/j.nuclphysb.2017.03.021 ◽

2017 ◽

Vol 919 ◽

pp. 470-503 ◽

Cited By ~ 13

Author(s):

Lokman Tsui ◽

Yen-Ta Huang ◽

Hong-Chen Jiang ◽

Dung-Hai Lee

Keyword(s):

Phase Transitions ◽

Critical Points ◽

Central Charge ◽

Topological Phases ◽

Symmetry Protected

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Central charge, trace and gravitational anomalies in two dimensions

Physical Review D ◽

10.1103/physrevd.38.2482 ◽

1988 ◽

Vol 38 (8) ◽

pp. 2482-2489 ◽

Cited By ~ 3

Author(s):

E. Guadagnini

Keyword(s):

Central Charge ◽

Two Dimensions ◽

Gravitational Anomalies

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Chiral edge states in (2+1)-dimensional topological phases

International Journal of Modern Physics A ◽

10.1142/s0217751x19501719 ◽

2019 ◽

Vol 34 (29) ◽

pp. 1950171

Author(s):

Carlos A. Hernaski ◽

Pedro R. S. Gomes

Keyword(s):

Degrees Of Freedom ◽

Quantum Wires ◽

Central Charge ◽

Gauge Fields ◽

Topological Phases ◽

Edge States ◽

Conformal Field Theories ◽

Conformal Field ◽

Fermionic Fields ◽

Gauge Anomalies

Chiral edge states of [Formula: see text]-dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and noninteger values of central charge, respectively. In this work we describe certain edge states in terms of constrained fermionic fields that realize chiral coset CFT structures. This construction arises naturally in the so-called quantum wires approach for topological phases and allows for representing fractionalized edge states directly in terms of fermionic degrees of freedom. At the same time, the constrained fermions description introduces some subtleties concerning gauge anomalies since it involves the coupling of chiral fermions to gauge fields. We describe in this paper how to handle these issues.

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