Disordered Dirac fermions: the marriage of three different approaches

Bhaseen, M. J.; Caux, Jean-Sébastien; Kogan, Ian I.; Tsvelik, A. M.

doi:10.1016/s0550-3213(01)00432-1

Cited by 53 publications

(81 citation statements)

References 76 publications

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“…Our general goal is to explore in physical terms certain non-unitary CFTs of physical importance. Belonging to this family of theories are the various supergroup Wess-Zumino-Witten (WZW) and sigma models used in the description of phase transitions in disordered electronic materials [1,2,3,4,5,6], the Liouville theory which describes the conformal mode of 2D gravity [7,8], and the sl(2, R) WZW model which plays a crucial role in the study of strings on AdS 3 [9].…”

Section: Introductionmentioning

confidence: 99%

The WZW model and the βγ system

et al. 2002

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The bosonic βγ ghost system has long been used in formal constructions of conformal field theory. It has become important in its own right in the last few years, as a building block of field theory approaches to disordered systems, and as a simple representative -due in part to its underlying su(2) −1/2 structure -of non-unitary conformal field theories. We provide in this paper the first complete, physical, analysis of this βγ system, and uncover a number of striking features. We show in particular that the spectrum involves an infinite number of fields with arbitrarily large negative dimensions. These fields have their origin in a twisted sector of the theory, and have a direct relationship with spectrally flowed representations in the underlying su(2) −1/2 theory. We discuss the spectral flow in the context of the operator algebra and fusion rules, and provide a re-interpretation of the modular invariant consistent with the spectrum.

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Section: Introductionmentioning

confidence: 99%

The WZW model and the βγ system

et al. 2002

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“…(When supersymmetric disorder averaging is used, this is [14] the WZW model on Osp(2|2) at level −ν [15].) We emphasise that the WZW term cannot appear for any two-dimensional disordered systems on a lattice, such as disordered d x 2 −y 2 -wave superconductors on the square lattice.…”

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confidence: 99%

Lattice Model of a Three-Dimensional Topological Singlet Superconductor with Time-Reversal Symmetry

2009

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We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these particle-hole symmetric systems the topological phases are characterized by an even-numbered winding number ν. At a two-dimensional (2D) surface the topological properties of this quantum state manifest themselves through the presence of ν flavors of gapless Dirac fermion surface states, which are robust against localization from random impurities. We construct a tightbinding model on the diamond lattice that realizes a topologically nontrivial phase, in which the winding number takes the value ν = ±2. Disorder corresponds to a (non-localizing) random SU(2) gauge potential for the surface Dirac fermions, leading to a power-law density of states ρ(ǫ) ∼ ǫ 1/7 . The bulk effective field theory is proposed to be the (3+1) dimensional SU(2) Yang-Mills theory with a theta-term at θ = π.PACS numbers: 73.20.At, 74.25.Fy, 73.20.Fz, 03.65.Vf Bloch-Wilson band insulators are commonly believed to be simple and well understood electronic states of matter. However, recent theoretical [1,2,3,4,5,6] and experimental [7,8] progress has shown that band insulators can exhibit unusual and conducting boundary modes, which are topologically protected, analogous to the edge states of the integer quantum Hall effect (QHE). These so-called Z 2 topological insulators (also known as 'quantum spin Hall' insulators), which exist in two-and threedimensional (3D) time-reversal invariant (TRI) systems, are characterized by a topological invariant, similar to the Chern number of the integer QHE. Given these newly discovered topological states, one might wonder whether there exists a general organizing principle for topological insulators. Indeed, the integer QHE and the Z 2 topological insulators are in fact part of a larger scheme, discussed in Ref. [6], which provides an exhaustive classification of topological insulators and superconductors in terms of spatial dimension and the presence or absence of the two most generic symmetries of the Hamiltonian, time-reversal and particle-hole symmetry [9].Using this classification scheme which was originally introduced in the context of disordered systems [10], it was shown in Ref.[6] that, besides the 3D Z 2 topological insulator, there are precisely four more 3D topological quantum states. Among these there is one which is particularly interesting from the point of view of possible experimental realizations. It is called the topological superconductor in symmetry class CI in the terminology of Ref.[6] and can be realized in time-reversal invariant singlet BCS superconductors. While the bulk is fully gapped in this topological quantum state, there are gapless robust Dirac states at the two-dimensional boundary. The CI topological superconductor is unique among 3D topological quantum states in that it does not break SU(2) spin rotation symmetry, and therefore supports the transport of spin through gapless surface modes. The different topological phases of the CI topological supercon...

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“…This formulation is motivated by the network model by Chalker and Coddington [19] and it is in contrast to other formulations like that using the conformal field theory. Therefore it is not so surprising even if the decay power of the correlator (3.7) is different from that obtained in other methods [8]. The power-decay behaviour (3.7) means the existence of the extended states anyway.…”

Section: Lsusy and Localizationmentioning

confidence: 82%

“…This system is closed related with the phase transition between plateaus in the quantum Hall states and quasiexcitations in the d-wave supercondctor [1,2,3,4,5,6,7,8]. However it is still controversial if there exist extended states at the band center.…”

Section: Introductionmentioning

confidence: 99%

Lattice Dirac Fermions in a Non-Abelian Random Gauge Potential: Many Flavors, Chiral Symmetry Restoration and Localization

Ichinose

2002

Mod. Phys. Lett. A

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In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed there that at strong-disorder limit correlation function of the fermion local density of states decays algebraically at the band center. In this paper, we shall reexamine the multiflavor or multi-species case rather in detail and argue that the correlator at the band center decays exponentially for the case of a large number of flavors. This means that a delocalization-localization phase transition occurs as the number of flavors is increased. This discussion is supported by the recent numerical studies on multiflavor QCD at the strong-coupling limit, which shows that the phase structure of QCD drastically changes depending on the number of flavors. The above behaviour of the correlator of the random Dirac fermions is closely related with how the chiral symmetry is realized in QCD.

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Disordered Dirac fermions: the marriage of three different approaches

Cited by 53 publications

References 76 publications

The WZW model and the βγ system

The WZW model and the βγ system

Lattice Model of a Three-Dimensional Topological Singlet Superconductor with Time-Reversal Symmetry

Lattice Dirac Fermions in a Non-Abelian Random Gauge Potential: Many Flavors, Chiral Symmetry Restoration and Localization

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