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Anyons in an exactly solved model and beyond
, 2005
"... A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge f ..."
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A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are nonAbelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and nonAbelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
Momentum space topology of fermion zero modes on brane
, 2008
"... We discuss fermion zero modes within the 3+1 brain – the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime, or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by nontrivial ..."
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We discuss fermion zero modes within the 3+1 brain – the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime, or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by nontrivial momentumspace topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity. The idea that our Universe lives on a brane embedded in higher dimensional space [1] is popular at the moment. It is the further development of an old ideas of extra compact dimensions introduced by Kaluza [2] and Klein [3]. In a new approach the compactification occurs because the lowenergy physics is concentrated within the brane, for example, in a flat 4dimensional
Momentum space topology and quantum phase transitions
, 2008
"... Most probably, our quantum vacuum belongs to strongly correlated and strongly interacting systems, which cannot be treated perturbatively. However, there are universal features which do not depend on details of the system. Here we illustrate this on some examples of quantum phase transitions, which ..."
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Most probably, our quantum vacuum belongs to strongly correlated and strongly interacting systems, which cannot be treated perturbatively. However, there are universal features which do not depend on details of the system. Here we illustrate this on some examples of quantum phase transitions, which can occur in the quantum vacuum or in the ground state of the condensed matter system. They are determined by the momentum space topology in combination with the vacuum symmetry. 1 Introduction. There are two schemes for the classification of states in condensed matter physics and relativistic quantum fields: classification by symmetry (GUT scheme) and by momentum space topology (antiGUT scheme). For the first classification method, a given state of the system is characterized
THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS SERIES EDITORS
"... 117. G. E. Volovik: The universe in a helium droplet ..."
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VORTICES OBSERVED AND TO BE OBSERVED
, 2000
"... Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and l ..."
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Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and lowdensity atomic BoseEinstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in 3 HeA and chiral Bose condensates; halfquantum vortices (Alice strings) in 3 HeA and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and dwave superconductors; vortex sheets in 3 HeA and chiral superconductors; the nexus – combined object formed by vortices and monopoles. Some properties of vortices related to the fermionic quasiparticles living in the vortex core are also discussed. PACS numbers: 67.57.Fg, 03.75.Fi, 74.90.+n, 11.27.+d 1.
MomentumSpace Topology of Standard Model
, 1999
"... The momentumspace topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetr ..."
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The momentumspace topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetric phase above the electroweak transition (the mass protection). All the invariants become zero in the broken symmetry phase, as a result all the elementary fermions become massive. Relation of the momentumspace invariants to chiral anomaly is also discussed. PACS numbers:71.10.w, 11.30.j, 67.57.z, 11.30.R 1.
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, 2008
"... Momentum space topology of fermion zero modes on brane ..."
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unknown title
, 2008
"... Interplay of real space and momentum space topologies in strongly correlated fermionic systems. ..."
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Interplay of real space and momentum space topologies in strongly correlated fermionic systems.