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Research

הדפסה דוא

graphene                                           

FIELD THEORETICAL EFFECTS IN CONDENSED MATTER SYSTEMS

 

     Condensed matter systems with emergent relativistic invariance may serve as an arena for the experimental observation of various effects typical for the high - energy physics. In particular, some of such effects were predicted and checked experimentally in 2+1 D graphene, where the relativistic 2+1 D fermions appear in the vicinity of the Fermi points (see the detailed review in 1). The emergent 3+1 D relativistic fermions appear in He-3A superfluid. (For the description of various emergent relativistic effects in He-3 see 2.) Recently, the 3+1 D relativistic fermions were discovered experimentally in the novel materials - the Dirac and Weyl semimetals. Weyl semimetals differ from Dirac semimetals by the difference in the positions of the Fermi points for the left - handed and the right - handed fermions. In Dirac semimetals the left - handed and the right - handed Weyl fermions always come in pairs located at the same Dirac point. The description of certain relativistic effects that may exist in Dirac and Weyl semimetals was given already before the experimental discovery of Dirac semimetals and Weyl semimetals. It is planned to proceed the previous investigation of condensed matter systems with emergent relativistic invariance. In the previous papers we concentrated on the 2+1 D graphene and the 3+1 D Dirac and Weyl semimetals. In particular, the emergent gravity was discussed, and the effects of emergent gravity and emergent gauge fields were investigated in the presence of dislocations. The Aharonov - Bohm and Stodolsky effects in the scattering of the quasiparticles on the dislocations were discussed. I am planning to consider various effects of emergent gravity in Dirac/Weyl semimetals as well as in He3-A and apply the general expressions to the case, when the dislocations (or vortices, in case of the superfluid) are present. Since the Dirac/Weyl semimetals as well as He3-A simulate truly relativistic high - energy theories, the discussion of anomalies in the these theories may be applied to them (with some reservations, though). In this respect it is worth mentioning that there is a certain contradiction in the results published to date 3. Namely, it was reported that in the presence of torsion the chiral anomaly includes the topological Nieh - Yan term. In particular, this has been demonstrated using Fujikawa method. However, it was also argued (this was based on the perturbative calculations with Pauli - Villars regularization) that there is no Nieh - Yan term in the chiral anomaly. The alternative derivation of the Nieh - Yan term in the anomaly was given that is based on the consideration of massless fermions of opposite chirality as living on the boundary of the 4+1 D topological isolator. Thus, the presence of the Nieh - Yan term in chiral anomaly remains an open question. I do not exclude, that the appearance of this term may depend essentially on the type of the considered system (semimetal or superfluid) and even on the microscopic theory of the particular system. It is planned to investigate various subjects related to anomalies in Dirac and Weyl semimetals. In the previous papers on graphene and Dirac semimetals we neglected completely Coulomb interactions between the quasiparticles. These interactions are strong due to the large effective coupling constant and break the emergent relativistic invariance. However, the investigation of graphene indicates (see the mentioned above monograph by M.Katsnelson), that such interactions may be neglected for the consideration of certain properties of the systems. For example, the Aharonov - Bohm and Stodolsky effects in the scattering of the quasiparticles on the dislocations in Dirac and Weyl semimetals and in graphene as well as the chiral anomaly driven by the emergent magnetic field are such effects that survive when the Coulomb interaction is turned on. (Stodolsky effect is the correction to the Aharonov – Bohm phase due to gravity.) However, the effect of strong Coulomb interactions should be investigated in relation to the other properties of these materials, and this investigation is planned. It is supposed to work on this subject in collaboration with the lattice groups which perform extensive numerical simulations

 

 

graphene 

 

     In the previous papers the Anomalous Quantum Hall Effect (AQHE) was considered within the lattice regularized quantum field theory and within the tight - binding models of the solid state physics. The expression for the Hall current (through the topological invariant in momentum space N3) in the quasi two dimensional condensed matter systems is well – known from the classical works of G.E.Volovik. I reproduced this result basing on the technique of the derivative expansion applied to the Wigner transform of the two - point Green function. Next, I applied the same technique to the AQHE in the 3+1 D lattice models. The obtained expression relates the AQHE current to the new topological invariant. The technique of its calculation is developed. This methodology allows to predict the appearance of the AQHE both in the Weyl semi - metals and in certain topological insulators. It is supposed to proceed developing this method, which relates various nondissipative currents to the momentum space topological invariants. One of the interesting questions is how to improve the so – called chiral kinetic theory4 in order to describe properly the system of chiral fermions in the presence of external electric and magnetic fields. There are several important predictions of the chiral kinetic theory. At the same time we know that the equilibrium chiral magnetic effect does not exist while the present version of the chiral kinetic theory predicts it. This means that this theory should be reconsidered and improved. I suppose to work on this using my previous experience in the consideration of the chiral magnetic effect in lattice regularized quantum field theory and in the lattice models of solids

  

qcd

 

                          APPLICATIONS OF THE APPROACHES OF CONDENSED MATTER PHYSICS TO HIGH ENERGY PHYSICS

  

            Study of momentum space topology was initiated within the condensed matter physics (see the mentioned above monograph by G.E.Volovik). In particular, the momentum space topological invariants protect gapless fermions on the boundaries of topological insulators. Topological invariants in momentum space protect also the bulk gapless fermions in Dirac and Weyl semimetals. The large variety of topological defects and textures exist in the fermionic superfluids, and the gapless fermions associated with these objects are described by momentum space topology. Momentum space topology was also discussed in the context of relativistic quantum field theory (QFT). In my previous works the topological invariants in momentum space have been considered for the lattice regularization of QFT with Wilson fermions. Appearance of the massless fermions at the intermediate values of bare mass parameter was related to the jump of the introduced momentum space topological invariant. This invariant may actually be used for the description of a certain class of topological insulators. Also I studied the model with overlap fermions on the same grounds. In particular, the possible physical meaning of the zeros of the Green function has been discussed. The momentum space topological invariants are expressed in terms of the Green functions. Therefore, they are applicable both to the non - interacting and to the interacting systems. Suppose, that we start from the model without interactions. When the interactions are turned on, the value of the topological invariant is not changed until the phase transition is encountered. This means, that the properties of the system described by the given topological invariant are robust to the introduction of interactions. The more simple non - interacting model may be investigated in order to describe such properties of the complicated interacting system. It is planned to proceed the work on the application of the methodology of momentum space topology to the solution of various problems existing in the high energy physics. In particular, it is supposed to apply it to the consideration of various phases of the Standard Model of fundamental interactions and, in particular, of QCD. In QCD there are several phases, the investigation of which is still in its infancy (unlike the conventional Hadronic phase of QCD). Those are, for example, various color superconductor phases and the quark – gluon plasma phase. The topological defects in the quark matter (and the fermion zero modes on them) may be described effectively by the topological invariants in momentum space. Besides, momentum space topological invariants should help in the classification of the phases of QCD (and also of the whole Standard Model and its extensions) and may, possibly, help to predict the phases, which were not known earlier. Previously the relation was considered of momentum space topology to the response of electric current to the external fields. This relation allows to describe properly the non – dissipative Hall current and allows to prove that the equilibrium version of chiral magnetic effect does not exist in the lattice regularized quantum field theory. It would be interesting to apply this methodology to the investigation of the chiral anomaly in lattice regularizationAlthough certain results related to this issue are already known, the concept of momentum space topology here is new, and it may shed light on the silent features of the anomalies in quantum field theory

 

sm

 

 

      The idea, that the 125 GeV Higgs boson of the SM may be composed of fermions follows the analogy with the models of superconductivity and superfluidity. Historically, first it was suggested, that Higgs boson is composed of additional technifermions. This theory contains an additional set of fermions that interact with the Technicolor (TC) gauge bosons. This interaction is attractive and, therefore, by analogy with BCS superconductor theory it may lead to the formation of fermionic condensate. This condensate, in turn, breaks Electroweak symmetry down to Electromagnetism. It is worth mentioning that TC theory suffers from the problems related to fermion mass generation. Extended Technicolor (ETC) interactions do not pass precision Electroweak tests due to the flavor changing neutral currents and due to the contributions to the Electroweak polarization operators (S and T parameters). The so-called walking technicolor improves the situation essentially, but the ability to generate top quark mass remains problematical. It was suggested by V.A. Miransky and co - authors 5 in 1989, that the SM Higgs boson may be composed of the heaviest known fermion - the top quark. This approach was developed later in a number of papers. Actually, the idea, that Higgs boson may be composed of known SM fermions was suggested already in 1977 by H.Terazawa and co - authors 6 together with certain composite preon models. Unfortunately, in that paper there was no emphasis on top quark as the dominant component of the composite Higgs boson (this issue was even not mentioned in the abstract), and the paper was missed by many physicists working on the idea of top quark condensation. In addition to the TC and the top – quark condensation models, models were developed (topcolor, topcolor assisted Technicolor, top seesaw, colorons, etc) that contain the elements of both mentioned approaches. Other models were suggested, in which the Higgs boson appears as the Goldstone boson of the broken approximate symmetry. In particular, the realization of this idea was given in the framework of Little Higgs Models. It is planned to construct and investigate the conceptually new models, in which Higgs bosons are composed, in particular, of known SM fermions. It is supposed, that the constructed models will avoid difficulties of the models of Technicolor and the conventional models of top – quark condensation. The new models will be based on the analogy with certain condensed matter systems, like the superfluid He-3, in which the condensates are more complicated, than in the Technicolor models and the conventional models of top – quark condensation. The latter models are based on the analogy with the simplest s-wave superconductors   

 

 

     
1 M.I. Katsnelson, Graphene: Carbon in Two Dimensions, Cambridge Univ. Press, Cambridge, 2012

2 G.E. Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford (2003); G.E. Volovik, “Analog of gravity in superfluid He3-A”, JETP Lett. 44, 498--501 (1986); P. Horava, “Stability of Fermi surfaces and K-theory”, Phys. Rev. Lett. 95, 016405 (2005)

3 O.Chandia and J.Zanelli, ``Topological invariants, instantons and chiral anomaly on spaces with torsion,'' Phys. Rev.D 55 (1997) 7580 [hep-th/9702025]; E.W.Mielke, ``Anomalies and gravity,'' AIP Conf.Proc. 857B (2006) 246 [hep-th/0605159]; D.Kreimer and E.W.Mielke, ``Comment on: Topological invariants, instantons, and the chiral anomaly on spaces with torsion,'' Phys. Rev. D 63 (2001) 048501 [gr-qc/9904071]; Onkar Parrikar, Taylor L. Hughes, Robert G. Leigh, Phys. Rev. D 90, 105004 (2014), arXiv:1407.7043

4 M. A. Stephanov and Y. Yin, “Chiral Kinetic Theory,” Phys. Rev. Lett. 109 (2012) 162001 doi:10.1103/PhysRevLett.109.162001 [arXiv:1207.0747 [hep-th]] J. Y. Chen, D. T. Son and M. A. Stephanov, “Collisions in Chiral Kinetic Theory,” Phys. Rev. Lett. 115 (2015) no.2, 021601 doi:10.1103/PhysRevLett.115.021601 [arXiv:1502.06966 [hep-th]].

5 V.A. Miransky, Masaharu Tanabashi, and Koichi Yamawaki, “Is the t quark responsible for the mass of W and Z bosons?" Mod. Phys. Lett. A 4, 1043-1053 (1989)

 6 H.Terazawa, Y.Chicashige, K.Akama, Phys. Rev. D 15, 480 (1977)

עדכון אחרון ב-רביעי, 21 פברואר 2018 13:21
 

 

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