Introduction to<i>quantum matter</i>

Wilczek, Frank

doi:10.1088/0031-8949/2012/t146/014001

Cited by 8 publications

(11 citation statements)

References 7 publications

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“…For example, starting from purely real Hamiltonians H, one finds that depending on symmetry of H the effective quasiparticles emerging near the crossing point may behave as Majorana, Dirac or Weyl fermions. [6][7][8] This suggests that appearance of complex numbers in quantum mechanics is also the emergent phenomenon, i.e. complex numbers emerge in the low energy description of the underlying high energy theory together with Weyl particles and gauge and gravitational fields.…”

Section: Symmetry and Topology Of Green's Functionsmentioning

confidence: 99%

From standard model of particle physics to room-temperature superconductivity

Volovik¹

2015

Phys. Scr.

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Topological media are gapped or gapless fermionic systems, whose properties are protected by topology, and thus are robust to deformations of the parameters of the system and generic. We discuss here the class of gapless topological media, which contains the quantum vacuum of Standard Model in its symmetric phase, and also the condensed matter systems with zeroes in the fermionic energy spectrum, which form Fermi surfaces, Weyl and Dirac points, Dirac lines, Khodel-Shaginyan flat bands, etc. Some zeroes are topologically protected, being characterized by topological invariants, expressed in terms of Green's function. For the stability of the others the p-space topology must be accompanied by symmetry.Vacua with Weyl points serve as a source of effective relativistic quantum fields emerging at low energy: chiral fermions, effective gauge fields and tetrad gravity emerge together in the vicinity of a Weyl point. The accompanying effects, such as chiral anomaly, electroweak baryo-production and chiral vortical effect, are expressed via the symmetry protected p-space invariants.The gapless topological media exhibit the bulk-surface and bulk-vortex correspondence: which in particular may lead to the flat band on the surface of the system or in the core of topological defects. The materials with flat band in bulk, on the surface or within the dislocations have singular density of states, which crucially influences the critical temperature of the superconducting transition in such media. While in all the known superconductors the transition temperature is exponentially suppressed as a function of the pairing interaction, in the flat band the transition temperature is proportional to the pairing interaction, and thus can be essentially higher. So the p-space topology may give us the general recipe for the search or artificial fabrication of the room-temperature superconductors.PACS numbers: I. WEYL POINT, LEVEL CROSSING AND BERRY PHASE MONOPOLESome features of topological matter can be formulated in terms of the Berry's connection in momentum space p. For example, the Weyl points in the fermionic spectrum in Standard Model (SM) or in condensed matter Weyl materials such as superfluid 3 He-A, can be viewed as the Berry's phase monopoles in momentum space 1 . Such monopole represents the topologically nontrivial point of level crossing (the conical or diabolical point) in the 3D space of parameters, where the parameters are three components of the (quasi)particle momentum (p x , p y , p z ). Fig. 1 demonstrates the elementary case of the level crossing, where only two branches of spectra touch each other. Near the crossing point the complex n × n Hamiltonian is effectively reduced to the 2 × 2 matrixwhere σ are the Pauli matrices. In the vicinity of the Weyl point p (0) , only linear terms in expansion of the Hamiltonian are important, and one obtains the effective HamiltonianIn the non-uniform situation the parameters of expansion e i k and p (0) become the fields, and then the Hamiltonian (2) describes the Weyl relativis...

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Section: Symmetry and Topology Of Green's Functionsmentioning

confidence: 99%

From standard model of particle physics to room-temperature superconductivity

Volovik¹

2015

Phys. Scr.

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“…Wilczek [4] considers a simple quantum problem of level-crossing in a two-level system described by a real Hermitian Hamiltonian…”

Section: Iii-b C Matrixmentioning

confidence: 99%

“…2 , and the eigenfunction ( 48) is immediately obtained. The Hamiltonian (45) has been re-written in [4] in the following form…”

Section: Iii-b C Matrixmentioning

confidence: 99%

“…A new perspective on geometry and topology of complex numbers and the properties of the matrix C constitute section III. An important consequence on the nature of topological defect is used to analyze Z 2 vortex for a real Hermitian Hamiltonian describing a two-level quantum system [4]. It is shown in section IV that the nonrelativistic Schroedinger equation ( 2) under the transformation (6) becomes a pair of coupled wave equations with real wavefunctions.…”

Section: Introductionmentioning

confidence: 99%

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Real wave equations, spin origin of charge, and outlook on particle physics

Tiwari

2019

Preprint

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Radical revision on the conventional spacetime picture, illusion or emergent phenomenon, has been the focus of the speculations on the unified frameworks for fundamental interactions in nature. Compared to strong experimental credence to the standard model of particle physics there is practically no relation of these speculations with the world of real particles. In this paper we present a new conceptual framework for particle physics in which nontrivial geometry and topology of space and time have fundamental reality. To develop this model we proceed with the analysis of the standard wave equations and make them real using the transformation ruleTopological significance is attached to i in terms of a point defect in 1D directed line. New interpretation of Schroedinger wave equation and Z2 vortex throw light on the nature of spin. A new meaning is also obtained on U(1) gauge symmetry and charge. Novel properties of C-matrix and known applications are presented. Topological origin of spin is inferred from the interpretation of Pauli algebra that they signify 2D directed area in phase space as topological obstruction. Electron magnetic moment decomposition in QED serves the basis for the proposition: spin origin of charge (SOC). A dynamical logarithmic spiral geometric structure comprising of 2+1D braids, 3 vortices with associated three 2-spinors is envisaged based on SOC. It is termed as meta-electron; meta-neutrino has 2-vortex structure. These are the only building blocks of all particles having the knotted vortex structures in our model. Coupling strengths of the three fundamental interactions are related with the magnitudes of the spin angular momentum of constituent spinors of the metaelectron. Unification has radically new paradigm compared to gauge theories: effective coupling constant with weight factors. To put the role of i in perspective a discussion on previous works is also presented. Outlook on particle physics is elaborated in this new framework.

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“…Inspired by the searches for Majorana fermions [23], in this work we study the topological properties of superconducting states in generic semimetals and related systems under general superconducting proximity conditions. Topological semimetals studied here are systems consist of two-bands crossing points (TBCPs) around the Fermi level which can be viewed as k-space vortices [7,24]. Away from the TBCP the two bands do not overlap unless through other TBCPs.…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian topological superconductors from topological semimetals and related systems under the superconducting proximity effect

Jiang

2013

J. Phys.: Condens. Matter

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Non-Abelian topological superconductors are characterized by the existence of zero-energy Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an odd Chern number. It is found that in topological semimetals with a single two-band crossing point all the gapped superconductors are non-Abelian ones. Such a property is generalized to related but more generic systems which will be useful in the search for non-Abelian superconductors and Majorana fermions.

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Introduction toquantum matter

Cited by 8 publications

References 7 publications

From standard model of particle physics to room-temperature superconductivity

From standard model of particle physics to room-temperature superconductivity

Real wave equations, spin origin of charge, and outlook on particle physics

Non-Abelian topological superconductors from topological semimetals and related systems under the superconducting proximity effect

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