Dear Colleagues,

In recent years, a vast field of topological methods has dynamically flourished: multi-electron interacting planar quantum systems in the magnetic or Berry fields. Topological insulators, spin Hall systems, fractional and integer quantum Hall effect in graphene monolayer and bilayer, competition of superfluidity of inter-layer excitons in double Hall systems with correlated Hall states drew attention to the topological non-local conditioning of multi-electron correlation organization in 2D in the presence of a magnetic field and made a significant contribution to the development of over 30-years old quantum Hall physics – one of the most important and illuminating domains in condensed matter. Recently there was a rapid development of the Hall experiment in new materials, as well as a new topological perspective on correlations in various types of topological insulators and their experimental implementation also in optical planar networks. The Haldane states for planar systems without a magnetic field or Kosterlitz Tauless's phase transitions (NP 2016) emphasised that the topological quantum effects are impossible to be understood in the framework of local quantum physics. The relationship of topological phases with long range multi-particle quantum entanglement distinguishes the associated quantum transitions from standard phase transitions with spontaneous symmetry violation and desribed in terms of binary quantum entanglement. We propose this Special Issue of Materials to seek out papers in this dynamically developing area of quantum physics of correlated states.

Prof. Lucjan Jacak
Dr. Janusz E. Jacak
Guest Editors

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• Topology methods in quantum physics 
• Correlations in integer and fractional quantum Hall effects 
• Topological insulators 
• Superfluidity of excitons in bilayer Hall systems
• Graphene monolayer and bilayer 
• Hall states without Landau levels 
• Homotopy phases in 2D electron systems at magnetic and Berry fields 
• Topological structure of composite fermions 
• Spin Hall systems
• Long range quantum entanglement in topological phases 
• Topology in planar optical lattices 
• Topological invariants and braid groups 
• Exact diagonalization of small Hall systems 
• New material for demonstration of IQHE and FQHE 
• Path integration in multiply-connected configuration spaces 
• Correlation patterns in higher Landau levels 
• Anyons and fractional statistics 
• Chern-Simons field approach to 2D correlated states