Strongly Correlated Fermi Systems : A New State of Matter This book focuses on the topological fermion condensation quantum phase transition (FCQPT) a phenomenon that reveals the complex behavior of all strongly correlated Fermi systems such as heavy fermion metals quantum spin liquids quasicrystals and two dimensional systems considering these as a new state of matter. The book combines theoretical evaluations with arguments based on experimental grounds demonstrating that the entirety of very different strongly correlated Fermi systems demonstrates a universal behavior induced by FCQPT. In contrast to the conventional quantum phase transition whose physics in the quantum critical region are dominated by thermal or quantum fluctuations and characterized by the absence of quasiparticles the physics of a Fermi system near FCQPT are controlled by a system of quasiparticles resembling the Landau quasiparticles. The book discusses the modification of strongly correlated systems under the action of FCQPT representing the “missing” instability which paves the way for developing an entirely new approach to condensed matter theory; and presents this physics as a new method for studying many body objects. Based on the authors’ own theoretical investigations as well as salient theoretical and experimental studies conducted by others the book is well suited for both students and researchers in the field of condensed matter physics. Chapter 1 Introduction Chapter 2 Landau Fermi liquid theory Chapter 3 Density Functional Theory of Fermion Condensation Chapter 4 Topological fermion condensation quantum phase transition Chapter 5 Rearrangement of the single particle degrees of freedom Chapter 6 Topological FCQPT in strongly correlated Fermi systems Chapter 7 Effective mass and its scaling behavior Chapter 8 Quantum spin liquid in geometrically frustrated magnets and the new state of matter Chapter 9 One dimensional quantum spin liquid Chapter 10 Dynamic magnetic susceptibility of quantum spin liquid Chapter 11 Spin lattice relaxation rate and optical conductivity of quantum spin liquid Chapter 12 Quantum spin liquid in organic insulators and 3He Chapter 13 Universal behavior of the thermopower of HF compounds Chapter 14 Universal behavior of the heavy fermion metal β − YbAlB4 Chapter 15 The universal behavior of the archetypical heavy fermion metals YbRh2Si2 Chapter 16 Heavy fermion compounds as the new state of matter Chapter 17 Quasi classical physics within quantum criticality in HF compounds Chapter 18 Asymmetric conductivity of strongly correlated compounds Chapter 19 Asymmetric conductivity pseudogap and violations of time and charge symmetries Chapter 20 Violation of the Wiedemann Franz law in Strongly Correlated Electron Systems. Chapter 21 Quantum criticality of heavy fermion compounds.