Extremely Correlated Quantum Liquids

Abstract

We formulate the theory of an extremely correlated electron liquid, generalizing the standard Fermi liquid. This quantum liquid has specific signatures in various physical properties, such as the Fermi surface volume and the narrowing of electronic bands by spin and density correlation functions. We use Schwinger's source field idea to generate equations for the Greens function for the Hubbard operators. A local (matrix) scale transformation in the time domain to a quasiparticle Greens function, is found to be optimal. This transformation allows us to generate vertex functions that are guaranteed to reduce to the bare values for high frequencies, i.e. are ``asymptotically free''. The quasiparticles are fractionally charged objects, and we find an exact Schwinger Dyson equation for their Greens function. We find a hierarchy of equations for the vertex functions, and further we obtain Ward identities so that systematic approximations are feasible. An expansion in terms of the density of holes measured from the Mott Hubbard insulating state follows from the nature of the theory. A systematic presentation of the formalism is followed by some preliminary explicit calculations.

40 pages, typos removed

References in corpus (4)

• Variational cluster approach to correlated electron systems in low dimensions
• Electro Thermal Transport Coefficients at Finite Frequencies
• Phase diagram and single-particle spectrum of CuO${}_2$ layers within a variational cluster approach to the 3-band Hubbard model
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• Strong-coupling diagrammatic Monte Carlo technique for correlated fermions and frustrated spins
• Extremely Correlated Fermi Liquids in the limit of infinite dimensions
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• Diagrammatic $\lambda$ series for extremely correlated Fermi liquids
• A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators
• Numerical solution of the t-J model with random exchange couplings in d=infinity dimensions
• Hubbard-I approach to the Mott transition
• Nature of Split Hubbard Bands at Low Densities
• Dielectric response of electrons with strong local correlations and long-ranged Coulomb interactions
• Fermi Surface Volume of Interacting Systems
• Functional renormalization group for extremely correlated electrons
• Low-lying quasiparticle excitations in strongly-correlated superconductors: An ansatz from BCS quasiparticle excitations?
• Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet
• On non-canonical degrees of freedom