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Bulletin of the American Physical Society

Extremely Correlated Fermi Liquids

Sriram Shastry

Published Feb 28, 2012• 0 citations
OpenAlex

Abstract

We present the theory of an extremely correlated Fermi liquid with $U\ensuremath{\rightarrow}\ensuremath{\infty}$. This liquid has an underlying auxiliary Fermi liquid Green's function that is further caparisoned by extreme correlations. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct $T$ dependent left skew. An important energy scale $\ensuremath{\Delta}(\stackrel{\ensuremath{\rightarrow}}{k},x)$ emerges as the average inelasticity of the FL Green's function, and influences the photoemission spectra profoundly. A duality is identified wherein a loss of coherence of the ECFL results from an excessively sharp FL.

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Electronic spectral properties of the two-dimensional infinite- U Hubbard model

Ehsan Khatami, Daniel Hansen, Edward Perepelitsky +2 more

A strong-coupling series expansion for the Green's function and the extremely correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-$U$ Hubbard model. Results from these two complementary methods agree very well at both low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the peak location of the spectral function in the strongly correlated regime. This is examined by the ECFL results at low temperatures, where it is shown that the spectral function is largely skewed towards the occupied states.

arXiv:1303.2657•Physical Review B•Apr 29, 2013•8 citations
We present the theory of an extremely correlated Fermi liquid with U\ensuremath→\ensuremath∞U\ensuremath{\rightarrow}\ensuremath{\infty}U\ensuremath→\ensuremath∞. This liquid has an underlying auxiliary Fermi liquid Green's function that is further caparisoned by extreme correlations. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct TTT dependent left skew. An important energy scale \ensuremathΔ(k\ensuremath→,x)\ensuremath{\Delta}(\stackrel{\ensuremath{\rightarrow}}{k},x)\ensuremathΔ(k\ensuremath→​,x) emerges as the average inelasticity of the FL Green's function, and influences the photoemission spectra profoundly. A duality is identified wherein a loss of coherence of the ECFL results from an excessively sharp FL.
We present the theory of an extremely correlated Fermi liquid with U→∞. This liquid has an underlying auxiliary Fermi liquid Green's function that is further caparisoned by extreme correlations. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct T dependent left skew. An important energy scale Δ(k[over →],x) emerges as the average inelasticity of the FL Green's function, and influences the photoemission spectra profoundly. A duality is identified wherein a loss of coherence of the ECFL results from an excessively sharp FL.
We present the detailed formalism of the extremely correlated Fermi liquid theory, developed for treating the physics of the $t\ensuremath{-}J$ model. We start from the exact Schwinger equation of motion for the Green's function for projected electrons, and develop a systematic expansion in a parameter $\ensuremath{\lambda}$, relating to the double occupancy. The resulting Green's function has a canonical part arising from an effective Hamiltonian of the auxiliary electrons, and a caparison part playing the role of a frequency-dependent adaptive spectral weight. This adaptive weight balances the requirement at low $\ensuremath{\omega}$ of the invariance of the Fermi volume, and at high $\ensuremath{\omega}$ of decaying as $\frac{{c}_{0}}{i\ensuremath{\omega}}$, with a correlation-depleted c0<1{c}_{0}<1c0​<1. The effective Hamiltonian Heff{H}_{\mathrm{eff}}Heff​ describing the auxiliary fermions is given a natural interpretation with an effective interaction Veff{V}_{\mathrm{eff}}Veff​ containing both the exchange Jij{J}_{ij}Jij​ and the hopping parameters tij{t}_{ij}tij​. It is made Hermitian by adding suitable terms that ultimately vanish, in the symmetrized theory developed in this paper. Simple but important shift invariances of the $t\ensuremath{-}J$ model are noted with respect to translating its parameters uniformly. These play a crucial role in constraining the form of Veff{V}_{\mathrm{eff}}Veff​ and also provide checks for further approximations. The auxiliary and physical Green's function satisfy two sum rules, and the Lagrange multipliers for these are identified. A complete set of expressions for the Green's functions to second order in $\ensuremath{\lambda}$ is given, satisfying various invariances. A systematic iterative procedure for higher order approximations is detailed. A superconducting instability of the theory is noted at the simplest level with a high transition temperature.
We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the ttt-JJJ model in two dimensions, developed recently by Shastry [Phys. Rev. Lett. 107, 056403 (2011); Phys. Rev. B 87, 125124 (2013)]. The second-order theory in the parameter $\ensuremath{\lambda}$, related to the density, is argued to be quantitatively valid in the overdoped regime for $0\ensuremath{\le}n\ensuremath{\lesssim}0.75$, with nnn denoting the particle density. The calculation involves the self-consistent solution of equations for an auxiliary Fermi liquid Green's function and an adaptive spectral weight. We present numerical results at low as well as high TTT, at various low to intermediate densities in the normal phase, using a minimal set of band parameters relevant to the cuprate superconductors. We display the momentum space occupation function mk{m}_{k}mk​, energy dispersion curves locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions on an absolute scale. The line shapes have an asymmetric shape and a broad background that is also seen in experiments, and our calculations validate approximate recent versions of the theory. The results also display the experimentally noted high-energy kink and provide an in-depth understanding of its origin and dependence on band parameters.
The Extremely Correlated Fermi Liquids (ECFL) theory is reviewed as a framework for understanding the ttt-JJJ model in metallic systems close to the Mott insulating limit. This overview presents the underlying ideas and the resulting equations in a form accessible to nonexperts. We compare theoretical results with all available resistivity data for single-layer High-Tc_{c}c​ systems, and with some spectral data. The highlighted results include a density dependent quasilinear T-dependence in resistivity, an unusually small quasiparticle weight, and distinct low-temperature emergent scales that dominate transport, thermodynamics and spectral properties of single-layer High Tc_cc​ systems. Suggestions are made for further experiments to probe the physics of these challenging quantum many-body systems.
In this work, we describe the simplifications to the Extremely Correlated Fermi Liquid Theory (ECFL) \\cite{ECFL, Monster} which occur in the limit of infinite spatial dimensions. In particular, we show that the single-particle electron Green's function G(k) can be written in terms of two momentum-independent self-energies. Moreover, we elucidate the nature of the ECFL \\lambda expansion in the limit of infinite dimensions and carry out this expansion explicitly to O(\\lambda^2). Additionally, we demonstrate the vanishing of vertex corrections to the optical conductivity in general and to each order in \\lambda in the limit of infinite dimensions. We generalize the ECFL formalism to the infinite-U Anderson impurity model (AIM) , and demonstrate a Dynamical Mean-Field Theory (DMFT) like mapping between the ECFL objects of the infinite-dimensional t-J model and the infinite-U AIM, and show that this mapping holds to each order in \\lambda. We compute the spectral function for the AIM to O (\\lambda^2) and make comparisons with results obtained through Numerical Renormalization Group (NRG) computations. Finally, we develop a novel formalism for the high-temperature expansion of dynamical correlation functions in the infinite-U Hubbard model which is more efficient than any used previously and gives results for an arbitrary number of spin species. We use it to calculate the single-particle Green's function G(k) to fourth order in (\\beta t) for m spin-species on a d-dimensional hypercube.
A strong-coupling series expansion for the Green's function and the extremely correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-UUU Hubbard model. Results from these two complementary methods agree very well at both low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the peak location of the spectral function in the strongly correlated regime. This is examined by the ECFL results at low temperatures, where it is shown that the spectral function is largely skewed towards the occupied states.