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Journal of Physics Condensed Matter

Effective projection theory in a correlated electron system

Juyeon Yi, Seong‐Jin Kim, Jaegon Um, Sun-Yong Hwang, Ara Go, Gun Sang Jeon

Published Nov 17, 2010• 2 citations
Publisher

Abstract

We propose an efficient method for nonperturbative calculation of Green's function in a correlated electron system. The key idea of the method is to project out irrelevant operators having zero norm in the ground state, which we refer to as effective projection theory. We apply the method to a mesoscopic Anderson model and show that for a given wavefunction ansatz, equations of motion can be closed only by relevant operators, allowing easy calculation of the zero-temperature Green's function. It turns out that the resulting Green's functions reproduce exact limits of both weak and strong interactions. The accuracy is also verified for small systems by comparison with exact diagonalization results, revealing that effective projection theory captures the essential correlated features in the entire regime of interactions.

DOI
10.1088/0953-8984/22/48/485604

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The authors consider a systematic projection method for terminating the Green function equations of motion for Hubbard X-operators. This gives a set of mean fields that depend on the operators chosen. When applied to lowest order in the N-fold-degenerate U to infinity Anderson model an expression for the one-electron Green function is obtained that is exact for N=1 and in the limit N to infinity . This approach avoids the necessity of introducing auxiliary fields, such as constraint fields or slave bosons, to obtain asymptotically exact mean fields in the large-N limit and has general applicability in similar strongly correlated problems.
We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of chemisorption and adsorbate reactions on metal surfaces, physics of intermediate valence systems, theory of heavy fermions, physics of quantum dots and other nanostructures. While standard treatments are generally based on perturbation methods, our approach is based on the non-perturbative technique for the thermodynamic Green functions. The method of the irreducible Green functions is used as the basic tool. This irreducible Green functions method allows one to describe the quasiparticle spectra with damping of the strongly correlated electron systems in a very general and natural way and to construct the relevant dynamical solution in a self-consistent way on the level of Dyson equation without decoupling the chain of the equations of motion for the Green functions. The subject matter includes the improved interpolating solution of the Anderson model. It was shown that an interpolating approximation, which simultaneously reproduces the weak-coupling limit up to second order in the interaction strength U and the strong-coupling limit up to second order in the hybridization V (and thus also fulfils the atomic limit) can be formulated self-consistently. This approach offers a new way for the systematic construction of approximate interpolation dynamical solutions of strongly correlated electron systems.
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