Projection Operator Formalism for the Calculation of the Susceptibility Green's Function

We present a Green's-function theory of magnetic short-range order in the $S=1/2$ easy-plane $\mathrm{XXZ}$ chain based on the projection method for the dynamic spin susceptibility and a decoupling of three-spin operator products introducing vertex parameters. The longitudinal and transverse static susceptibilities and two-point correlation functions of arbitrary range are calculated self-consistently for all wave numbers, temperatures, and anisotropy parameters $\ensuremath{-}1<~\ensuremath{\Delta}<~1.$ In the easy-plane ferromagnetic region $(\ensuremath{\Delta}<0),$ the longitudinal correlators of spins at distance n change sign at a finite temperature ${T}_{0}(n,\ensuremath{\Delta}),$ in reasonable agreement with recent data obtained by finite-chain diagonalizations. The temperature dependence of the uniform static susceptibilities exhibits a maximum which is explained as an effect of magnetic short-range order which decreases with increasing temperature.We present a Green's-function theory of magnetic short-range order in the $S=1/2$ easy-plane $\mathrm{XXZ}$ chain based on the projection method for the dynamic spin susceptibility and a decoupling of three-spin operator products introducing vertex parameters. The longitudinal and transverse static susceptibilities and two-point correlation functions of arbitrary range are calculated self-consistently for all wave numbers, temperatures, and anisotropy parameters $\ensuremath{-}1<~\ensuremath{\Delta}<~1.$ In the easy-plane ferromagnetic region $(\ensuremath{\Delta}<0),$ the longitudinal correlators of spins at distance n change sign at a finite temperature ${T}_{0}(n,\ensuremath{\Delta}),$ in reasonable agreement with recent data obtained by finite-chain diagonalizations. The temperature dependence of the uniform static susceptibilities exhibits a maximum which is explained as an effect of magnetic short-range order which decreases with increasing temperature.

arXiv:cond-mat/9911447Physical review. B, Condensed matterNov 1, 20009 citations

Effective projection theory in a correlated electron system

Juyeon Yi, Seong‐Jin Kim, Jaegon Um +3 more

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.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.

Journal of Physics Condensed MatterNov 17, 20102 citations

Mathematical foundations of the projection-operator method

Steven M. Moore

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoSep 1, 19792 citations

We present a Green's-function theory of magnetic short-range order in the

S=1/2

easy-plane

\mathrm{XXZ}

chain based on the projection method for the dynamic spin susceptibility and a decoupling of three-spin operator products introducing vertex parameters. The longitudinal and transverse static susceptibilities and two-point correlation functions of arbitrary range are calculated self-consistently for all wave numbers, temperatures, and anisotropy parameters $\ensuremath{-}1<~\ensuremath{\Delta}<~1.$ In the easy-plane ferromagnetic region $(\ensuremath{\Delta}<0),$ the longitudinal correlators of spins at distance n change sign at a finite temperature ${T}_{0}(n,\ensuremath{\Delta}),$ in reasonable agreement with recent data obtained by finite-chain diagonalizations. The temperature dependence of the uniform static susceptibilities exhibits a maximum which is explained as an effect of magnetic short-range order which decreases with increasing temperature.