Regensburg 2013 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 14: Correlated Electrons: Low-Dimensional Systems - Models 2

TT 14.12: Talk

Monday, March 11, 2013, 18:00–18:15, H9

Correlations of quantum spin chains from functional equations and su(2) diagrammatics — •Andreas Klümper — Bergische Universität Wuppertal, Theoretische Physik, Gauss-Strasse 20, 42119 Wuppertal

For integrable quantum spin chains a lattice path integral formulation with finite but arbitrary Trotter number allows to derive a set of discrete functional equations with respect to the spectral parameters appearing in the R-matrices of local interactions. We show that these equations yield a unique characterisation of the density operator and present solutions for the S=1/2 and S=1 Heisenberg chains.

For generic cases, we report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of a spin-1/2 quantum chain. For efficient computations, we make systematic use of the su(2) symmetry at all steps of the calculations: (i) the matrix space is set up as a direct sum of irreducible representations, (ii) the local matrices with state-valued entries are set up as superposition of su(2) singlet operators, (iii) products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols.

Results on quantum phase transitions in the considered models are discussed.