Regensburg 2010 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 38: CE: Quantum-Critical Phenomena 2

TT 38.8: Talk

Friday, March 26, 2010, 12:30–12:45, H18

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model with plaquette deformations — Andreas Fledderjohann, K.-H. Mütter, and •Andreas Klümper — Universität Wuppertal

The low energy behaviour of the 2d antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0, 1, 2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix of 4 neighbouring ‘n clusters’ of size 2ⁿ × 2ⁿ from the corresponding quantities of the ‘n clusters’. Conservation of total spin S is implemented. An inhomogeneous Heisenberg model with plaquette distortion is investigated. Depending on the plaquette-plaquette coupling J, we find two regimes: ‘confinement’ J_c < J ≤ 1, where the singlet ground state forms an infinite (‘confined’) cluster in the thermodynamical limit. Here the singlet-triplet gap vanishes, which is the signature for long range spin-spin correlators. We find ‘deconfinement’ 0 ≤ J < J_c , where the singlet ground state ‘deconfines’ – i.e. factorizes – into finite n-clusters of size 2ⁿ × 2ⁿ, with n ≤ n_c(J). Here the singlet-triplet gap is finite and the gap exponent is determined. The critical value turns out to be J_c = 0.4822... in the chosen truncation scheme.