Study of critical behavior of the supersymmetric spin chain that models plateau transitions.pdf

Ann. Phys. (Leipzig) 8 (1999) 5, 000 – 000 9 Study of critical behavior of the supersymmetric spin 9 chain that models plateau transitions in the integer 9 1 quantum Hall effect g u Shan-Wen Tsai and J. B. Marston A Department of Physics, Brown University, Providence, RI 02912-1843, USA 2 tsai@barus.physics.brown.edu 1 Received 29 July 1999, accepted dd.mm.yyyy by ue ] l Abstract. We use the density-matrix renormalization-group (DMRG) algorithm and finite- l a size scaling to study a supersymmetric (SUSY) spin chain that models plateau transitions h in the integer quantum Hall effect. To illustrate the method, we first present results for the - S = 1 antiferromagnetic spin chain. Different scaling behavior of the dimerization operator is s e obtained for the Haldane phase, the dimerized phase, and at the critical point separating the two phases. We then investigate the supersymmetric spin chain. As the on-site Hilbert space m has infinite dimension, it is non-compact. We present DMRG calculations for supersymmetric . t truncations of the on-site Hilbert space and also for non-supersymmetric truncations. These a two cases scale differently, in accord with a Lieb-Schultz-Mattis type theorem. m - Keywords: quantum Hall effect, quantum spin chains, metal-insulator transitions d PACS: 73.40.Hm, 71.30.+h, 75.10.Jm n o c [ 1 Introduction 1 v Quantum critical points are characterized by fluctuations over all length and time 0