Critical theory of the topological quantum phase transition in the AKLT--SZH chain

POSTER

Abstract

We systematically study the phase diagram of $S=2$ spin chain by means of density-matrix renormalization group and exact diagonalization. We find two gapped phases which are topologically distinct: the AKLT phase is characterized by $S=1$ edge spins while the SZH phase by $S=3/2$ edge spins. Except from a multicritical point where a direct topological quantum phase transition occurs, we identify a dimer phase between both gapped phases. The whole phase boundary between dimer and SZH phases, including the multicritical point, is a critical line with central charge $c=5/2$. Finally, we propose and confirm that this line corresponds to $\rm SO(5)_1$ Wess--Zumino--Witten conformal field theory.

Authors

  • Hong-Chen Jiang

    • Microsoft Research, Station Q, UCSB
    • Microsoft Research, Station Q, University of California, Santa Barbara, CA 93106

  • Stephan Rachel

    • Yale University
    • Yale University, Department of Physics, New Haven, CT 06520
    • Physics Department, Yale University

  • Zheng-Yu Weng

    • Institute for Advanced Study, Tsinghua University, Beijing, 100084, P.\,R.\,China

  • Shou-Cheng Zhang

    • Department of Physics, McCullough Building, Stanford University, Stanford, CA 94305

  • Zhenghan Wang

    • Microsoft Research, Station Q, University of California, Santa Barbara, CA 93106