Multi-critical topological transition at quantum criticality

AbstractThe investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.

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TOPOLOGICAL QUANTUM PHASE TRANSITIONS IN TWO-DIMENSIONAL HEXAGONAL LATTICE BILAYERS

SPIN ◽

10.1142/s2010324713300065 ◽

2013 ◽

Vol 03 (02) ◽

pp. 1330006 ◽

Cited By ~ 4

Author(s):

XUECHAO ZHAI ◽

GUOJUN JIN

Keyword(s):

Phase Transition ◽

Band Gap ◽

Quantum Phase Transition ◽

Quantum Phase Transitions ◽

Hexagonal Lattice ◽

Short Review ◽

Quantum Phase ◽

Two Dimensional ◽

Topological Quantum ◽

Bulk Band

Since the successful fabrication of graphene, two-dimensional hexagonal lattice structures have become a research hotspot in condensed matter physics. In this short review, we theoretically focus on discussing the possible realization of a topological insulator (TI) phase in systems of graphene bilayer (GBL) and boron nitride bilayer (BNBL), whose band structures can be experimentally modulated by an interlayer bias voltage. Under the bias, a band gap can be opened in AB-stacked GBL but is still closed in AA-stacked GBL and significantly reduced in AA- or AB-stacked BNBL. In the presence of spin–orbit couplings (SOCs), further demonstrations indicate whether the topological quantum phase transition can be realized strongly depends on the stacking orders and symmetries of structures. It is observed that a bulk band gap can be first closed and then reopened when the Rashba SOC increases for gated AB-stacked GBL or when the intrinsic SOC increases for gated AA-stacked BNBL. This gives a distinct signal for a topological quantum phase transition, which is further characterized by a jump of the ℤ2 topological invariant. At fixed SOCs, the TI phase can be well switched by the interlayer bias and the phase boundaries are precisely determined. For AA-stacked GBL and AB-stacked BNBL, no strong TI phase exists, regardless of the strength of the intrinsic or Rashba SOCs. At last, a brief overview is given on other two-dimensional hexagonal materials including silicene and molybdenum disulfide bilayers.

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