Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model

We theoretically investigate topological properties of the one-dimensional superlattice anyon-Hubbard model, which can be mapped to a superlattice bose-Hubbard model with an occupation-dependent phase factor by fractional Jordan-Wigner transformation. The topological anyon-Mott insulator is identified by topological invariant and edge modes using exact diagonalization and the density matrix renormalization group algorithm. When only the statistical angle is varied and all other parameters are fixed, a statistically induced topological phase transition can be realized, which provides insights into the topological phase transitions. What's more, we give an explanation of the statistically induced topological phase transition. The topological anyon-Mott phases can also appear in a variety of superlattice anyon-Hubbard models.

Figure 1

System size dependence of the gap $\mathrm{\Delta }\mu$ of anyon in anyon-Hubbard superlattice with statistical angle $\theta =0,\pi /5,2\pi /5,3\pi /5,4\pi /5,\pi ,U=10,V=10, \delta =2\pi /3,\alpha =\nu =1/3$.

Figure 2

The density distribution of the quasiparticle along the lattice sites at $N=30,L=90$. The other parameters are the same as those for Fig. 1.

Figure 3

System size dependence of the gap $\mathrm{\Delta }\mu$ of anyon in anyon-Hubbard superlattice with statistical angle $\theta =0,\pi /5,2\pi /5,3\pi /5,4\pi /5,\pi$, and $U=2,V=1,\delta =2\pi /3, \alpha =\nu =1/3$.

Figure 4

The quasiparticle and quasihole energy spectra vs the statistical angle $\theta$ for anyon-Hubbard superlattice with $L=120,U=2, V=1,\delta =2\pi /3,\alpha =\nu =1/3$. (a) Period boundary condition. (b) Open boundary condition.

Figure 5

The quasiparticle energy spectrum ${\mu }_p\left(N\right)$ ($N=41$, 40, 39, and 38) with respect to phase parameter $\delta$ for anyon-Hubbard superlattice with $L=120,U=2,V=1$, and $\theta =0,\pi /5,2\pi /5,3\pi /5,4\pi /5,\pi$ under OBC.

Figure 6

The distribution of the quasiparticle along the lattice sites at $L=120,0⩽\theta ⩽\pi$. The other parameters are the same as those for Fig. 3.

Figure 7

(a) The phase diagram for the system with $L=15,N=5$, and $V=1$. (b) The Mott gap of the system with $L=18,N=6,V=1$, and $\delta =2\pi /3$.

Figure 8

The distribution of the quasiparticle along the lattice sites at $L=120$. The other parameters are $\alpha =\nu =1/2,U=1, V=0.9,\delta =0$.