Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

Abstract

The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state densitymatrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

Cumulants and scaling functions of infinite matrix product states

“…7 shows the cumulants of O 2 string as a function of J ⊥ . From these figures, O 2 string vanishes, while its variance, skewness and curtosis diverge at J c ⊥ ∼ 2.21, consistent with previous results of J c ⊥ = 2.214 [20]. Unlike the case of the 1D TFI model where the magnetization order parameter M is finite in the ordered phase and zero in the disordered phase, O 2 string remains finite in both SPT and topologically trivial phases and only vanishes at the critical point.…”

“…When s = s * , as in the bottom figure, U 4 (m, J ⊥ )∀m intersect at J ⊥ = 2.21, which is taken as the critical point J c ⊥ , in agreement with Ref. [20]. Since s = s * , this intersection point satisfies ∂U4(m,B) ∂m = 0, which is unlike the top figure of Fig.…”

“…As shown in Ref. [20], O 2 string can be expressed as a correlation function O 2 string = lim |j−k|→∞ p(j)p(k) , where p(j) = i<j (−1)…”

“…The iMPS ground state generated here is enforced with U(1) particle number symmetry to conserve particle number and SU(2) spin rotation symmetry. When J ⊥ < J c ⊥ , the ground state is in a symmetryprotected topological (SPT) phase protected by inversion symmetry and undergoes a topological phase transition into a topologically trivial state consisting of local Kondo singlets when J ⊥ > J c ⊥ [20]. This phase transition occurs with the vanishing of the charge excitation gap while the spin excitation gap remains nonzero and finite.…”

“…This gives κ ∼ 1.027, α 1 = −0.106, α 2 = 0.701, α 3 = 1.552 and α 4 = 2.455. The central charge c of this phase transition has been shown to be c ∼ 1 [20] which was obtained through the relation of the entanglement entropy S and ξ given by [21]…”