$Z_2\times Z_2$ symmetry and $Z_4$ Berry phase of bosonic ladder

Yoshihito Kuno; Yasuhiro Hatsugai

doi:10.1103/PhysRevA.108.013319

paper

$Z_{2} \times Z_{2}$ symmetry and $Z_{4}$ Berry phase of bosonic ladder

arXiv:2304.09533 · doi:10.1103/PhysRevA.108.013319

Abstract

Bose gas on a two-leg ladder exhibits an interesting topological phase. We show the presence of a bosonic symmetry-protected-topological (SPT) phase protected by $Z_{2} \times Z_{2}$ symmetry. This symmetry leads to $Z_{4}$ fractional quantization of $Z_{4}$ Berry phase, that is a topological order parameter to identify the bulk. Using the $Z_{4}$ Berry phase, we have shown that the interacting bosonic system possesses rich topological phases depending on particle density and strength of interaction. Based on the bulk-edge correspondence, each edge state of the SPT phases is discussed in relation to the $Z_{4}$ Berry phases. Especially we have found an intermediate phase that is not adiabatically connected to a simple adiabatic limit, that possesses unconventional edge states, which we have numerically demonstrate by employing the density-matrix-renormalization group algorithm.

arXiv comment12 pages, 14 figures

$Z_{2} \times Z_{2}$ symmetry and $Z_{4}$ Berry phase of bosonic ladder

Abstract

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Z2​×Z2​ symmetry and Z4​ Berry phase of bosonic ladder

Abstract

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$Z_{2} \times Z_{2}$ symmetry and $Z_{4}$ Berry phase of bosonic ladder