TY - JOUR

T1 - Symmetry-protected topological phases and competing orders in a spin-12 XXZ ladder with a four-spin interaction

AU - Ogino, Takuhiro

AU - Furukawa, Shunsuke

AU - Kaneko, Ryui

AU - Morita, Satoshi

AU - Kawashima, Naoki

N1 - Funding Information:
The authors would like to thank Y. Fuji, R. K. Kaul, S. Ono, M. Sato, and K. Sugimoto for useful comments. This research was supported by JSPS KAKENHI Grants No. JP18K03446, JP19H01809, and JP20K03780. The numerical computations were performed on computers at the Supercomputer Center, the Institute for Solid State Physics (ISSP), the University of Tokyo.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/8/15

Y1 - 2021/8/15

N2 - We study a spin-12 XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS∗ and Haldane∗ phases, in which twisted singlet pairs (|↑↓)+|↓↑))/2 are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge c=1 occur between the featureless phases and between the ordered phases while Ising transitions with c=1/2 occur between the featureless and ordered phases. The two types of transition lines cross at the SU(2)-symmetric point, where the criticality is described by the SU(2)2 Wess-Zumino-Witten theory with c=3/2. The RS-Haldane∗ and RS∗-Haldane transitions give examples of topological phase transitions. Interestingly, the RS∗ and Haldane∗ phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.

AB - We study a spin-12 XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS∗ and Haldane∗ phases, in which twisted singlet pairs (|↑↓)+|↓↑))/2 are formed between the two legs. We argue and demonstrate that Gaussian transitions with the central charge c=1 occur between the featureless phases and between the ordered phases while Ising transitions with c=1/2 occur between the featureless and ordered phases. The two types of transition lines cross at the SU(2)-symmetric point, where the criticality is described by the SU(2)2 Wess-Zumino-Witten theory with c=3/2. The RS-Haldane∗ and RS∗-Haldane transitions give examples of topological phase transitions. Interestingly, the RS∗ and Haldane∗ phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.

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U2 - 10.1103/PhysRevB.104.075135

DO - 10.1103/PhysRevB.104.075135

M3 - Article

AN - SCOPUS:85114023376

SN - 2469-9950

VL - 104

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 7

M1 - 075135

ER -