## Building models of topological quantum criticality from pivot Hamiltonians

Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen

SciPost Phys. 14, 013 (2023) · published 2 February 2023

- doi: 10.21468/SciPostPhys.14.2.013
- Submissions/Reports

### Abstract

Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension $d>1$. Here, we show how the recently introduced notion of the pivot Hamiltonian—generating rotations between SPT phases—facilitates such a construction. We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT phase. The pivot Hamiltonian generates a $U(1)$ pivot symmetry which helps to stabilize a direct SPT transition. The sign-problem free nature of the model—with an additional Ising interaction preserving the pivot symmetry—allows us to obtain the phase diagram using quantum Monte Carlo simulations. We find evidence for a direct transition between trivial and SPT phases that is consistent with a deconfined quantum critical point with emergent $SO(5)$ symmetry. The known anomaly of the latter is made possible by the non-local nature of the $U(1)$ pivot symmetry. Interestingly, the pivot Hamiltonian generating this symmetry is nothing other than the staggered Baxter-Wu three-spin interaction. This work illustrates the importance of $U(1)$ pivot symmetries and proposes how to generally construct sign-problem-free lattice models of SPT transitions with such anomalous symmetry groups for other lattices and dimensions.

### Cited by 9

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Nathanan Tantivasadakarn, -
^{2}^{3}^{4}Ryan Thorngren, -
^{2}Ashvin Vishwanath, -
^{2}Ruben Verresen

^{1}California Institute of Technology [CalTech]^{2}Harvard University^{3}Massachusetts Institute of Technology [MIT]^{4}Kavli Institute for the Physics and Mathematics of the Universe [IPMU]