Zou, HaiyuanZhao, ErhaiGuan, Xi-WenLiu, W. Vincent2020-06-292020-06-290031-9007http://hdl.handle.net/1885/205590A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1=2 systems in one dimension. Realizing these SPT phases, however, often demands finetuningshardtoreachexperimentally.Andthelackofanalyticalsolutionshinderstheunderstandingoftheir many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described byaspinmodelwhoseexchangecouplingscanbetunedbyanexternalfieldtoreachparameterregionsnot studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wavefunctioncanbeobtainedexactlyalongalineandataspecialpoint,forthesetwophases,respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation and discuss the phase transitions between the two SPT phases and their experimental signatures.This work is supported by National Natural Science Foundation of China Grant No. 11804221 (H. Z.), Science and Technology Commission of Shanghai Municipality Grant No. 16DZ2260200 (H. Z. and W. V. L), AFOSR Grant No. FA9550-16-1-0006 (E. Z. and W. V. L.), NSF Grant No. PHY-1707484 (E. Z.) and MURI-ARO Grant No. W911NF-17-1-0323, ARO Grant No. W911NF-11-1-0230, and the Overseas Scholar Collaborative Program of NSF of China Grant No. 11429402 sponsored by Peking University (W. V. L.). X. W. G. is partially supported by the key NSFC Grant No. 11534014 and the National Key R&D Program of China Grant No. 2017YFA0304500.application/pdfen-AU© 2019 American Physical Society201910.1103/PhysRevLett.122.1804012020-01-19