Characterizing symmetry breaking patterns in a lattice by dual degrees of freedom

Abstract

A duality transformation in quantum field theory is usually established first through partition functions. It is always important to explore the dual relations between various correlation functions in the transformation. Here, we explore such a dual relation to study quantum phases and phase transitions in an extended boson Hubbard model at 1/3 (2/3) filling on a triangular lattice. We develop systematically a simple and effective way to use the vortex degrees of freedom on dual lattices to characterize both the density wave and valence bond symmetry breaking patterns of the boson insulating states in the direct lattices. In addition to a checkerboard charge density wave (X-CDW) and a stripe CDW, we find a novel CDW-VBS phase which has both local CDW and local valence bond solid (VBS) orders. Implications for Quantum Monte Carlo simulations are addressed. The possible experimental realizations of cold atoms loaded on optical lattices are discussed.

Keywords:

• duality
• valence bond solid
• frustrated lattice
• vortex

Acknowledgments

We thank Fuchun Zhang and Zidan Wang for their hospitality during our visit at Hong Kong University which initiated the collaboration. YC was supported by NSFC-10874032 and 11074043, the State Key Programs of China (Grant no. 2009CB929204) and Shanghai Municipal Government. JY was supported by NSF-DMR-1161497, NSFC-11074173,11174210, Beijing Municipal Commission of Education under grant No.PHR201107121, at KITP, was supported in part by the NSF under grant No. PHY-0551164. JY thanks Han Pu for his hospitality during his visit at Rice University where part of this work was done.