Correlated Quantum Phases

We are interested in exotic quantum phases emerging from strong interactions in many-body systems. Below are a few aspects we have studied recently:

• Quantum spin liquids in frustrated magnets
• Symmetry protected topological (SPT) phases
• Symmetry enriched topological (SET) orders
• Fractional quantum Hall liquids
• Symmetry and filling constraints on topology: Lieb-Schultz-Mattis (LSM) theorems

Recent highlights:

• Higher-order SPT phases (w/ Alex Rasmussen)

"Higher-order" SPT phases are featured by gapless hinge or corner modes, which are protected by certain global symmetries and stablized by certain crystalline symmetries. We provide a systematic way to classify and construct the higher-order SPT phases of interacting bosons, in the case when the total symmetry group is a direct product of global and crystalline symmetries (arXiv:1809.07325). Generalizing this framework to fermionic systems, we also show how to construct intrinsically interacting fermionic crystalline SPT phases, which go beyond both boson SPT phases and free fermion phases (arXiv:1810.12317).

• Field-induced spinon Fermi surface in antiferromagnetic Kitaev model (arXiv:1809.08247)

Combining theoretical and numerical efforts, we identify the gapless phase in AFM Kitaev model under an intermediate perpendicular field as a U(1) QSL with spinon Fermi surfaces. We also obtain the phase diagram of the anisotropic AFM Kitaev model under a field, and study the quantum phase transitions between the 4 different phases therein.

• Lieb-Schultz-Mattis theorems for SPT phases
• In a series of papers, we reveal a class of generalized Lieb-Schultz-Mattis theorems, where a proper choice of symmetries and local Hilbert space enforces any short-range entangled ground state to be a SPT phase. Examples include integer quantum Hall insulators, quantum spin Hall insulators, chiral and helical topological superconductors, and bosonic SPT phases, enforced by magnetic translation symmetries.