4.6 Article

Emergent topological orders and phase transitions in lattice Chern-Simons theory of quantum magnets

Journal

PHYSICAL REVIEW B
Volume 106, Issue 12, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.106.L121117

Keywords

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Funding

  1. National Natural Science Foundation of China [11904225, 11774420, 12274458, 12274206]
  2. National Key R&D Program of China [2017YFA0302900, 2017YFA0303200, 2016YFA0300503]
  3. UMass Amherst

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Topological phase transitions involving intrinsic topological orders cannot be described by conventional mean-field theories, but lattice Chern-Simons theory shows that traditional concepts can still play a crucial role in certain cases, while simplifying the transitions to effective mean-field theories based on fermionic degrees of freedom.
Topological phase transitions involving intrinsic topological orders are usually characterized by qualitative changes of ground state quantum entanglement, which cannot be described by conventional mean-field theories with local order parameters. Here, we apply the lattice Chern-Simons theory to study frustrated quantum magnets and show that the conventional concepts, such as the order parameter and symmetry breaking, can still play a crucial role in certain topological phase transitions. The lattice Chern-Simons representation establishes a nonlocal mapping from quantum spin models to interacting spinless Dirac fermions. We show that breaking certain emergent symmetries of the fermionic theory could provide a unified approach to describing both magnetic and topological orders, as well as the topological phase transitions between them. We apply this method to the perturbed spin-1/2 J(1)-J(2) XY model on the honeycomb lattice and predict a nonuniform chiral spin liquid ground state in the strong frustration region. This is further verified by our high-precision tensor network calculations. These results suggest that the lattice Chern-Simons theory can simplify the complicated topological phase transitions to effective mean-field theories in terms of fermionic degrees of freedom, which lead to different understandings that help to understand the frustrated quantum magnets.

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