Journal
NUCLEAR PHYSICS B
Volume 976, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.nuclphysb.2022.115712
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Funding
- National Key Research and Development Project of China [2017YFA0302901]
- National Natural Science Foundation of China [11888101, 11874095, 11804107]
- Strategic Priority Research Program of Chinese Academy of Sciences [XDB33000000]
- HUST
- Deutsche Forschungsgemeinschaft (DFG) [SFB 1143, 247310070]
- CAS-DAAD Doctoral Joint Scholarship Program
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In this paper, the authors propose a pure chiral approach for constructing torus wave functions, which is conceptually simpler and provides the anyon eigenbasis of degenerate ground states. Using SO(n)(1) and SU(n)(1) chiral spin liquids as examples, they construct the complete set of degenerate ground states and characterize their topological orders by analytically computing the associated modular S and T matrices.
Model wave functions constructed from (1+1)D conformal field theory (CFT) have played a vital role in studying chiral topologically ordered systems. There usually exist multiple degenerate ground states when such states are placed on the torus. The common practice for dealing with this degeneracy within the CFT framework is to take a full correlator on the torus, which includes both holomorphic and antiholomorphic sectors, and decompose it into several conformal blocks. In this paper, we propose a pure chiral approach for the torus wave function construction. By utilizing the operator formalism, the wave functions are written as chiral correlators of holormorphic fields restricted to each individual topological sector. This method is not only conceptually much simpler, but also automatically provides us the anyon eigenbasis of the degenerate ground states (also known as the minimally entangled states). As concrete examples, we construct the full set of degenerate ground states for SO(n)(1) and SU(n)(1) chiral spin liquids on the torus, the former of which provide a complete wave function realization of Kitaev's sixteenfold way of anyon theories. We further characterize their topological orders by analytically computing the associated modular S and T matrices. (C) 2022 The Author(s). Published by Elsevier B.V.
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