Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus

Hua-Chen, Zhang,; Wu, Ying-Hai; Tu, Hong-Hao; Xiang, Tao

doi:10.1103/physrevb.103.075130

Cited by 7 publications

(11 citation statements)

References 52 publications

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“…2N A +1 (the hat " ˆ" on an object indicates that the object is to be omitted). In appendix B, we prove that for all n ≥ 3, these wave functions can be represented as RVB states with fermionic partons, which generalize our earlier results for n = 3 [30].…”

Section: Anyon Eigenbasis From Chiral Correlators Of the So(n) 1 Wzw ...supporting

confidence: 83%

“…Another advantage of the RVB form is that the translation invariance of the wave functions on a regular lattice can be easily proven. The proof of translation invariance was given for the wave functions with n = 3 on the square lattice [30]. The generalization to cases with n ≥ 4 is straightforward and will not be repeated here.…”

Section: B Resonating Valence Bond Approach To So(n) 1 States On the ...mentioning

confidence: 99%

“…Another highlight is that the wave functions constructed from the SO(n) 1 WZW models provide a specific realization of Kitaev's sixteenfold way [9], which is a classification of 2D topological orders described by free or weakly interacting fermions coupled to Z 2 gauge fields [33][34][35][36][37][38]. In a previous work of the same authors [30], it was shown that the wave functions constructed from the SO(3) 1 WZW model are equivalent to certain resonating valence bond (RVB) states in terms of fermionic partons. We will prove that similar equivalences hold for the SO(n) 1 WZW model with n ≥ 3.…”

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confidence: 95%

“…It is valid for many chiral topological orders and allows for a systematic construction of trial wave functions for such systems. This method has been generalized from the continuum to the lattice, both on the plane [13][14][15][16][17][18][19][20][21][22][23][24][25][26] and on the torus [27][28][29][30]. One instructive progress is to express the resulting wave functions as infinite-dimensional matrix product states [31].…”

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confidence: 99%

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Chiral conformal field theory for topological states and the anyon eigenbasis on the torus

Zhang,

Wu,

Xiang

et al. 2021

Preprint

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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.

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Section: Anyon Eigenbasis From Chiral Correlators Of the So(n) 1 Wzw ...supporting

confidence: 83%

Section: B Resonating Valence Bond Approach To So(n) 1 States On the ...mentioning

confidence: 99%

mentioning

confidence: 95%

mentioning

confidence: 99%

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Chiral conformal field theory for topological states and the anyon eigenbasis on the torus

Zhang,

Wu,

Xiang

et al. 2021

Preprint

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“…After publishing this work as preprint, we were notified by the authors of[38] who had obtained a similar ansatz for rectangular lattices with periodic boundary conditions 5. In general, the RBM state obtained after training will be a linear combination of the three groundstates.…”

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confidence: 99%

Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model

Noormandipour

Sun

Haghighat

2021

Mach. Learn.: Sci. Technol.

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In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model with periodic boundary conditions is investigated. The measured groundstate (GS) energy of the system is compared and, for small lattice sizes (e.g. 3×3 with 18 spinors), shown to agree with the analytically derived value of the energy up to a deviation of 0.09 %. Moreover, the wave-functions we find have 99.89 % overlap with the exact ground state wave-functions. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them for possible future applications in quantum computation. Using the correspondence between topological field theories in (2+1)d and 2d CFTs, we propose an identification between our RBM states with the Moore-Read state and conformal blocks of the 2 d Ising model.

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Ising-like and Fibonacci anyons from KZ-equations

Haghighat

Liu

2022

J. High Energ. Phys.

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In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising-like and Fibonacci Anyons. We solve these equations around regular singular points in configuration space in terms of hypergeometric functions and derive explicit monodromy representations of the braid group action. This confirms the correct non-Abelian statistics of the solutions. One novelty of our approach is that we explicitly keep track of spin basis states and identify conformal blocks uniquely with such states at relevant points in moduli space.

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Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus

Cited by 7 publications

References 52 publications

Chiral conformal field theory for topological states and the anyon eigenbasis on the torus

Chiral conformal field theory for topological states and the anyon eigenbasis on the torus

Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model

Ising-like and Fibonacci anyons from KZ-equations

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