Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks

Chen, Yu-Hsueh; Huang, Ching-Yu; Kao, Ying-Jer

doi:10.1103/physrevb.104.045131

Cited by 3 publications

(1 citation statement)

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“…For instance, whether PEPS can faithfully represent the chiral shin liquids (CSL) is still under heated debate. While several efforts are devoted to representing gapped CSL using PEPS, they all exhibit infinite correlation length [67][68][69][70][71][72][73][74][75], consistent with the no-go theorem proven in the free-fermion case that the parent Hamiltonian of a chiral PEPS is gapless [76]. Nonetheless, in a very recent paper, Hasik et al argue that a faithful representation of the CSL phase is in fact possible [46].…”

Section: Discussion and Outlookmentioning

confidence: 73%

Variational Tensor Network Operator

Chen¹,

Hsü²,

Tu³

et al. 2022

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We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By applying these operators to simple initial states, accurate variational ground state wave functions with extremely few parameters can be obtained. Furthermore, the framework can be applied to study spontaneously symmetry breaking, symmetry protected topological, and intrinsic topologically ordered phases, and we show that symmetries of the local tensors associated with these phases can emerge directly after the optimization without any gauge fixing. This provides a universal way to identify quantum phase transitions without prior knowledge of the system.

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