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Abstract
It is well known that the matrix product state (MPS) description of a gapped ground state with a global onsite symmetry can exhibit "symmetry fractionalization." Namely, even though the symmetry acts as a linear representation on the physical degrees of freedom, the MPS matrices  which act on some virtual degrees of freedom  can transform under a projective representation. This was instrumental in classifying gapped symmetryprotected phases that manifest in onedimensional (1D) quantum manybody systems. Here we consider the multiscale entanglement renormalization ansatz (MERA) description of 1D ground states that have global onsite symmetries. We show that, in contrast to the MPS, the symmetry does not fractionalize in the MERA description if the ground state is gapped, assuming that the MERA preserves the symmetry at all length scales. However, it is still possible that the symmetry can fractionalize in the MERA if the ground state is critical, which may be relevant for characterizing critical symmetryprotected phases. Our results also motivate the presumed use of symmetric tensors to implement global onsite symmetries in MERA algorithms.
Original language  English 

Article number  195139 
Pages (fromto)  110 
Number of pages  10 
Journal  Physical Review B 
Volume  99 
Issue number  19 
DOIs  
Publication status  Published  22 May 2019 
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Projects
 1 Active

ARC Centre of Excellence for Quantum Engineered Systems (EQuS) (RAAP)
Volz, T. & Doherty, A. C.
5/04/17 → …
Project: Research