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Boson condensation and instability in the tensor network representation of string-net states

Shukla, Sujeet K. and Şahinoglu, M. Burak and Pollmann, Frank and Chen, Xie (2018) Boson condensation and instability in the tensor network representation of string-net states. Physical Review B, 98 (12). Art. No. 125112. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20161107-095433292

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Abstract

The tensor network representation of many-body quantum states, given by local tensors, provides a promising numerical tool for the study of strongly correlated topological phases in two dimensions. However, the representation may be vulnerable to instabilities caused by small variations in the local tensors. For example, the topological order in the tensor network representations of the toric code ground state has been shown in Chen, Zeng, Gu, Chuang, and Wen, Phys. Rev. B 82, 165119 (2010)to be unstable if the variations break certain Z_2 symmetry of the tensor. In this work, we ask whether other types of topological orders suffer from similar kinds of instability and if so, what is the underlying physical mechanism and whether we can protect the order by enforcing certain symmetries on the tensor. We answer these questions by showing that the tensor network representations of all string-net models are indeed unstable, but the matrix product operator (MPO) symmetries of the tensors identified in Şahinoğlu, Williamson, Bultinck, Mariën, Haegeman, Schuch, and Verstraete, arXiv:1409.2150 can help to protect the order. In particular, we show that a subset of variations that break the MPO symmetries lead to instability by inducing the condensation of bosonic quasiparticles, which destroys the topological order in the wave function. Therefore such variations must be forbidden for the encoded topological order to be reliably extracted from the local tensors. On the other hand, if a tensor network based variational algorithm is used to simulate the phase transition due to boson condensation, such variation directions may prove important to access the continuous transition correctly.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.98.125112DOIArticle
https://arxiv.org/abs/1610.00608arXivDiscussion Paper
Additional Information:© 2018 American Physical Society. Received 15 March 2018; revised manuscript received 20 July 2018; published 7 September 2018. S.K.S. would like to thank Pinaky Bhattacharyya for help with the numerical calculations. X.C. is supported by the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20161107-095433292
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161107-095433292
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71767
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:07 Nov 2016 19:25
Last Modified:23 Jan 2019 22:17

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