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Renormalization group approach to symmetry protected topological phases

van Nieuwenburg, Evert P. L. and Schnyder, Andreas P. and Chen, Wei (2018) Renormalization group approach to symmetry protected topological phases. Physical Review B, 97 (15). Art. No. 155151. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20180425-144715290

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Abstract

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.97.155151DOIArticle
https://arxiv.org/abs/1801.07082arXivDiscussion Paper
Additional Information:© 2018 American Physical Society. (Received 22 January 2018; revised manuscript received 13 April 2018; published 23 April 2018)
Group:Institute for Quantum Information and Matter, IQIM
Record Number:CaltechAUTHORS:20180425-144715290
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180425-144715290
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86045
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Apr 2018 23:00
Last Modified:25 Apr 2018 23:00

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