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Boson condensation in topologically ordered quantum liquids

Author(s): Neupert, Titus; He, Huan; von Keyserlingk, Curt; Sierra, German; Bernevig, Bogdan A.

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dc.contributor.authorNeupert, Titus-
dc.contributor.authorHe, Huan-
dc.contributor.authorvon Keyserlingk, Curt-
dc.contributor.authorSierra, German-
dc.contributor.authorBernevig, Bogdan A.-
dc.date.accessioned2020-10-30T19:20:30Z-
dc.date.available2020-10-30T19:20:30Z-
dc.date.issued2016-03-01en_US
dc.identifier.citationNeupert, Titus, He, Huan, von Keyserlingk, Curt, Sierra, German, Bernevig, B Andrei. (2016). Boson condensation in topologically ordered quantum liquids. PHYSICAL REVIEW B, 93 (10.1103/PhysRevB.93.115103en_US
dc.identifier.issn2469-9950-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr17r6z-
dc.description.abstractBoson condensation in topological quantum field theories (TQFT) has been previously investigated through the formalism of Frobenius algebras and the use of vertex lifting coefficients. While general, this formalism is physically opaque and computationally arduous: analyses of TQFT condensation are practically performed on a case by case basis and for very simple theories only, mostly not using the Frobenius algebra formalism. In this paper, we provide a way of treating boson condensation that is computationally efficient. With a minimal set of physical assumptions, such as commutativity of lifting and the definition of confined particles, we can prove a number of theorems linking Boson condensation in TQFT with chiral algebra extensions, and with the factorization of completely positive matrices over Z(+). We present numerically efficient ways of obtaining a condensed theory fusion algebra and S matrices; and we then use our formalism to prove several theorems for the S and T matrices of simple current condensation and of theories which upon condensation result in a low number of confined particles. We also show that our formalism easily reproduces results existent in the mathematical literature such as the noncondensability of five and ten layers of the Fibonacci TQFT.en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW Ben_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleBoson condensation in topologically ordered quantum liquidsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevB.93.115103-
dc.date.eissued2016-03-01en_US
dc.identifier.eissn2469-9969-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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