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arXiv:hep-th/9711024 · Nuclear Physics B

Factored coset models: a unifying approach to different bosonization schemes

A.N. Theron, F.G. Scholtz, H.B. Geyer

Published Sep 1, 1998• 1 citation
arXivHTMLPDF
DOI
10.1016/s0550-3213(98)00311-3

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Analysis of quantum phase transition in some different Curie-Weiss models: a unified approach

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A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum Hamiltonian by an appropriate factor, rewriting the Hamiltonian in terms of $SU(2)$ operators only, and obtention of a classical Hamiltonian. $SU(2)$ operators are obtained from creation and annihilation operators as linear combinations in the case of fermions and as an inverse Holstein-Primakoff transformation in the case of bosons. This scheme is successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.

arXiv:1712.07634•Dec 20, 2017•0 citations
We discuss various bosonization schemes from a path integral perspective. Our analysis shows that the existence of different bosonization schemes, such as abelian bosonization of non-abelian models and non-abelian bosonization of fermions with colour and flavour indices, can be understood as different ways of factoring out a dynamically trivial coset which contains the fermions. From this perspective follows the importance of the coset model in ensuring the correct superselection rules on the bosonic level.
We present a unified framework for upgrading a broad class of cryptographic primitives to support constant-rate certified deletion. Previous constructions require a linear number of qubits per encrypted bit of certified-deletable plaintext. In contrast, we obtain the first constant-rate constructions in the plain model that achieve certified deletion while preserving everlasting security. Our approach applies to a wide range of "all-or-nothing"-type primitives based on BB84-style encodings, including commitment schemes, public-key encryption, attribute-based encryption, and fully homomorphic encryption. Beyond this class, we also obtain constant-rate certified deletion for primitives built from subspace coset states, such as blind delegation, secure software leasing, functional encryption, and differing-inputs iO, and CCA-PKE. Importantly, our framework does not introduce any additional assumptions beyond those required by the underlying certified deletion primitives. Finally, under the hardness of SIS, we show that public verifiability can be incorporated into BB84- and coset-based certified deletion. In combination with our constant-rate constructions, this yields publicly verifiable certified deletion schemes with constant rate.
A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum Hamiltonian by an appropriate factor, rewriting the Hamiltonian in terms of SU(2)SU(2)SU(2) operators only, and obtention of a classical Hamiltonian. SU(2)SU(2)SU(2) operators are obtained from creation and annihilation operators as linear combinations in the case of fermions and as an inverse Holstein-Primakoff transformation in the case of bosons. This scheme is successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.