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Condensed Matter > Strongly Correlated Electrons
Title: Parafermionization, bosonization, and critical parafermionic theories
(Submitted on 14 Dec 2020 (v1), last revised 2 Apr 2021 (this version, v4))
Abstract: We formulate a $\mathbb{Z}_k$-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality at $k=2$. The $\mathbb{Z}_k$-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory when $k>2$. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical $\mathbb{Z}_k$-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the $\mathbb{Z}_k$-parafermionic minimal models, complementing earlier works on fermionic cases.
Submission history
From: Yuan Yao [view email][v1] Mon, 14 Dec 2020 13:54:00 GMT (196kb,D)
[v2] Tue, 22 Dec 2020 03:51:25 GMT (193kb,D)
[v3] Sat, 6 Feb 2021 12:05:13 GMT (195kb,D)
[v4] Fri, 2 Apr 2021 00:09:45 GMT (197kb,D)
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