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23 April 2024 |
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Article overview
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$so(N)_1$ criticality in generalized cluster models | | Ville Lahtinen
; Eddy Ardonne
; | | Date: |
27 Apr 2015 | | Abstract: | We show that $so(N)_1$ universality class quantum criticality emerges when
one-dimensional generalized cluster models -- the N-cluster models -- are
perturbed with Ising or Zeeman terms. Each critical point is described by a
low-energy theory of N linearly dispersing fermions, whose spectrum we show to
precisely match the prediction by $so(N)_1$ conformal field theory.
Furthermore, by an explicit construction we show that the N-cluster models are
dual to N non-locally coupled transverse field Ising chains, which enables to
identify local representations for the primary fields and shows that the
N-cluster models provide the simplest representation of the recently introduced
hierarchy of $so(N)_1$ critical spin models. For the experimentally most
realistic case of N=3, that corresponds to the original one-dimensional cluster
model, our results show that $su(2)_2 simeq so(3)_1$ Wess-Zumino-Witten model
can emerge in a local, translationally invariant and Jordan-Wigner solvable
spin-1/2 model. | | Source: | arXiv, 1504.7044 | | Services: | Forum | Review | PDF | Favorites | |
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