Kavli Affiliate: Ke Wang
| First 5 Authors: Ke Wang, T. A. Sedrakyan, , ,
| Summary:
We consider Lifshitz criticalities with dynamical exponent $z=2$ that emerge
in a class of topological chains. There, such a criticality plays a fundamental
role in describing transitions between symmetry-enriched conformal field
theories (CFTs). We report that, at such critical points in one spatial
dimension, the finite-size correction to the energy scales with system size,
$L$, as $sim L^{-2}$, with universal and anomalously large coefficient. The
behavior originates from the specific dispersion around the Fermi surface,
$epsilon propto pm k^2$. We also show that the entanglement entropy exhibits
at the criticality a non-logarithmic dependence on $l/L$, where $l$ is the
length of the sub-system. In the limit of $lll L$, the maximally-entangled
ground state has the entropy, $S(l/L)=S_0+2n(l/L)log(l/L)$. Here $S_0$ is some
non-universal entropy originating from short-range correlations and $n$ is
half-integer or integer depending on the degrees of freedom in the model. We
show that the novel entanglement originates from the long-range correlation
mediated by a zero mode in the low energy sector. The work paves the way to
study finite-size effects and entanglement entropy around Lifshitz
criticalities and offers an insight into transitions between symmetry-enriched
criticalities.
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