TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.4.134
TI  - Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
PY  - 2022/04/20
UR  - https://www.scipost.org/SciPostPhys.12.4.134
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 4
SP  - 134
A1  - Wang, Ke
AU  - Sedrakyan, Tigran
AB  - 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 $l\ll L$, the maximally-entangled ground state has the entropy, $S(l/L)=S_0+(l/L)\log(l/L)$. Here $S_0$ is some non-universal entropy originating from short-range correlations. 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.
ER  -

@Article{10.21468/SciPostPhys.12.4.134,
	title={{Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains}},
	author={Ke Wang and T. A. Sedrakyan},
	journal={SciPost Phys.},
	volume={12},
	pages={134},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.4.134},
	url={https://scipost.org/10.21468/SciPostPhys.12.4.134},
}