TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.9.1.013
TI  - Critical properties of a comb lattice
PY  - 2020/07/27
UR  - https://www.scipost.org/SciPostPhys.9.1.013
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 9
IS  - 1
SP  - 013
A1  - Chepiga, Natalia
AU  - White, Steven
AB  - In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice -- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as $1/(NL)$, and not as $1/N$ or $1/L$ typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length $L$, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, $L-1$. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length $2L$.
ER  -

@Article{10.21468/SciPostPhys.9.1.013,
	title={{Critical properties of a comb lattice}},
	author={Natalia Chepiga and Steven R. White},
	journal={SciPost Phys.},
	volume={9},
	pages={013},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.9.1.013},
	url={https://scipost.org/10.21468/SciPostPhys.9.1.013},
}