Critical properties of a comb lattice
Natalia Chepiga, Steven R. White
SciPost Phys. 9, 013 (2020) · published 27 July 2020
- doi: 10.21468/SciPostPhys.9.1.013
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 $2L$.
Cited by 2
De Tomasi et al., Effects of critical correlations on quantum percolation in two dimensions
Phys. Rev. B 105, 224316 (2022) [Crossref]
Hart et al., From compact localized states to many-body scars in the random quantum comb
Phys. Rev. Research 2, 043267 (2020) [Crossref]
Ontology / TopicsSee full Ontology or Topics database.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Natalia Chepiga,
- 2 Steven White