Entanglement spectrum as a diagnostic of chirality of topological spin liquids: Analysis of SU(3) projected entangled pair states

Autor(en)

Mark J. Arildsen, Ji-Yao Chen, Norbert Schuch, Andreas W. W. Ludwig

Abstrakt

We address the key question of representation of chiral topological quantum states in (2+1) dimensions (i.e., with non-zero chiral central charge) by Projected Entangled Pair States (PEPS). A noted result (due to Wahl, Tu, Schuch, and Cirac [Phys. Rev. Lett. 111, 236805 (2013)], and Dubail and Read [Phys. Rev. B 92, 205307 (2015)]) says that this is possible for non-interacting fermions, but the answer is as yet unknown for interacting systems. Characteristic counting of degeneracies of low-lying states in the entanglement spectrum (ES) at fixed transverse momentum of bipartitioned long cylinders ("Li-Haldane counting") provides often-used supporting evidence for chirality. However, non-chiral PEPS (with zero chiral central charge), yet with strong breaking of time-reversal and reflection symmetries, with invariance under the product of these two operations (i.e., "apparently" chiral states), are known whose low-lying ES exhibits the same Li-Haldane counting as a chiral state in certain topological sectors [Kure\v{c}i\'c, Vanderstraeten, and Schuch, Phys. Rev. B 99, 045116 (2019); Arildsen, Schuch, and Ludwig, Phys. Rev. B 108, 245150 (2023)]. In the present work, we identify a distinct indicator and hallmark of chirality in the ES of PEPS with global $\mathrm{SU}(3)$ symmetry: the splittings of conjugate irreps. We prove that in the ES of the chiral states conjugate irreps are exactly degenerate, because the operators that would split them [related to the cubic Casimir invariant of $\mathrm{SU}(3)$] are forbidden. By contrast, in the ES of non-chiral states, conjugate splittings are demonstrably non-vanishing. Such a diagnostic provides an unambiguous and powerful tool to distinguish chiral and non-chiral topological states in (2+1) dimensions via their entanglement spectra.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation, Institut für Mathematik

Externe Organisation(en)

University of California, Santa Barbara, Scuola Internazionale Superiore di Studi Avanzati, Sun Yat-sen University

Journal

Physical Review B

Band

110

Anzahl der Seiten

23

ISSN

2469-9950

DOI

https://doi.org/10.48550/arXiv.2305.13240

Publikationsdatum

12-2024

Peer-reviewed

Ja

ÖFOS 2012

101028 Mathematische Modellierung, 103025 Quantenmechanik, 103036 Theoretische Physik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/20a63fb2-8062-40c5-87fb-9c06801459f7