TY - JOUR

T1 - A nonvanishing spectral gap for AKLT models on generalized decorated graphs

AU - Lucia, Angelo

AU - Young, Amanda

N1 - Funding Information:
A.L. was supported by Grant Nos. PID2020-113523GB-I00 and CEX2019-000904-S, funded by MCIN/AEI/10.13039/501100011033, by Grant No. RYC2019-026475-I, funded by MCIN/AEI/10.13039/501100011033 and “ESF Investing in your future,” and by Comunidad de Madrid (Grant No. QUITEMAD-CM, Ref. No. S2018/TCS-4342). A.Y. was supported by the DFG under Grant No. EXC-2111–390814868. The authors acknowledge the support of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), where part of this work was carried out during the “Tensor Networks: Mathematical Structures and Novel Algorithms” workshop. They also thank Bruno Nachtergaele for his helpful discussions during the development of this work, as well as the reviewers whose careful assessments of our work led to improvements in our results and proofs.
Publisher Copyright:
© 2023 Author(s).

PY - 2023/4/1

Y1 - 2023/4/1

N2 - We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of G with a chain of n sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States approach from [Abdul-Rahman et al., Analytic Trends in Mathematical Physics, Contemporary Mathematics (American Mathematical Society, 2020), Vol. 741, p. 1.], we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy.

AB - We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of G with a chain of n sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States approach from [Abdul-Rahman et al., Analytic Trends in Mathematical Physics, Contemporary Mathematics (American Mathematical Society, 2020), Vol. 741, p. 1.], we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy.

UR - http://www.scopus.com/inward/record.url?scp=85153801348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85153801348&partnerID=8YFLogxK

U2 - 10.1063/5.0139706

DO - 10.1063/5.0139706

M3 - Article

AN - SCOPUS:85153801348

SN - 0022-2488

VL - 64

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 4

M1 - A147

ER -