Affiliation:
1. Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
2. Department of Applied Physics and Applied Mathematics, Department of Mathematics, Columbia University, New York, New York 10027, USA
Abstract
The discrete Hamiltonian of Su, Schrieffer, and Heeger (SSH) [Phys. Rev. Lett. 42, 1698–1701 (1979)] is a well-known one-dimensional translation-invariant model in condensed matter physics. The model consists of two atoms per unit cell and describes in-cell and out-of-cell electron-hopping between two sub-lattices. It is among the simplest models exhibiting a non-trivial topological phase; to the SSH Hamiltonian, one can associate a winding number, the Zak phase, which depends on the ratio of hopping coefficients and takes on values 0 and 1 labeling the two distinct phases. We display two homotopically equivalent continuum Hamiltonians whose tight binding limits are SSH models with different topological indices. The topological character of the SSH model is, therefore, an emergent rather than fundamental property, associated with emergent chiral or sublattice symmetry in the tight-binding limit. In order to establish that the tight-binding limit of these continuum Hamiltonians is the SSH model, we extend our recent results on the tight-binding approximation [J. Shapiro and M. I. Weinstein, Adv. Math. 403, 108343 (2022)] to lattices, which depend on the tight-binding asymptotic parameter λ.
Funder
Swiss National Science Foundation
NSF
Simons Foundation
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献