Symmetry protected phases in inhomogeneous spin chains

Abstract

It has been shown recently that inhomogenous spin chains can exhibit exotic phenomena such as the breaking of the area law of the entanglement entropy. An example is given by the rainbow model where the exchange coupling constants decrease from the center of the chain. Here we show that by folding the chain around its center, the long-range entanglement becomes short-range which can lead to topological phases protected by symmetries (SPT). The phases are trivial for bond-centered foldings, and non trivial for site-centered ones. In the latter case, the folded spin 1/2 chain with $U(1)$ symmetry belongs to the Su-Schrieffer-Heeger class, while the folded chain with $SU(2)$ symmetry is in the Haldane phase. Finally, we extend these results to higher spin chains where we find a correspondence between the symmetry protection of gapped and gapless phases.

11 pages (5 pages of main text and 6 pages of supplemental materials), 9 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Area laws in quantum systems: mutual information and correlations
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• Unusual area-law violation in random inhomogeneous systems
• Designing a symmetry protected molecular device

Cited by in corpus (11)

• Entanglement as geometry and flow
• Ising analogues of quantum spin chains with multispin interactions
• Link representation of the entanglement entropies for all bipartitions
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Entanglement links and the quasiparticle picture
• Entanglement in non-critical inhomogeneous quantum chains
• Depletion in fermionic chains with inhomogeneous hoppings
• Exotic correlation spread in free-fermionic states with initial patterns
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Emergent geometry from entanglement structure
• $su(2)$ symmetry of XX spin chains