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.

arXiv comment11 pages (5 pages of main text and 6 pages of supplemental materials), 9 figures

References in corpus (27)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Entanglement in quantum critical phenomena
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Topological Materials: Weyl Semimetals
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Calculation of reduced density matrices from correlation functions
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• Area laws in quantum systems: mutual information and correlations
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Entanglement spectrum of topological insulators and superconductors
• Solving Gapped Hamiltonians Locally
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• An order parameter for symmetry-protected phases in one dimension
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Persistent currents through a quantum dot
• 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