String order and symmetries in quantum spin lattices

Abstract

We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection is established, we provide a complete characterization of local symmetries in these states. The results allow to understand in a straightforward way many of the properties of string order parameters, like their robustness/fragility under perturbations and their typical disappearance beyond strictly one-dimensional lattices. We propose and discuss an alternative definition, ideally suited for detecting phase transitions, and generalizations to two and more spatial dimensions.

5 pages, 1 figure

References in corpus (6)

• Matrix product states represent ground states faithfully
• DMRG and periodic boundary conditions: a quantum information perspective
• Valence Bond Solids for Quantum Computation
• Hidden order in 1D Bose insulators
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Fragility of String Orders

Cited by in corpus (10)

• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• On topological phases of spin chains
• Symmetry protection of measurement-based quantum computation in ground states
• Non-local order parameters for the 1D Hubbard model
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Entanglement, fractional magnetization and long-range interactions
• Exploiting Matrix Symmetries and Physical Symmetries in Matrix Product States and Tensor Trains
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Maximized string order parameters in the valence bond solid states of quantum integer spin chains