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Entanglement spectrum of a topological phase in one dimension
We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of
Quasiparticle statistics and braiding from ground state entanglement
Topologically ordered phases are gapped states, defined by the properties of excitations when taken around one another. Here we demonstrate a method to extract the statistics and braiding of
Symmetry protection of topological phases in one-dimensional quantum spin systems
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-S Haldane phase is a topologically nontrivial
Absence of Quantum Time Crystals.
A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.
Boundary critical phenomena in the three-state Potts model
Boundary critical phenomena are studied in the three-state Potts model in two dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary
Magnetization Plateaus in Spin Chains: “Haldane Gap” for Half-Integer Spins
We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, $S$, the magnetization curve can have plateaus and we argue that
Inequivalent Berry Phases for the Bulk Polarization
We address the widespread confusion in characterizing the polarization for insulators under the periodic boundary condition in terms of the Berry phase. The Berry phase can be formulated in terms of
Generalized Boundary Condition Applied to Lieb-Schultz-Mattis-Type Ingappabilities and Many-Body Chern Numbers
We introduce a new boundary condition which renders the flux-insertion argument for the Lieb-Schultz-Mattis type theorems in two or higher dimensions free from the specific choice of system sizes. It
Bose-Einstein condensation of dilute magnons in TlCuCl3.
A Hartree-Fock-type calculation based on a Bose-Einstein condensation of magnons is shown to describe the temperature dependence of the magnetization well.