Extracting Excitations From Model State Entanglement

We extend the concept of entanglement spectrum from the geometrical to the particle bipartite partition. We apply this to several Fractional Quantum Hall (FQH) wavefunctions on both sphere and torus geometries to show that this new type of entanglement spectra completely reveals the physics of bulk quasihole excitations. While this is easily understood when a local Hamiltonian for the model state exists, we show that the quasiholes wavefunctions are encoded within the model state even when such a Hamiltonian is not known. As a nontrivial example, we look at Jain's composite fermion states and obtain their quasiholes directly from the model state wavefunction. We reach similar conclusions for wavefunctions described by Jack polynomials.Comment: 5 pages, 7 figures, updated versio

D-Algebra Structure of Topological Insulators

In the quantum Hall effect, the density operators at different wave-vectors generally do not commute and give rise to the Girvin MacDonald Plazmann (GMP) algebra with important consequences such as ground-state center of mass degeneracy at fractional filling fraction, and W_{1 + \infty} symmetry of the filled Landau levels. We show that the natural generalization of the GMP algebra to higher dimensional topological insulators involves the concept of a D-algebra formed by using the fully anti-symmetric tensor in D-dimensions. For insulators in even dimensional space, the D-algebra is isotropic and closes for the case of constant non-Abelian F(k) ^ F(k) ... ^ F(k) connection (D-Berry curvature), and its structure factors are proportional to the D/2-Chern number. In odd dimensions, the algebra is not isotropic, contains the weak topological insulator index (layers of the topological insulator in one less dimension) and does not contain the Chern-Simons \theta form (F ^ A - 2/3 A ^ A ^ A in 3 dimensions). The Chern-Simons form appears in a certain combination of the parallel transport and simple translation operator which is not an algebra. The possible relation to D-dimensional volume preserving diffeomorphisms and parallel transport of extended objects is also discussed.Comment: 5 page

Low-energy excitations in the magnetized state of the bond-alternating quantum S=1 chain system NTENP

High intensity inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 (NTENP) are performed in magnetic fields of up to 14.8~T. Excitation in the high field magnetized quantum spin solid (ordered) phase are investigated. In addition to the previously observed coherent long-lived gap excitation [M. Hagiwara et al., Phys. Rev. Lett 94, 177202 (2005)], a broad continuum is detected at lower energies. This observation is consistent with recent numerical studies, and helps explain the suppression of the lowest-energy gap mode in the magnetized state of NTENP. Yet another new feature of the excitation spectrum is found at slightly higher energies, and appears to be some kind of multi-magnon state.Comment: 5 pages, 4 fugure

Bulk-Edge Correspondence in the Entanglement Spectra

Li and Haldane conjectured and numerically substantiated that the entanglement spectrum of the reduced density matrix of ground-states of time-reversal breaking topological phases (fractional quantum Hall states) contains information about the counting of their edge modes when the ground-state is cut in two spatially distinct regions and one of the regions is traced out. We analytically substantiate this conjecture for a series of FQH states defined as unique zero modes of pseudopotential Hamiltonians by finding a one to one map between the thermodynamic limit counting of two different entanglement spectra: the particle entanglement spectrum, whose counting of eigenvalues for each good quantum number is identical (up to accidental degeneracies) to the counting of bulk quasiholes, and the orbital entanglement spectrum (the Li-Haldane spectrum). As the particle entanglement spectrum is related to bulk quasihole physics and the orbital entanglement spectrum is related to edge physics, our map can be thought of as a mathematically sound microscopic description of bulk-edge correspondence in entanglement spectra. By using a set of clustering operators which have their origin in conformal field theory (CFT) operator expansions, we show that the counting of the orbital entanglement spectrum eigenvalues in the thermodynamic limit must be identical to the counting of quasiholes in the bulk. The latter equals the counting of edge modes at a hard-wall boundary placed on the sample. Moreover, we show this to be true even for CFT states which are likely bulk gapless, such as the Gaffnian wavefunction.Comment: 20 pages, 6 figure

Field-Induced Disorder Point in Non-Collinear Ising Spin Chains

We perform a theoretical study of a non-collinear Ising ferrimagnetic spin chain inspired by the compound Co(hfac)2NITPhOMe. The basic building block of its structure contains one Cobalt ion and one organic radical each with a spin 1/2. The exchange interaction is strongly anisotropic and the corresponding axes of anisotropy have a period three helical structure. We introduce and solve a model Hamiltonian for this spin chain. We show that the present compound is very close to a so-called disorder point at which there is a massive ground state degeneracy. We predict the equilibrium magnetization process and discuss the impact of the degeneracy on the dynamical properties by using arguments based on the Glauber dynamics.Comment: revtex 4, 10 pages, 7 figure

Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets at filling $\nu=1/m$ is described by the Haldane statistics of particles in a box of finite size. This principle explains the observed deviations of the OES counting from the edge-mode conformal field theory counting and directly provides us with a topological number of the FQH states inaccessible in the thermodynamic limit- the boson compactification radius. It also suggests that the entanglement gap in the Coulomb spectrum in the conformal limit protects a universal quantity- the statistics of the state. We support our conjecture with ample numerical checks.Comment: 4.1 pages, published versio

Atypical Fractional Quantum Hall Effect in Graphene at Filling Factor 1/3

We study the recently observed graphene fractional quantum Hall state at a filling factor $\nu_G=1/3$ using a four-component trial wave function and exact diagonalization calculations. Although it is adiabatically connected to a 1/3 Laughlin state in the upper spin branch, with SU(2) valley-isospin ferromagnetic ordering and a completely filled lower spin branch, it reveals physical properties beyond such a state that is the natural ground state for a large Zeeman effect. Most saliently, it possesses at experimentally relevant values of the Zeeman gap low-energy spin-flip excitations that may be unveiled in inelastic light-scattering experiments.Comment: 4 pages, 3 figures; slightly modified published versio