Momentum polarization: an entanglement measure of topological spin and chiral central charge

Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial translation operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure

The likely Fermi Detection of the Supernova Remnant RCW 103

We report on the results from our $\gamma$-ray analysis of the supernova remnant (SNR) RCW 103 region. The data were taken with the Large Area Telescope on board the Fermi Gamma-ray Space Telescope. An extended source is found at a position consistent with that of RCW 103, and its emission was only detected above 1 GeV (10$\sigma$ significance), having a power-law spectrum with a photon index of 2.0$\pm$0.1. We obtain its 1--300 GeV spectrum, and the total flux gives a luminosity of 8.3$\times 10^{33}$ erg s$^{-1}$ at a source distance of 3.3 kpc. Given the positional coincidence and property similarities of this source with other SNRs, we identify it as the likely Fermi $\gamma$-ray counterpart to RCW 103. Including radio measurements of RCW 103, the spectral energy distribution (SED) is modeled by considering emission mechanisms based on both hadronic and leptonic scenarios. We find that models in the two scenarios can reproduce the observed SED, while in the hadronic scenario the existence of SNR--molecular-cloud interaction is suggested as a high density of the target protons is required.Comment: 6 pages, 3 figures, accepted for publication in Ap

Coexistence of Localized and Extended States in Disordered Systems

It is commonly believed that Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states in a band in a class of disordered quasi-1D and quasi-2D systems. The systems are partially disordered in a way that a band of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized. The extended states can overlap with the localized states both in energy and in space, achieving the aforementioned coexistence. We demonstrate such coexistence in disordered multi-chain and multi-layer systems.Comment: 5 pages, 3 figure

Entanglement entropy of critical spin liquids

Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterize their quantum structure. In particular we calculate the Renyi entropy $S_2$, on model wavefunctions obtained by Gutzwiller projection of a Fermi sea. Although the wavefunctions are not sign positive, $S_2$ can be calculated on relatively large systems (>324 spins), using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi-sea state violates the boundary law, with $S_2$ enhanced by a logarithmic factor. This is an unusual result for a bosonic wave-function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.Comment: 4+ pages, 2 figures, to be published in PR