Spectral Evidence for Emergent Order in Ba1−x_{1-x}Nax_xFe2_2As2_2

We report an angle-resolved photoemission spectroscopy study of the iron-based superconductor family, Ba$_{1-x}$Na$_x$Fe$_2$As$_2$. This system harbors the recently discovered double-Q magnetic order appearing in a reentrant C$_4$ phase deep within the underdoped regime of the phase diagram that is otherwise dominated by the coupled nematic phase and collinear antiferromagnetic order. From a detailed temperature-dependence study, we identify the electronic response to the nematic phase in an orbital-dependent band shift that strictly follows the rotational symmetry of the lattice and disappears when the system restores C$_4$ symmetry in the low temperature phase. In addition, we report the observation of a distinct electronic reconstruction that cannot be explained by the known electronic orders in the system

The folding fingerprint of visual cortex reveals the timing of human V1 and V2

Primate neocortex contains over 30 visual areas. Recent techniques such as functional magnetic resonance imaging (fMRI) have successfully identified many of these areas in the human brain, but have been of limited value for revealing the temporal dynamics between adjacent visual areas, a critical component of understanding visual cognition. The voltages recorded at the scalp, electroencephalography (EEG), is a direct measure of neural activity that reflects the summed activity across all brain areas. Identifying the cortical sources that contribute to the EEG is a difficult problem. We developed an anatomically constrained dipole search method that solves the traditional problems by combining fMRI, EEG and many stimuli that activate small cortical regions. The method provides a means to validate the extracted waveforms. Both V1 and V2 waveforms have similar onset latencies as well as dynamics that can explain previous controversial findings about the responses of these areas

Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators

The energy and entanglement spectrum of fractionally filled interacting topological insulators exhibit a peculiar manifold of low energy states separated by a gap from a high energy set of spurious states. In the current manuscript, we show that in the case of fractionally filled Chern insulators, the topological information of the many-body state developing in the system resides in this low-energy manifold. We identify an emergent many-body translational symmetry which allows us to separate the states in quasi-degenerate center of mass momentum sectors. Within one center of mass sector, the states can be further classified as eigenstates of an emergent (in the thermodynamic limit) set of many-body relative translation operators. We analytically establish a mapping between the two-dimensional Brillouin zone for the Fractional Quantum Hall effect on the torus and the one for the fractional Chern insulator. We show that the counting of quasi-degenerate levels below the gap for the Fractional Chern Insulator should arise from a folding of the states in the Fractional Quantum Hall system at identical filling factor. We show how to count and separate the excitations of the Laughlin, Moore-Read and Read-Rezayi series in the Fractional Quantum Hall effect into two-dimensional Brillouin zone momentum sectors, and then how to map these into the momentum sectors of the Fractional Chern Insulator. We numerically check our results by showing the emergent symmetry at work for Laughlin, Moore-Read and Read-Rezayi states on the checkerboard model of a Chern insulator, thereby also showing, as a proof of principle, that non-Abelian Fractional Chern Insulators exist.Comment: 32 pages, 9 figure

Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators

We propose an improved scheme to construct many-body trial wave functions for fractional Chern insulators (FCI), using one-dimensional localized Wannier basis. The procedure borrows from the original scheme on a continuum cylinder, but is adapted to finite-size lattice systems with periodic boundaries. It fixes several issues of the continuum description that made the overlap with the exact ground states insignificant. The constructed lattice states are translationally invariant, and have the correct degeneracy as well as the correct relative and total momenta. Our prescription preserves the (possible) inversion symmetry of the lattice model, and is isotropic in the limit of flat Berry curvature. By relaxing the maximally localized hybrid Wannier orbital prescription, we can form an orthonormal basis of states which, upon gauge fixing, can be used in lieu of the Landau orbitals. We find that the exact ground states of several known FCI models at nu=1/3 filling are well captured by the lattice states constructed from the Laughlin wave function. The overlap is higher than 0.99 in some models when the Hilbert space dimension is as large as 3x10^4 in each total momentum sector.Comment: 36 pages, 13 figure