Wigner crystals in two-dimensional transition-metal dichalcogenides: Spin physics and readout

Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.Comment: 15 pages, 12 figure

Non-locality of non-Abelian anyons

Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that can encode exotic entangled states. To reveal the non-local character of these encoded states we demonstrate the violation of suitable Bell inequalities. We provide an explicit recipe for the preparation, manipulation and measurement of the desired correlations for a large class of topological models. This proposal gives an operational measure of non-locality for anyonic states and it opens up the possibility to violate the Bell inequalities in quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure

Defect mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference

Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.Comment: 16 pages, 7 figure

GMRT mini-survey to search for 21-cm absorption in Quasar-Galaxy Pairs at z~0.1

We present the results from our 21-cm absorption survey of a sample of 5 quasar-galaxy pairs (QGPs), with the redshift of the galaxies in the range 0.03<zg<0.18, selected from the SDSS. The HI 21-cm absorption was searched towards the 9 sight lines with impact parameters ranging from 10 to 55 kpc using GMRT. 21-cm absorption was detected only in one case i.e. towards the Quasar (zq=2.625 SDSS J124157.54+633241.6)-galaxy (zg=0.143 SDSS J124157.26+633237.6) pair with the impact parameter 11 kpc. The quasar sight line in this case pierces through the stellar disk of a galaxy having near solar metallicity (i.e (O/H)+12=8.7) and star formation rate uncorrected for dust attenuation of 0.1 M_odot/yr. The quasar spectrum reddened by the foreground galaxy is well fitted with the Milky Way extinction curve (with an Av of 0.44) and the estimated HI column density is similar to the value obtained from 21-cm absorption assuming spin temperature of 100K. Combining our sample with the z<0.1 data available in the literature, we find the detectability of 21-cm absorption with integrated optical depth greater than 0.1 km\s to be 50% for the impact parameter less than 20 kpc. Using the surface brightness profiles and relationship between the optical size and extent of the HI disk known for nearby galaxies, we conclude that in most of the cases of 21-cm absorption non-detection, the sight lines may not be passing through the HI gas. We also find that in comparison to the absorption systems associated with these QGPs, z<1 DLAs with 21-cm absorption detections have lower CaII equivalent widths despite having higher 21-cm optical depths and smaller impact parameters. This suggests that the current sample of DLAs may be a biased population that avoids sight lines through dusty star-forming galaxies. A systematic survey of QGPs is needed to confirm these findings and understand the nature of 21-cm absorbers.Comment: 17 pages, 5 tables, 19 figures, accepted for publication in MNRAS (abstract abridged

Qudit surface codes and gauge theory with finite cyclic groups

Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group of the surface complex. These code states can be actively stabilized by measurements or, alternatively, can be prepared by cooling to the ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2 (qubit) lattices, such ground states have been proposed as topologically protected memory for qubits. We extend these constructions to lattices or more generally cell complexes with qudits, either of prime level or of level $d^\ell$ for $d$ prime and $\ell \geq 0$, and therefore under tensor decomposition, to arbitrary finite levels. The Hamiltonian describes an exact $\mathbb{Z}_d\cong\mathbb{Z}/d\mathbb{Z}$ gauge theory whose excitations correspond to abelian anyons. We provide protocols for qudit storage and retrieval and propose an interferometric verification of topological order by measuring quasi-particle statistics.Comment: 26 pages, 5 figure

The nature of LINER galaxies: Ubiquitous hot old stars and rare accreting black holes

Galaxies, which often contain ionised gas, sometimes also exhibit a so-called low-ionisation nuclear emission line region (LINER). For 30 years this was attributed to a central mass-accreting supermassive black hole (AGN) of low luminosity, making LINER galaxies the largest AGN-sub-population, dominating in numbers over higher luminosity Seyfert galaxies and quasars. This, however, poses a serious problem. While the inferred energy balance is plausible, many LINERs clearly do not contain any other independent signatures of an AGN. Using integral field spectroscopic data from the CALIFA survey, we aim at comparing the observed radial surface brightness profiles with what is expected from illumination by an AGN. Essential for this analysis is a proper extraction of emission-lines, especially weak lines such as the Balmer Hb line which is superposed on an absorption trough. To accomplish this, we use the GANDALF code which simultaneously fits the underlying stellar continuum and emission lines. We show for 48 galaxies with LINER-like emission, that the radial emission-line surface brightness profiles are inconsistent with ionisation by a central point-source and hence cannot be due to an AGN alone. The most probable explanation for the excess LINER-like emission is ionisation by evolved stars during the short but very hot and energetic phase known as post-AGB. This leads us to an entirely new interpretation. Post-AGB stars are ubiquitous and their ionising effect should be potentially observable in every galaxy with gas present and stars older than ~1 Gyr, unless a stronger radiation field from young hot stars or an AGN outshines them. This means that galaxies with LINER-like emission are in fact not a class defined by a property, but rather by the absence of a property. It also explains why LINER emission is observed mostly in massive galaxies with old stars and little star formation.Comment: 8 pages, 7 figure

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