Exact ground states of a staggered supersymmetric model for lattice fermions

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic expressions for the ground states in the limit of small and large staggering for the model on the class of doubly decorated lattices. On this type of lattice there are two ground states, each with a different density. In one limit we find these ground states to be a simple Wigner crystal and a valence bond solid (VBS) state. In the other limit we find two types of quantum liquids. As a special case, we investigate the quantum liquid state on the one dimensional chain in detail. It is characterized by a massless kink that separates two types of order.Comment: 21 pages, 6 figures, v2: largely rewritten version with more emphasis on physical interpretatio

Quantum phases of supersymmetric lattice models

We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays critical behavior described by superconformal field theory. On 2D lattices we generically find superfrustration, characterized by an extensive ground state entropy. For certain 2D lattices analytical results on the ground state structure reveal yet another quantum phase, which we tentatively call 'supertopological'.Comment: 5 pages, 1 figure, 1 table, contribution to the proceedings of the XVI International Congress on Mathematical Physics (2009) in Prague, Czeck Republi

Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D

We present a full identification of lattice model properties with their field theoretical counter parts in the continuum limit for a supersymmetric model for itinerant spinless fermions on a one dimensional chain. The continuum limit of this model is described by an $\mathcal{N}=(2,2)$ superconformal field theory (SCFT) with central charge c=1. We identify states and operators in the lattice model with fields in the SCFT and we relate boundary conditions on the lattice to sectors in the field theory. We use the dictionary we develop in this paper, to give a pedagogical explanation of a powerful tool to study supersymmetric models based on spectral flow. Finally, we employ the developed machinery to explain numerically observed properties of the particle density on the open chain presented in Beccaria et al. PRL 94:100401 (2005).Comment: 28 pages, 7 figures, 3 tables, 1 appendix, this work is based on chapter 4 of the authors PhD Thesis: L. Huijse, A supersymmetric model for lattice fermions, University of Amsterdam (2010

A multiplet analysis of spectra in the presence of broken symmetries

We introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R*. In Theorem 1 these generalised symmetries are characterised in terms of repeated commutators of H with M. Breaking supersymmetry by adding a term linear in the supercharges is discussed as a motivating example. The complex parameter gamma which appears in the definition of a generalised symmetry is necessarily real when the spectrum of M is discrete. Theorem 2 shows that gamma must also be real when the spectrum of H is fully discrete and R and R* are bounded operators. Any generalised symmetry induces a partitioning of the spectrum of H in what we call M-multiplets. The hydrogen atom in the presence of a symmetry breaking external field is discussed as an example. The notion of stability of eigenvectors of H relative to the generalised symmetry M is discussed. A characterisation of stable eigenvectors is given in Theorem 3

A staggered fermion chain with supersymmetry on open intervals

A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the staggering parameter are examined. In particular, a connection between certain ground-state components and solutions of non-linear recursion relations associated with the Painlev\'e VI equation is conjectured. Moreover, various local occupation probabilities in the ground state have the so-called scale-free property, and allow for an exact resummation in the limit of infinite system size.Comment: 21 pages, no figures; v2: typos correcte

Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality

We study a model for itinerant, strongly interacting fermions where a judicious tuning of the interactions leads to a supersymmetric Hamiltonian. On the triangular lattice this model is known to exhibit a property called superfrustration, which is characterized by an extensive ground state entropy. Using a combination of numerical and analytical methods we study various ladder geometries obtained by imposing doubly periodic boundary conditions on the triangular lattice. We compare our results to various bounds on the ground state degeneracy obtained in the literature. For all systems we find that the number of ground states grows exponentially with system size. For two of the models that we study we obtain the exact number of ground states by solving the cohomology problem. For one of these, we find that via a sequence of mappings the entire spectrum can be understood. It exhibits a gapped phase at 1/4 filling and a gapless phase at 1/6 filling and phase separation at intermediate fillings. The gapless phase separates into an exponential number of sectors, where the continuum limit of each sector is described by a superconformal field theory.Comment: 50 pages, 12 figures, 2 appendice

The VVV Survey RR Lyrae Population in the Galactic Center Region

Indexación: Scopus.We gratefully acknowledge the use of data from the ESO Public Survey program ID 179.B-2002 taken with the VISTA telescope, and data products from the Cambridge Astronomical Survey Unit (CASU). Support for the authors is provided by the BASAL Center for Astrophysics and Associated Technologies (CATA) through grant PFB-06, and the Ministry for the Economy, Development, and Tourism, Programa Iniciativa Cientifica Milenio through grant IC120009, awarded to the Millennium Institute of Astrophysics (MAS). D.M. and M.Z. acknowledge support from FONDECYT Regular grants No. 1170121, and 1150345, respectively. P.H. acknowledges financial support from FONDECYT regular grant 1170305. F.G. acknowledge support from CONICYT-PCHA Doctorado Nacional 2017-21171485 and Proyecto Fondecyt Regular 1150345. J.A.-G. acknowledges support by FONDECYT Iniciacion 11150916. D.M. is also grateful for the hospitality of the Vatican Observatory. This research made use of Astropy, a community-developed core Python package for astronomy; Scikit-learn, NumPy, and matplotlib, a Python library for publication-quality graphics; and Aladin Sky Atlas, developed at CDS, Strasbourg Observatory, France, and TOPCAT.Deep near-IR images from the VISTA Variables in the V a L ctea (VVV) Survey were used to search for RR Lyrae stars within 100 arcmin from the Galactic Center. A large sample of 960 RR Lyrae of type ab (RRab) stars were discovered. A catalog is presented featuring the positions, magnitudes, colors, periods, and amplitudes for the sample, in addition to estimated reddenings, distances, and metallicities, and measured individual relative proper motions. We use the reddening-corrected Wesenheit magnitudes, defined as WKs Ks 0.428 J Ks = - ( - ), in order to isolate bona fide RRL belonging to the Galaxy Center, finding that 30 RRab are foreground/background objects. We measure a range of extinctions from AKs 0.19 = to 1.75 mag for the RRab in this region, finding that large extinction is the main cause of the sample incompleteness. The mean period is P =0.5446±0.0025 days, yielding a mean metallicity of [Fe/H] =-1.30±0.01 (ς = 0.33) dex for the RRab sample in the Galactic Center region. The median distance for the sample is D =8.05±0.02 kpc. We measure the RRab surface density using the less reddened region sampled here, finding a density of 1000 RRab/sq deg at a projected Galactocentric distance RG =1.6 deg. Under simple assumptions, this implies a large total mass (M>109Me) for the old and metal-poor population contained inside RG. We also measure accurate relative proper motions, from which we derive tangential velocity dispersions of ςVl =125.0 and ςVb =124.1 km s-1 along the Galactic longitude and latitude coordinates, respectively. The fact that these quantities are similar indicate that the bulk rotation of the RRab population is negligible, and implies that this population is supported by velocity dispersion. In summary, there are two main conclusions of this study. First, the population as a whole is no different from the outer bulge RRab, predominantly a metal-poor component that is shifted with respect to the Oosterhoff type I population defined by the globular clusters in the halo. Second, the RRab sample, as representative of the old and metal-poor stellar population in the region, has high velocity dispersions and zero rotation, suggesting a formation via dissipational collapse. ©2018. The American Astronomical Society. All rights reserved.https://iopscience.iop.org/article/10.3847/1538-4357/aacf9

Superfrustration of charge degrees of freedom

We review recent results, obtained with P. Fendley, on frustration of quantum charges in lattice models for itinerant fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to models possessing supersymmetry. In such models frustration takes the form of what we call superfrustration: an extensive degeneracy of supersymmetric ground states. We present a gallery of examples of superfrustration on a variety of 2D lattices.Comment: 8 pages, 5 figures, contribution to the proceedings of the XXIII IUPAP International Conference on Statistical Physics (2007) in Genova, Ital

Proper motions in the VVV Survey: Results for more than 15 million stars across NGC 6544

Context: In the last six years, the VVV survey mapped 562 sq. deg. across the bulge and southern disk of the Galaxy. However, a detailed study of these regions, which includes $\sim 36$ globular clusters (GCs) and thousands of open clusters is by no means an easy challenge. High differential reddening and severe crowding along the line of sight makes highly hamper to reliably distinguish stars belonging to different populations and/or systems. Aims: The aim of this study is to separate stars that likely belong to the Galactic GC NGC 6544 from its surrounding field by means of proper motion (PM) techniques. Methods: This work was based upon a new astrometric reduction method optimized for images of the VVV survey. Results: Photometry over the six years baseline of the survey allowed us to obtain a mean precision of $\sim0.51$ mas/yr, in each PM coordinate, for stars with Ks < 15 mag. In the area studied here, cluster stars separate very well from field stars, down to the main sequence turnoff and below, allowing us to derive for the first time the absolute PM of NGC 6544. Isochrone fitting on the clean and differential reddening corrected cluster color magnitude diagram yields an age of $\sim$ 11-13 Gyr, and metallicity [Fe/H] = -1.5 dex, in agreement with previous studies restricted to the cluster core. We were able to derive the cluster orbit assuming an axisymmetric model of the Galaxy and conclude that NGC 6544 is likely a halo GC. We have not detected tidal tail signatures associated to the cluster, but a remarkable elongation in the galactic center direction has been found. The precision achieved in the PM determination also allows us to separate bulge stars from foreground disk stars, enabling the kinematical selection of bona fide bulge stars across the whole survey area. Our results show that VVV data is perfectly suitable for this kind of analysis.Comment: 13 pages, 12 figures, accepted in A&

Spin chains with dynamical lattice supersymmetry

Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the N=(2,2) superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension admits a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured.Comment: Revised version, 52 pages, 2 figure