Person: Martín Benito, Mercedes
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First Name
Mercedes
Last Name
Martín Benito
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Department
Física Teórica
Area
Física Teórica
Identifiers
3 results
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Now showing 1 - 3 of 3
Item Quantum group spin nets: refinement limit and relation to spin foams(Physical Review D, 2014) Dittrich, Bianca; Martín Benito, Mercedes; Steinhaus, SebastianSo far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so-called “spin nets,” for quantum groups SU(2)_k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse-graining procedure, we find a vast nontrivial fixed-point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed-point intertwiners, inspired by Reisenberger’s construction principle [M. P. Reisenberger, J. Math. Phys. (N.Y.) 40, 2046 (1999)] and the recent work [B. Dittrich and W. Kaminski, arXiv:1311.1798], as the initial parametrization. In this new parametrization fine-tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse-graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.Item Coarse graining methods for spin net and spin foam models(New Journal of Physics, 2012) Dittrich, Bianca; Eckert, Frank C.; Martín Benito, MercedesWe undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large-scale analysis by numerical and computational methods. In particular, we apply the Migdal–Kadanoff and tensor network renormalization (TNR) schemes to spin net and spin foam models based on finite Abelian groups and introduce 'cutoff models' to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the TNR analysis, a new Gauß constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We also describe the fixed point structure and establish the equivalence of certain models.Item Coarse graining of spin net models: dynamics of intertwiners(New Journal of Physics, 2013) Dittrich, Bianca; Martín Benito, Mercedes; Schnetter, ErikSpin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full four-dimensional models. We consider here simplified analogue models, so called spin nets, that retain the main dynamical ingredient of spin foams, the simplicity constraints. For a certain class of these spin net models we determine the phase diagram and therefore the continuum phases via a coarse graining procedure based on tensor network renormalization. This procedure will also reveal an unexpected fixed point, which turns out to define a new triangulation invariant vertex model. © IOP Publishing and Deutsche Physikalische Gesellschaft.