Investigations of topological phases for quasi-1d systems

Resumen

For a long time, quantum states of matter have been successfully characterized by the Ginzburg-Landau formalism that was able to classify all di¿erent types of phase transitions. This view changed with the discovery of the quantum Hall e¿ect and topological insulators. The latter are materials that host metallic edge states in an insulating bulk, some of which are protected by the existing symmetries. Complementary to the search of topological phases in condensed matter, great effortshavebeenmadeinquantumsimulationsbasedoncoldatomicgases. Sophisticated laser schemes provide optical lattices with di¿erent geometries and allow to tune interactions and the realization of arti¿cial gauge ¿elds. Atthesametime,newconceptscomingfromquantuminformation,basedonentanglement, are pushing the frontier of our understanding of quantum phases as a whole. Theconceptofentanglementhasrevolutionizedthedescriptionofquantummany-body states by describing wave functions with tensor networks (TN) that are exploited for numerical simulations based on the variational principle. Thisthesisfallswithintheframeworkofthestudiesincondensedmatterphysics: it focuses indeed on the so-called synthetic realization of quantum states of matter, more speci¿cally,oftopologicalones,whichmayhaveonthelong-runoutfallstowardsrobust quantum computers. We propose a theoretical investigation of cold atoms in optical lattice pierced by e¿ective (magnetic) gauge ¿elds and subjected to experimentally relevant interactions, by adding a modern numerical approach based on TN algorithms. More speci¿cally, this work will focus on (i) interacting topological phases in quasi-1D systems and, in particular, the Creutz-Hubbard model, (ii) the connection between condensed matter and high energy physics studying the Gross-Neveu model and the discretization of Wilson-Hubbard model, (iii) implementing tensor network-based algorithms.