Topological Heat Transport and Symmetry-Protected Boson Currents

The study of non-equilibrium properties in topological systems is of practical and fundamental importance. Here, we analyze the stationary properties of a two-dimensional bosonic Hofstadter lattice coupled to two thermal baths in the quantum open-system formalism. Novel phenomena appear like chiral edge heat currents that are the out-of-equilibrium counterparts of the zero-temperature edge currents. They support a new concept of dissipative symmetry-protection, where a set of discrete symmetries protects topological heat currents, differing from the symmetry-protection devised in closed systems and zero-temperature. Remarkably, one of these currents flows opposite to the decreasing external temperature gradient. As the starting point, we consider the case of a single external reservoir already showing prominent results like thermal erasure effects and topological thermal currents. Our results are experimentally accessible with platforms like photonics systems and optical lattices.Comment: RevTeX4 file, color figure

A bilayer Double Semion Model with Symmetry-Enriched Topological Order

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topo- logical orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bi- layer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braid- ing self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry.Comment: revtex4 file, color figure

Analytic Formulations of the Density Matrix Renormalization Group

We present two new analytic formulations of the Density Matrix Renormalization Group Method. In these formulations we combine the block renormalization group (BRG) procedure with Variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising Model in a transverse field (ITF model) and compute several of its critical properties which are then compared with the old BRG results.Comment: LATEX file, 25 pages, 8 figures available upon reques

The Renormalization Group Method and Quantum Groups: the postman always rings twice

We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence of a quantum group anomalous term which vanishes in the classical case. This is called {\em the quantum group anomaly}. We derive the new qRG equations for the XXZ model and show that the RG-flow diagram obtained in this fashion exhibits the correct line of critical points that the exact model has. In the ITF model the qRG-flow equations coincide with the tensor product decomposition of cyclic irreps of $SU_q(2)$ with $q^4=1$.Comment: LATEX file, 21 pages, no figures. To appear in "From Field Theory to Quantum Groups", World Scientific. Proceedings to honor J.Lukierski in his 60th birthda