Condensed Matter

We present an analytic, gauge invariant tensor network ansatz for the ground state of lattice Yang-Mills theory for nonabelian gauge groups. It naturally takes the form of a MERA, where the top level is the strong coupling limit of the lattice theory. Each layer performs a fine-graining operation defined in a fixed way followed by an optional step of adiabatic evolution, resulting in the ground state at an intermediate coupling. The ansatz is very much in the spirit of Kogut and Susskind's Hamiltonian approach to understanding confinement by starting from the strong coupling limit and perturbing, but exploiting a tensor network structure to go beyond perturbative approaches.

I will describe how to define a proper RG flow in the space of
tensor networks, with applications to the evaluation of classical
partition functions, euclidean path integrals, and overlaps of tensor
network states.

A featureless insulator is a gapped phase of matter that does not exhibit fractionalization or other exotic physics, and thus has a unique ground state. The classic albeit non-interacting example is an electronic band insulator. A standard textbook argument tells us that band insulators require an even number of electrons -- an integer number for each spin -- per unit cell. I will explore the converse question: given such an 'integer filling', is a featureless insulating state possible?  I will demonstrate that in most three-dimensional crystals, an insulating ground state cannot be unique -- and hence cannot be featureless -- except at certain special fillings fixed by the crystalline space group. This result, which remains valid more generally for interacting systems of fermions, bosons, or spins (as long as they have a conserved U(1) charge), relies on a combination of topological 'flux insertion' arguments and elementary crystallographic ideas. I will explore its implications through examples ranging from band theory, where it leads to the identification of protected semimetals, to frustrated magnetism, where it suggests new venues for spin liquid physics.

References: S.A. Parameswaran, A.M. Turner, D.P. Arovas and A. Vishwanath, Nature Physics 9, 299 (2013).
(see also related work in PNAS 110, 16378 (2013) and Phys. Rev. Lett. 110, 125301 (2013).)