## Abstracts for Condensed Matter Seminars

### Arun Paramekanti, September 21, 2015, Abstract:

Double perovskites are of great interest, providing us with material examples of metallic high Tc ferromagnets, Mott insulating ferromagnets, as well as geometrically frustrated magnets on

the fcc lattice. I will review our work studying the role of spin-orbit coupling in driving interesting topological states, topological transitions, and Kitaev spin Hamiltonians in these systems.

### Liling Sun, September 23, 2015, Abstract:

It has been established that the superconductivity of unconventional superconductors is dictated by their crystallographic structure, electronic charge, and orbital and spin degrees of freedom, which can all be manipulated by controlling parameters such as pressure, magnetic field and chemical composition. Pressure is a ‘clean’ way to tune basic electronic and structural properties without changing the chemistry, and can help to search for new superconductors and elucidate superconducting mechanisms. In this talk, I will describe some of our results obtained from high-pressure studies, in materials ranging from iron pnictide superconductors to alkaline iron selenide superconductors. New phenomena such as pressure-induced re-emergence of superconductivity, quantum criticality, and orbital selection will be described, and new insights into the correlations among magnetic long-ranged order, superconductivity, and structural superlattices will be presented.

### Yuval Baum, October 1, 2015, Abstract:

Topology in various guises plays a central role in modern condensed matter physics. Although the

original applications of topological ideas to band structures relied on the existence of a fully gapped

bulk spectrum, more recently it has been recognized that protected surface states can arise even in

gapless systems. The prototypical example of a gapless topological phase is a Weyl semi-metal.

Surface Fermi arcs are the most prominent manifestation of the topological nature of Weyl semi-

metals. In the presence of a static magnetic field oriented perpendicular to the sample surface, their

existence leads to unique inter-surface cyclotron orbits. We show how these inter-surface cyclotron

orbits aect the electronic properties of Weyl semi-metals already at the semi-classical level. As a

result, we are able to propose two experiments which directly probe the Fermi arcs: a magnetic field

dependent non-local DC voltage and sharp resonances in the transmission of electromagnetic waves at frequencies controlled by the field. We show that these experiments do not rely on quantum mechanical phase coherence, which renders them far more robust and experimentally accessible than

quantum effects. We also comment on the applicability of these ideas to Dirac semimetals.

### Roger Mong, October 12, 2015, Abstract:

The ν = 12/5 fractional quantum Hall plateau observed in GaAs wells is a suspect in the search for non-Abelian Fibonacci anyons. Fibonacci anyons are special in that they are capable of performing universal topological quantum computation. Using the infinite density matrix renormalization group, we find clear evidence that—in the absence of Landau level mixing—fillings ν = 12/5 and ν = 13/5 are in the k = 3 Read-Rezayi phase, and thus supports Fibonacci anyons. We also find an extremely close energetic competition between the Read-Rezayi phase and a charge-density ordered phase, which may explain the experimentally observed asymmetry between ν = 12/5 and 13/5.

### Roman Orus, October 14, 2015, Abstract:

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement Renyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. In this talk I will show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, I will present an efficient tensor network algorithm based on Projected Entangled Pair States (PEPS) to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for Renyi entropies, this approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. Moreover, I will show how the method also allows the identification of Minimally Entangled States (MES), thus providing a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states. If time allows I will also present briefly other ongoing projects at our group involving the use of tensor networks to study large-spin Kagome quantum antiferromagnets, 1d symmetry-protected topological order, continuous unitary transformations, and (1+1)d lattice gauge theories.

### Paul Fendley, October 26, 2015, Abstract:

Gapless edge or zero modes surviving the presence of disorder are common in a topological phase of matter. ``Weak'' zero modes, guaranteeing ground-state degeneracy, necessarily survive throughout a topological phase, A more dramatic effect occurs in the Ising chain/Majorana wire: ``strong'' edge zero modes result in identical spectra in even and odd fermion-number sectors, up to exponentially small finite-size corrections. There is a presumption that disorder is necessary to stabilize strong zero modes in the presence of interactions, but I show that their presence in a clean system is not a free-fermionic fluke. In this talk I construct an explicit strong zero mode in the XYZ chain/coupled Majorana wires; this operator possesses some remarkable structure apparently unknown in the integrability literature. I also present evidence for strong zero modes in the parafermionic cae, implying the existence of an unconventional ``eigenstate phase transition'' where the strong zero mode disappears, leaving only the weak one.