## 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.

### Kevin Slagle, October 19, 2015, Abstract:

Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions, each with connections to symmetry protected topological states (SPT). 1) The first is a continuous phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase. Because there is no spontaneous symmetry breaking, this transition cannot be described by the standard Gross-Neveu model. We argue that this phase transition is related to the Z_16 classification of the topological superconductor 3He-B phase with interactions. 2) The second is a quantum critical point between a quantum spin Hall insulator with spin S^z conservation and the previously mentioned strongly interacting gapped trivial phase. This transition can also be viewed as a direct transition between a bosonic SPT and a trivial state. At the critical point the single particle excitations remain gapped, while spin and charge gaps close. We argue that this transition is described by a bosonic O(4) nonlinear sigma model field theory with a topological Theta-term.

### 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.

### Shuichi Murakami, October 29, 2015, Abstract:

The Z2 topological insulators (TIs) are topological phases under time-reversal symmetry. In 2007, we theoretically proposed a universal phase diagram describing a phase transition between 3D TIs and normal insulators (NIs), and we showed that in a TI-NI transition, a Weyl semimetal phase necessarily intervenes between the two phases, when inversion symmetry is broken. In this talk, we show that this scenario holds for materials with any space groups without inversion symmetry. Namely, if the gap of an inversion-asymmetric system is closed by a change of an external parameter, the system runs either into (i) a Weyl semimetal or (ii) a nodal-line semimetal, but no insulator-to-insulator transition happens. This transition is realized for example in tellurium (Te). Tellurium has a unique lattice structure, consisting of helical chains, and therefore lacks inversion and mirror symmetries. According to our ab initio calculation, at high pressure the band gap of Te decreases and finally it runs into a Weyl semimetal phase. We also theoretically propose chiral transport in systems with such helical structures.

### Chen Fang, November 16, 2015, Abstract:

In the first part of the talk, I will show that a nonsymmorphic glide reflection symmetry can protect a new Z2 topological gapped phase in three-dimensions. Unlike topological insulators, this new phase can be realized in either spinful or spinless (or having full spin rotation symmetry) systems. I will show one realization in photonic crystals in detail. In the second part, I will discuss how nonsymmorphic symmetries can protect topological gapless phases, or topological semimetals. A twofold screw axis can protect a double-nodal line in a system with strong spin-orbital coupling; and a glide plane can protect a new type of Dirac semimetal, which, unlike any Dirac semimetal so far proposed, has protected double "Fermi arcs" on the surface. A proposal of materials realization in iridates will be discussed. Finally, I will demonstrate that the surface states of the topological semimetals that have protected Fermi arcs can be related to noncompact Riemann surfaces representing simple meromorphic functions.

### Xiao Hu, November 17, 2015, Abstract:

The honeycomb lattice plays an extremely important role in fostering the concept of topology in materials, as seen in the pioneer works by Haldane and by Kane and Mele. In this talk, I revisit electronic states in a honeycomb lattice and try to better highlight the uniqueness of the honeycomb structure. Based on this new observation, we propose a novel quantum anomalous Hall effect characterized by simultaneous non-zero charge and spin Chern numbers, or equivalently by spin-polarized and dissipationless edge currents in a finite sample. Next I show that the honeycomb lattice with uniform nearest-neighbor hopping integrals can be taken as a critical point of a topological phase transition, as signaled by the Dirac, semimetal energy dispersion. Exploring this view point, we reveal new routes to derive topologically nontrivial states by introducing modulations to the hopping integrals keeping certain crystalline symmetry. As two examples of this idea, I discuss a topological photonic crystal purely based on simple dielectric materials, such as silicon, and a quantum orbital Hall state in a honeycomb lattice with the so-called Kekule hopping texture.

### Ville Lahtinen, November 18, 2015, Abstract:

Semi-metallic materials, such as graphene in two dimensions (2D) and various Dirac and Weyl semi-metals in three dimensions (3D), are characterized by nodal band structures that give rise to exotic electronic properties. Their stability requires the presence of lattice symmetries or application of external fields, making them lack the inherent topological protection enjoyed by surface states of topological band insulators. Here we bridge this divide by showing that a self-organized topologically protected semi-metals, that in 1D exhibit an edge spin transport influencing valley anomaly and in 2D appear as a graphene-like semi-metal characterized by odd-integer quantum Hall effect, can emerge and be experimentally observed on extended defects in topological insulators. In particular, these states emerge on a grain boundary, a ubiquitous lattice defect in any crystalline material, thereby providing a novel and experimentally accessible route to topological semi-metals. The underlying mechanism is the hybridization of spinon modes bound to the grain boundary, whose generality suggests that new states of matter can emerge in any topological band insulator where lattice dislocations bind localized topological modes.

### Umesh Vazirani, November 20, 2015, Abstract

One of the central challenges in the study of quantum many-body systems is the exponential complexity of simulating them on a classical computer. A rare bright spot is the heuristic DMRG (Density Matrix Renormalization Group) which has been widely used, ever since its invention almost a quarter century ago, for solving 1D systems. A step towards rigorously justifying the success of DMRG was taken in the seminal result of Hastings proving that unique ground states of 1D gapped Hamiltonians satisfy an area law, thereby showing that they have bounded entanglement and admit succinct classical descriptions. Another was our result last year, showing that there is a polynomial time algorithm to actually compute this succinct classical description for such systems.

I will talk about a new algorithm, which works even when the ground state is degenerate. A small extension of the algorithm finds the poly(n) lowest energy states for a 1D system in n^O(logn) time. The algorithms establish a new operational description of the entanglement structure of the low energy states of local Hamiltonians in 1D. As a result, we vastly extend the family of states for which we can prove the existence of a succinct classical description and area laws. The algorithms are very natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is O(nM(n)), where M(n) is the time to multiply two nxn matrices.

Aside from the major algorithmic challenge they pose, these questions also touch upon some of the most fundamental problems in theoretical computer science. A local Hamiltonian is the direct quantum generalization of a constraint satisfaction problem (CSP), the energy of a state is the number of violated constraints, and the ground state corresponds to the optimal solution of the CSP.

Joint work with Itai Arad, Zeph Landau and Thomas Vidick.

### Avraham Klein, November 30, 2015, Abstract:

Quantum vortices in weakly coupled superfluids have a large healing length, so that many particles reside within the vortex core. They are characterized by topologically protected singular points, which in principal should keep their core structure rigid. I will describe how, in practice, the point singularity of a vortex deforms into a line singularity, in proportion with the Magnus force experienced by the vortex. The vortex structure is described by weak solutions of the Gross-Pitaevskii equation, similar to shock waves in hydrodynamics. I will discuss how the core deformation significantly affects many aspects of vortex dynamics.

### Ady Stern, December 7, 2015, Abstract:

Edges of gapped topological states may host gapless edge modes that cannot be realized as stand-alone systems. Examples include quantum Hall edge states, surface states of topological insulators and super-conductors, etc. In my talk I will examine situations in which these edge states form fractionalized phases of their own. Examples to be discussed include non-abelian defects in edges of abelian quantum Hall states, Haldane-type phases formed by these defects, and topologically ordered states on surfaces of weak topological insulators.