## 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.

### Felix Flicker, January 7, 2016, Abstract:

Recent experimental observations have been argued to demonstrate that one-dimensional quasicrystals - quasiperiodic slices through two-dimensional crystals - adopt the topological quantum numbers of their higher-dimensional parent lattice, exhibiting an equivalent to the quantum Hall effect. I demonstrate that the mathematics of both quasicrystals and the quantum Hall effect can be considered as different limits of a third problem: incommensurate charge order. The analysis suggests only 2D families of quasicrystals are able to demonstrate 2D quantum numbers, in agreement with the usual topological classification of free fermion systems. Transcending the mathematical equivalence, I provide a free energy analysis showing that charge order in real materials can lead to a true quasicrystalline ground state. This greatly extends the number of natural quasicrystals beyond the two known cases, both discovered in the same Siberian meteorite by Princeton-led teams.

### Steve Kivelson, February 22, 2016, Abstract:

Phases of the strongly interacting electron fluid which spontaneously break the point-group symmetries of the host crystal can sometimes be characterized as “electron nematic phases.” Such phases increasingly appear to play a significant role in the physics of a variety of “interesting” materials, including the Cu and Fe based high temperature superconductors. I will review some of the evidence that this is a useful perspective (as opposed to dismissing the phenomena as an uninteresting reflection of subtle structural changes in the crystal), and will also summarize some of the theoretical progress in understanding the origins of electronic nematicity, the quantum critical phenomena associated with the transition to the nematic state, and the effect of nematic order and fluctuations on other properties of the electron fluid.

### Michael Brenner, February 24, 2016, Abstract:

Biological systems provide an inspiration for creating a new paradigm for materials synthesis. Imagine it were possible to create an inanimate material that could both perform some function, e.g. catalyze a set of reactions, and also self replicate. Changing the parameters governing such a system would allow the possibility of evolving materials with interesting properties by carrying out “mutation-selection” cycles on the functional outcomes. Although we are quite far from realizing such a vision in the laboratory, recent experimental advances in coating colloidal scale objects with specific glues (e.g.using complementary DNA strands) have suggested a set of theoretical models in which the possibilities of realizing these ideas can be explored in a controlled way. This talk will describe our ongoing efforts to explore these ideas using theory and simulation, and also small scale experiments.

### Chaoxing Liu, March 8, 2016, Abstract:

Ever since the discovery of time reversal invariant topological insulators, intensive research interests are focused on how to identify new topological phases that are protected by symmetry (known as symmetry protected topological states) and how to search for new topological materials to realize these topological phases. A large variety of topological materials have been theoretically proposed for topological states in free fermion systems and many of them have been confirmed experimentally. In contrast, few topological materials have been for bosonic symmetry protected topological (BSPT) states, which normally require strong interactions, in two or higher dimensions. In this talk, I would like to propose the possible realization of BSPT phases in two existing topological material systems. One is to consider the zero Landau levels of bilayer graphene under a strong magnetic field and the other is the thin film of topological mirror Kondo insulators, such as SmB6. Our strategy is to first construct two copies of helical edge modes, which are protected by either spin Chern number or mirror Chern number, at the boundary of these two systems at the free fermion level. Then, by introducing strong interactions into this system, we find that the interaction can gap out all the local fermion degrees of freedom and the remaining degrees of freedom are of bosonic type, consistent with BSPT phases. This strategy allows us to conclude that BSPT phases are highly likely to be realized in these two topological material systems. I will also briefly discuss possible experimental signatures and the difference between these two topological material systems.

Reference:

[1] Bilayer Graphene as a platform for Bosonic Symmetry Protected Topological States, Zhen Bi, Ruixing Zhang, Yi-Zhuang You, Andrea Young, Leon Balents, Chao-Xing Liu, Cenke Xu, arXiv:1602.03190v1

### Haim Beidenkopf, March 21,2016, Abstract:

A defining property of a topological material is the existence of surface bands that cannot be realized but as the termination of a topological bulk. In a Weyl semi-metal these are given by the surface Fermi-arcs, whose open-contour Fermi-surface curves between pairs of surface projections of bulk Weyl points of opposite chirality. We visualize these Fermi arc states in scanning tunneling spectroscopic on the surface of the recently discovered Weyl semi-metal tantalum arsenide (TaAs) [1]. Its surface hosts 12 Fermi arcs alongside several surface bands of non-topological origin. Using the distinct structure and spatial distribution of the wavefunctions associated with the different bands we detect all possible scattering processes in which Fermi arcs are involved (intra- and inter arc and arc-trivial). Each of these imaged scattering processes entails information on the unique nature of Fermi arcs in TaAs: their contour, their dispersion and its relation with the Weyl points, the relative uniform structure of their Bloch wave function, and their association with tantalum sites which indicates their close relation with the tantalum derived bulk Weyl cones. The analysis technique we demonstrate, based on the structure of the Bloch wave function within the unit cell, is applicable to other electronic systems of interest such as high temperature superconductors and topological crystalline insulators.

1. Rajib Batabyal et al. arXiv 1603.00283

### Alexey Soluyanov, March 23, 2016, Abstract:

In recent years it was realized that our knowledge of possible quasiparticle excitations is incomplete even for non-interacting systems. I will talk about several novel topological excitations that appear in metals. One of them realizes a new type of Weyl fermion, hosting the behavior very different from its standard quantum field theory counterpart. In particular, we predict a new type of the chiral anomaly to appear in type-II Weyl metals. The second phase is that of a “dirty” Weyl point, where a Weyl point coexists with an additional electronic state, still topologically protected and producing Fermi arcs on the material’s surfaces. Finally, I will introduce a novel nodal chain phase, that is predicted to exhibit a variety of non-standard behavior in magnetic fields. Real material examples will be presented for all the above phases.

### Michael Gullans, March 24, 2016, Abstract:

In the semiclassical theory of nonlinear optics, the nonlinear response of the medium is typically treated perturbatively and characterized in terms of just a few phenomenological parameters. The remaining task, in this case, is to measure these coefficients as a function of frequency, wavevector, temperature, etc. However, when the medium becomes nonlinear at the level of a single photon, this paradigm is no longer valid. In this regime, the photons are strongly admixed with the microscopic degrees of freedom of the material (e.g., excitons, plasmons, phonons, or polarization) and the photon-photon interactions have to be treated non-perturbatively. As a result, theoretical treatments of the quantum nonlinear response of the medium requires accurate microscopic models, as well as methods to solve for the strongly-interacting, quantum dynamics. Such theoretical approaches are increasingly needed due to the rise (driven by experimental efforts in quantum information science) in controllable quantum systems, strongly coupled to light across the electromagnetic spectrum. In this talk, I will discuss the broad phenomenology of quantum nonlinear optics and detail current theoretical methods through examples from my own research in Rydberg polariton systems, two-dimensional van der Waals materials, and circuit quantum electrodynamics.

### Panagiotis Kotetes, March 31, 2016, Abstract:

Recent spin polarized scanning tunneling microscopy (SPSTM) experiments in magnetic chains [1] opened new routes for detecting the elusive Majorana fermions (MFs). Within the deep Shiba limit we calculate [2] the spatially resolved tunneling conductance of topological ferromagnetic chains [1,3] measurable by means of SPSTM. Our analysis reveals novel signatures of MFs arising from the interplay of their strongly anisotropic spin-polarization and the magnetization content of the tip. We investigate the occurrence and evolution of zero/finite bias peaks for a single or two coupled chains forming a Josephson junction, when a preexisting chiral symmetry controlling the number of MFs per chain edge is preserved or weakly broken. We also reveal alternative routes for engineering MFs without spin-orbit interaction (SOI). On one hand, we highlight that antiferromagnetic Shiba chains become topological by inducing an artificial SOI using external fields [4], while on the other, we pursue mechanisms for stabilizing magnetic textures and topological Shiba lattices following the self-organization principle for topological spiral chains [5].

[1] S. Nadj-Perge et al., Science 346, 602 (2014).

[2] P. Kotetes et al., Physica E 74, 614 (2015).

[3] A. Heimes, D. Mendler, and P. Kotetes, New J. Phys. 17 023051 (2015).

[4] A. Heimes, P. Kotetes, and G. Schön, PRB 90, 060507(R) (2014).

[5] M. Schecter et al., arXiv:1509.07399.

### Monika Aidelsburger, April 4, 2016, Abstract:

Many intriguing condensed matter phenomena such as the integer and fractional quantum Hall effect arise due to the non-trivial topological properties of the underlying system. Synthetic materials that consist of ultracold neutral atoms confined in crystal-like structures using laser beams have the potential to simulate and address the complex questions that arise in this context. In this talk I report on the experimental realization of very strong artificial magnetic fields based on laser-assisted tunneling which give rise to topological energy bands. Their properties are characterized by topological invariants - the Chern numbers - which are at the origin of the integer quantum Hall effect. In particular we were able to realize the Hofstadter model for an effective flux 1/4 and determined the Chern number of the lowest energy band through a direct measurement of bulk topological currents. These experimental results pave the way for future studies of interacting topological systems with ultracold atoms in optical lattices.

### Stuart Parkin, April 11, 2016, Abstract:

Memory-storage devices based on the current controlled motion of a series of domain walls (DWs) in magnetic racetracks promise performance and reliability beyond that of conventional magnetic disk drives and solid state storage devices(1). Racetracks that are formed from atomically thin, perpendicularly magnetized nano-wires, interfaced with adjacent metal layers with high spin-orbit coupling, give rise to narrow domain walls that exhibit a chiral Néel structure(2). These DWs can be moved very efficiently with current via chiral spin-orbit torques(2,3). Record-breaking current-induced domain wall speeds exceeding 1,000 m/sec are found in synthetic antiferromagnetic (SAF) structures(3) in which the net magnetization of the DWs is tuned to almost zero, making them “invisible”. Based on these recent discoveries, Racetrack Memory devices have the potential to operate on picosecond timescales and at densities more than 100 hundred times greater than other memory technologies.

1. S. S. P. Parkin et al. Science 320, 5873 (2008); S. S. P. Parkin and S.-H. Yang, Nature Nanotech. 10, 195 (2015).

2. K.-S. Ryu et al., Nature Nanotech. 8, 527 (2013).

3. S.-H. Yang, K.-S. Ryu and S. S. P. Parkin, Nature Nanotech.10, 221 (2015).

4. S. S. P. Parkin, Phys. Rev. Lett. 67, 3598 (1991).

### Qimiao Si, April 18, 2016, Abstract:

This talk will provide a brief overview of the field of the iron-based superconductivity (FeSC), and discuss several topical issues. In the beginning of the field, iron pnictides were the focus of attention. More recently, iron chalcogenides have taken the center stage, providing not only a renewed hope for even higher superconducting transition temperatures, but also new puzzles that contain clues to the underlying physics. I will address the implications of the bad-metal properties that are observed in the normal state of both classes of systems, including the recently discussed orbital selective Mott behavior. I will then present some recent studies which have been motivated by the puzzles coming from the iron chalcogenides. One is about magnetism, in particular how magnetic frustration influences the magnetic and nematic properties. The other concerns superconductivity, with an emphasis on the quasi-degeneracy of the pairing channels and how orbital selectivity relieves this degeneracy and gives rise to an unusual pairing state. These issues will be placed in the context of the overall physics of the FeSCs.

### Chetan Nayak, May 2, 2016, Abstract:

I will define what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of driven systems with discrete time-translation symmetry.

### Roderich Moessner, May 9, 2016, Abstract:

The excitation spectra of topological phases of matter contain rather `direct' information about their unusual quasiparticles, while the corresponding bulk ground states tend to be rather

featureless. Motivated by this observation, we have evaluated the dynamical structure factor of the Kitaev model on the honeycomb lattice, which is unusual in that it hosts a family of spin liquids amenable to an exact analysis. We find that the structure factor contains direct evidence of fractionalisation, in the form of both Majorana fermions and emergent gauge fluxes. It can be probed in experiments such as neutron scattering or Raman spectroscopy. As these are subject to different selection rules, they reveal complementary information. We discuss the situation on the experimental front, in particular on the 'proximate spin liquid' in $\alpha$-RuCl$_3$

J. Knolle et al, Phys. Rev. Lett. 112, 207203 (2014) J. Knolle et al, Phys. Rev. Lett. 113, 187201 (2014) A. Banerjee et al, arXiv:1504.08037 J. Nasu et al, arXiv:1602.05277

### Thomas Iadecola, May 12, 2016, Abstract:

Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases.

In this work, we present a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly-interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories.

### Dmitri Khveshchenko, May 16, 2016, Abstract:

Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).