**KEYNOTE SPEAKERS**

**David Huse**, Princeton University

*Localization-protected quantum order*

Systems that are many-body Anderson localized can exhibit symmetry-breaking long-range order or topological order in regimes where such order would be destroyed at equilibrium by thermal fluctuations. The ordering is dynamical: an ordered initial state stays ordered, being "protected" by the localization of all fluctuations. The simplest examples are quantum Ising models with static randomness. For the random quantum Ising chain this feature has been "known" but apparently not appreciated for close to half a century.

Ref.: Huse, et al., Phys. Rev. B 88, 014206 (2013).

**Young Lee**, Massachusetts Institute of Technology

*Experimental sightings of the quantum spin liquid*

New states of matter may be produced if quantum effects and frustration conspire to prevent the ground state from achieving classical order. An example of a new quantum phase is the quantum spin liquid. Such spin liquids cannot be characterized by local order parameters; rather, they are distinctive by their possession of long range quantum entanglement. I will describe recent experimental progress in the quest to study quantum spin liquids in frustrated magnets. The kagome lattice, composed of corner-sharing triangles, is highly frustrated for antiferromagnetic spins. Materials based on the kagome lattice with spin-1/2 are ideal hosts for quantum spin liquid ground states. I will discuss our group’s work which includes single crystal growth, bulk characterization, and neutron scattering measurements of the S=1/2 kagome lattice material ZnCu3(OH)6Cl2 (also known as herbertsmithite). Our inelastic neutron scattering measurements of the spin correlations in a single crystal sample reveal that the excitations are fractionalized, a hallmark signature of spin liquid physics.

**SPEAKERS**

**Dima Abanin**, Perimeter Institute

*Entanglement, Ergodicity, and Many-Body Localization*

We are used to describing systems of many particles by statistical mechanics. However, the basic postulate of statistical mechanics – ergodicity – breaks down in so-called many-body localized systems, where disorder prevents particle transport and thermalization. In this talk, I will present a theory of the many-body localized (MBL) phase, based on new insights from quantum entanglement. I will argue that, in contrast to ergodic systems, MBL eigenstates are not highly entangled. I will use this fact to show that MBL phase is characterized by an infinite number of emergent local conservation laws, in terms of which the Hamiltonian acquires a universal form. Turning to the experimental implications, I will describe the response of MBL systems to quenches: surprisingly, entanglement shows logarithmic in time growth, reminiscent of glasses, while local observables exhibit power-law approach to “equilibrium” values. I will support the presented theory with results of numerical experiments. I will close by discussing other directions in exploring ergodicity and its breaking in quantum many-body systems.

**Gang Chen,** University of Toronto

*Fractionalized Charge Excitations in a Spin Liquid on Partially-Filled*

Electron charge may fractionalize in a quantum spin liquid Mott insulator. We study the Mott transition from a metal to a cluster Mott insulator in the 1/4- and 1/8-filled pyrochlore lattice systems. Such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsion. The resulting cluster Mott insulator is a quantum spin liquid with spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in X-ray scattering experiments. This and other experimental signatures of the quantum spin and fractionalized charge liquid state are discussed in light of candidate materials with partially-filled bands on pyrochlore lattices. “Fractionalized Charge Excitations in a Spin Liquid on Partially-Filled Pyrochlore Lattice” Electron charge may fractionalize in a quantum spin liquid Mott insulator. We study the Mott transition from a metal to a cluster Mott insulator in the 1/4- and 1/8-filled pyrochlore lattice systems. Such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsion. The resulting cluster Mott insulator is a quantum spin liquid with spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in X-ray scattering experiments. This and other experimental signatures of the quantum spin and fractionalized charge liquid state are discussed in light of candidate materials with partially-filled bands on pyrochlore lattices.

**Jaime Forrest,** University of Waterloo

*Using β-NMR to Solve Hard Problems in Soft Condensed Matter*

Beta-detected nuclear spin relaxation of 8Li+ has been used to study important problems in polymer physics. In the first case we probe the depth dependence of molecular dynamics in high- and low-molecular-weight deuterated polystyrene (PS-d8). The average nuclear spin-lattice relaxation rate, 1/T1 avg, is a measure of the spectral density of the polymer dynamics at the Larmor frequency (41MHz at 6.55Tesla). The mean fluctuation rate decreases approximately exponentially with distance from the free surface, returning to bulk behavior for depths greater than ~10nm and the effective thickness of the surface region increases with increasing temperature. These results present challenges for the current understanding of dynamics near the free surface of polymer glasses. In the second case, we use the technique to make the first quantitative measurements of surface segregation in samples that are blends of two chemically identical polymers with different degrees of polymerization.

**Mingxuan Fu**, McMaster University

*Revealing the Local Magnetism of S=1/2 Kagomé Lattice *

Herbersmithite ZnCu3(OH)6Cl2 is known to be a promising candidate material hosting a quantum spin liquid ground state. The recent success in single crystal growth of ZnCu3(OH)6Cl2 as well as the discovery of a continuum of spinon excitations using inelastic neutron scattering [1] have opened a new chapter in the study of highly frustrated magnetism. However, the mechanism behind the realization of the non-magnetic ground state in ZnCu3(OH)6Cl2 remains controversial, mainly due to the difficulty in understanding the role of defects in its physical properties. To distinguish the intrinsic magnetism of the kagomé lattice from the defect contribution, we used 17O, 63Cu, 2H, and 35Cl NMR to probe the local behavior of spin susceptibility and spin dynamics, which provided invaluable insights into the nature of defects and their potential influence on the kagomé spin lattice [2].

*Present address: Material Sciences Division, Argonne National Laboratory, Argonne, IL 60439

[1] T. Han et al., Nature 492, 406 (2012).

[2] M. Fu, T. Imai et al., in preparation. Also see T. Imai et al., PRL 100, 077203 (2008); and PRB 84, 020411(R) (2012).

**Bruce Gaulin**, McMaster University

*Frozen Spin Ice Ground States in the Pyrochlore Magnet Tb2Ti2O7*

Tb2Ti2O7 was one of the first pyrochlore magnets to be studied as a candidate for a spin liquid or cooperative paramagnet, and its ground state has remained enigmatic for fifteen years. Recent time-of-flight neutron scattering studies have shown that it enters a glassy Spin Ice ground state, characterized by frozen short range order over about 8 conventional unit cells, and the formation of a ~ 0.08 meV gap in its spin excitation spectrum at the appropriate quasi-Bragg wave vectors. I will introduce the relevant Spin Ice physics background, and describe how the experiments are performed. The new H-T phase diagram for Tb2Ti2O7 in a [110] magnetic field will be presented. This shows that its frozen (i.e. glassy) Spin Ice ground state (at low temperature and zero field) and its conventional field-induced ordered phase (at low temperature and high fields) bracket the cooperative paramagnetic phase which generated the original interest in this fascinating magnet.

**Edwin Kermarrec**, McMaster University

*Exotic Magnetism on the FCC Lattice of 5dn Double Perovskites*

In the search for new exotic quantum states, the impact of strong spin-orbit interaction has been recently underlined with the discovery of the Jeff = ½ spin orbital Mott state in the 5d5 layered perovskites iridates [1]. The double perovskite structure, where the magnetic ions form a face-centered-cubic (fcc) sublattice, can accommodate a large variety of 5d transition metal elements, and therefore offers an ideal playground for systematic studies of the exotic magnetic and non-magnetic ground states stabilized by strong spin-orbit coupling [2]. Here, we report time-of-flight neutron scattering measurements on the antiferromagnetic, frustrated, cubic double perovskite system Ba2YOsO6. Its non-distorted fcc lattice is decorated with magnetic Os5+ (5d3) ions which undergo a magnetic transition to a long range ordered antiferromagnetic state below TN = 70 K, as revealed by magnetic Bragg peaks occuring at the [100] and [110] positions. Our inelastic data reveals a large spin gap to the spin-wave excitations Δ = 19(2) meV, unexpected for an orbitally quenched, d3 electronic configuration. We compare this result to the recent observation of a Δ=5 meV spin gap in the related cubic double perovskite Ba2YRuO6 (Ru5+, 4d3) [3], and conclude to a stronger spin-orbit coupling present in the heavier, 5d, osmate system.

[1] B. J. Kim et al., Science 323, 1329 (2009).

[2] G. Chen, R. Pereira and L. Balents, Phys. Rev. B 82, 174440 (2010);

G. Chen and L. Balents, Phys. Rev. B 84, 094420 (2011).

[3] J. P. Carlo et al., Phys. Rev. B 88, 024418 (2013).

**Adrian Lupascu**, University of Waterloo

*Measurements of Noise in Condensed Matter Systems Using Superconducting Qubits and Resonators*

Superconducting qubits based on Josephson junctions and resonators are presently leading candidates for the implementation of quantum computing. These systems couple strongly to their environment, which often makes preservation of coherence challenging. This strong coupling can be turned into an advantage: it enables the investigation of noise and loss at low temperatures. I will discuss two topics. The first topic is the use of superconducting flux qubits to measure magnetic flux noise. The second topic is the measurement of microwave loss in amorphous dielectric materials. Experiments with superconducting coherent systems can be used to extract new information on flux noise and dielectric loss, not accessible using other methods used in the past, providing useful input to theoretical developments.

**Ipsita Mandal,** Perimeter Institute

*Renormalization Group Analysis of a Non-Fermi Liquid System*

We devise a renormalization group analysis for quantum field theories with Fermi surface to study scaling behaviour of non- Fermi liquid states in a controlled approximation. The non-Fermi liquid fixed points are identified from a Fermi surface in (m+1) spatial dimensions, while the co-dimension of Fermi surface is also extended to a generic value. We also study superconducting instability in such systems as a function of dimension and co-dimension of the Fermi surface. The key point in this whole analysis is that unlike in relativistic QFT, the Fermi momentum kF enters as a dimensionful parameter, thus modifying the naive scaling arguments. The effective coupling constant is found to be a combination of the original coupling constant and kF.

**Jeff Rau**, University of Toronto

*Generic Spin Model for Honeycomb Iridates Beyond the Kitaev Limit*

Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the J=1/2 Mott insulator in these materials exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here we provide the generic nearest-neighbour spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120 degree and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.

**Evelyn Tang**, Massachusetts Institute of Technology

*Strain-Induced Helical Flat Band & Interface Superconductivity in Topological Crystalline Insulators*

Topological crystalline insulators in IV-VI compounds host novel topological surface states, that at low energy, consist of multi-valley massless Dirac fermions. We show that strain generically acts as an effective gauge field on these Dirac fermion surface states and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict this is naturally realized in IV-VI semiconductor heterostructures due to the spontaneous formation of a misfit dislocation array at the interface, where the zero-energy Landau orbitals form a nearly flat band. We propose that the high density of states of this topological flat band gives rise to the experimentally observed interface superconductivity in IV-VI semiconductor multilayers at temperatures that are unusually high for semiconductors, and explains its non-BCS dependence on dislocation array period.

**Juven Wang**, Massachusetts Institute of Technology

*Non-Abelian String and Particle Braiding in 3+1D Topological Order*

String and particle excitations are examined in a class of 3+1D topological order described by a discrete gauge theory with a gauge group G and a 4-cocycle twist ω4∈H4(G,R/Z) of G's cohomology group. We demonstrate the topological spin and the spin-statistics relation for the closed strings, and their multi-string braiding. The 3+1D twisted gauge theory can be characterized by a representation of SL(3,Z) modular transformation, which we find its generators Sxyz and Txy in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the 3D's direction z into a compact circle inserted with a gauge flux b, we can use the generators of SL(2,Z) subgroup of SL(3,Z), Sxy and Txy, to study the dimension reduction of the 3D topological order C3D to a direct sum of degenerate states of 2D topological orders C2Db in different fluxb sectors: C3D=⊕bC2Db. The 2D topological orders C2Db are described by 2D gauge theories of the group G twisted by the 3-cocycles ω3(b)dimensionally reduced from the 4-cocycle ω4. We show that the SL(2,Z) generators, Sxy and Txy, fully encodes a particular type of three-string braiding statistics for the connected sum of two Hopf links 221#221 configuration. With certain 4-cocycle twist, we find that, by threading a third string through two-string unlink 021 into three-string Hopf links 221#221 configuration, Abelian two-string statistics is promoted to non-Abelian three-string statistics. (Work done in arxiv.org/abs/1404.7854)