**Lukasz Cincio**, Perimeter Institute

*Tensor Networks: an Overview*

Tensor network algorithms provide highly competitive tools for analyzing ground state properties of quantum lattice models in one and two spatial dimensions. The most notable examples involve matrix product states, projected entangled pair states and multiscale entanglement renormalization ansatz. The key underlying idea of all the approaches is to decompose a quantum many-body state into a carefully chosen network of tensors. In this talk I will give an introduction to the subject and show how tensor networks can be used to characterize topological order.

**Pat Clancy**, University of Toronto

*Studies of Rh-doped Sr2Ir2O4*

The physics of iridium-based 5d transition metal oxides has attracted significant interest due to the potential for exotic magnetic and electronic ground states driven by strong spin-orbit coupling effects. Among the most extensively studied iridates is the layered perovskite Sr2IrO4, which was recently proposed as the first experimental realization of a novel Jeff=1/2 spin-orbital Mott insulating state. Intriguing similarities between Sr2IrO4 and La2CuO4, the parent compound of the high-Tc cuprates, have also led to speculation that it may be possible to induce superconductivity in this system through chemical doping. We have investigated the magnetic properties of the doped system Sr2Ir1-xRhxO4 using a combination of resonant magnetic x-ray scattering (RMXS), resonant inelastic x-ray scattering (RIXS), and x-ray absorption spectroscopy (XAS) techniques. These measurements reveal the effect of Rh-doping on the magnetic structure, phase diagram, and characteristic magnetic excitations of Sr2IrO4, and provide fundamental information about the role of quenched Rh impurities.

**Radu Coldea**, University of Oxford

*Reaching Experimentally Quantum Criticality: A Playground to Explore Novel Correlated Quantum States of Matter*

Realizing experimentally continuous phase transitions in the electronic ground state of materials near zero temperature as a function of tuning some external parameter (magnetic field, pressure etc.) offers a unique opportunity to probe the extreme regime (near the transition point) where strong quantum correlations encompass the macroscopic sample as a whole, so called “quantum criticality” [1]. In this regime of strong correlations small perturbations/interactions can stabilize novel forms order or collective fluctuations that otherwise do not exist. One of the theoretically most studied paradigms for quantum criticality is a chain of Ising spins driven by a transverse field to a critical point separating spontaneous magnetic order and paramagnetic phases. We have realized this system experimentally by applying strong magnetic fields to the quasi-one-dimensional Ising ferromagnet CoNb2O6 and have probed via single-crystal inelastic neutron scattering the evolution of the magnetic order and spin excitation spectrum as a function of applied field at mili-Kelvin temperatures [2]. Near the critical point the spin excitations were theoretically predicted nearly two decades ago to have a set of quantum resonances (collective modes of vibration of the interacting spins) with universal ratios between their frequencies reflecting an exceptional mathematical structure of the quantum many-body eigenstates with a “hidden” E8 symmetry governing the physics in the scaling limit. Experiments indeed observed evidence for a spectrum of resonances and the ratio between the frequencies of the two lowest modes approached the "golden ratio" near the critical point, as predicted by field theory. As a second example of novel physics near quantum criticality I will discuss how an amplitude-modulated incommensurate spin-density wave (SDW) order appears near the field-induced critical point in the quasi-1D spin-1/2 XY antiferromagnet Cs2CoCl4. Incommensurate SDWs are very uncommon in magnetic insulators and are not stable zero-temperature ground states at the classical mean-field level, we propose that here such a state is stabilized by the strong quantum fluctuations associated with the proximity to the critical point and the weak frustrated inter-chain couplings.

[1] S. Sachdev, in Quantum Phase Transitions (Cambridge, 2011); S. Sachdev and B. Keimer, Physics Today 64, 29 (2011).

[2] R. Coldea et al., Science 327, 177 (2010).

Spin excitations in the Ising chain magnet CoNb2O6: data and calculation [2].

**Katharina Fritsch**, McMaster University

*New Neutron Scattering Results on the Enigmatic Ground State of the Pyrochlore Magnet Tb2Ti2O7*

The ground state of the candidate spin liquid pyrochlore magnet Tb2Ti2O7 (TTO) has been long debated. Despite theoretical expectations of magnetic order below ~1K based on classical Ising-like Tb3+ spins, earlier muSR and neutron scattering experiments showed no long range order down to 50mK. This motivated two theoretical scenarios to account for the apparently disordered ground state: a quantum spin ice scenario and a non-magnetic singlet ground state. I will discuss new neutron scattering measurements on TTO that show short range spin correlations developing below ~ 0.5 K with a (½, ½, ½) ordering wavevector, and a concomitant opening of a spin gap across most of the Brillouin zone. Our measurements also refine the crystal field ground state for Tb3+ in TTO and in its sister, “soft” spin ice compound Tb2Sn2O7.

**Zhihao Hao**, University of Waterloo

*Spin-1/2 Heisenberg Antiferromagnet on the Kagome Lattice: a Z2 Spin Liquid with Fermionic Spinons*

Motivated by recent numerical and experimental studies of the spin-1/2 Heisenberg antiferromagnet on kagome, we formulate a many-body model for fermionic spinons, which are just uncoupled spins. The spinons interact with an emergent U(1) gauge field and experience strong short-range attraction in the S=0 channel. The ground state of the model is generically a Z(2) liquid. We calculate the edge of the two-spinon continuum and compare the theory to the slave-fermion approach to the Heisenberg model.

**Steve Kivelson**, Stanford University

*Theoretically Established States with a Pseudo-Fermi Surface*

The Fermi liquid phase of interacting electrons is familiar as the basis of our understanding of the low temperature behavior of “good” metals; it is, moreover, deceptively simple due to its smooth connection with non-interacting electrons. However, upon closer examination, the Fermi liquid is among the most remarkable of all quantum phases of matter – one would be tempted to call it “exotic” were it not theoretically understood and experimentally well characterized. Building on this understanding, I will demonstrate the existence of stable quantum phases ofmatter with “pseudo-Fermi-surfaces” – that is exotic phases with fermionic quasiparticles that are asymptotically free on a sharply defined surface in k-space, but which carry quantum numbers unrelated to those of the constituent electrons. Examples that will be explored include superconducting states in which the Bogoliubov quasiparticles are gapless on a pseudo-Fermi-surface, and various spin-liquids in which the quasiparticles are spinons. Candidate materials where some of these states may occur will also be mentioned.

**Jan Kycia**, University of Waterloo

*Absence of Pauling's Residual Entropy in Dy2Ti2O7*

The discovery of the spin-ice phase in Dy2Ti2O7 numbers among the most significant findings in magnetic materials in over a decade. The spin-ice model is based on an elegant analogy to Pauling’s model of geometrical frustration in water ice, and predicts the same residual entropy, as confirmed by numerous

measurements. Melko, den Hertog and Gingras, with numerical work using a loop algorithm to speed up equilibration times, were able to determine an ordering for this system. This had not been seen experimentally observed by several groups. I will present new experimental results for the specific heat

of Dy2Ti2O7, demonstrating why previous measurements were unable to correctly capture its low temperature behaviour. By carefully tracking the flow of heat into and out of the material, we observe a non-vanishing specific heat at low temperatures indicating the residual entropy does not actually agree with the Pauling value.

**Zhou Li**, McMaster University

*Higgs Boson in Condensed Matter: From Polaron to Topological Insulator*

In this talk I will briefly review the polaron physics, which has helped theorists to conceive the BCS theory of conventional superconductors as well as experimentalists to discover high temperature superconductors in the cuprates. Specifically I will talk about how charge carriers obtain their

masses from coupling to the phonon field in one, two, three or higher dimensions. More recently, there is increasing interest in topological insulators where a gap can be opened which may suggest new version of Higgs mechanism in condensed matter.

**Matteo Mariantoni**, University of Waterloo

*The Quantum von Neumann Architecture and the Future of Quantum Computing with Superconducting Circuits*

Superconducting quantum circuits have made significant advances over the past decade, allowing more complex and integrated circuits that perform with good fidelity. We have recently implemented a machine comprising seven quantum channels, with three superconducting resonators, two phase qubits, and two

zeroing registers. I will explain the design and operation of this machine, first showing how a single microwave photon |1> can be prepared in one resonator and coherently transferred between the three resonators [1]. I will then demonstrate how this machine can be used as the quantum-mechanical analog of the von Neumann computer architecture, which for a classical computer comprises a central processing unit and a memory holding both instructions and data. The quantum version comprises a quantum central processing unit (quCPU) that exchanges data with a quantum random-access memory (quRAM) integrated on one chip, with instructions stored on a classical computer [2]. Finally, I will demonstrate that the quantum von Neumann machine provides one unit cell of a two-dimensional qubit-resonator array that can be used for surface code quantum computing. This will allow the realization of a scalable, fault-tolerant quantum processor with the most forgiving error rates to date [3].

[1] M. Mariantoni et al., Nature Physics 7, 287-293 (2011)

[2] M. Mariantoni et al., Science 334, 61-65 (2011)

[3] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Phys. Rev. A 86, 032324 (2012)