4 Corner Southwest Symposium 2013
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.
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.
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.
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.
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.
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 .
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.
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” . In this regime of strong correlations small perturbations/interactions can stabilize novel forms order or collective fluctuations that otherwise do not exist.