School of MathematicsSchool of Mathematicshttp://hdl.handle.net/2262/12017-02-23T00:26:19Z2017-02-23T00:26:19ZIntegrable lattice models for strongly correlated electronsQuinn, Eoinhttp://hdl.handle.net/2262/793172017-02-10T11:24:49Z2013-01-01T00:00:00ZIntegrable lattice models for strongly correlated electrons
Quinn, Eoin
This thesis is dedicated to the study of a new family of integrable lattice models for strongly correlated electrons, namely the Hubbard- Shastry models. The techniques of exactly solvable models, and in particular those of integrable systems, are used. The models are constructed through the quantum inverse scattering method and are studied in one dimension through their Bethe ansatz solution.
2013-01-01T00:00:00ZSpectroscopy and scattering of mesons containing charm quarks from lattice QCDMoir, Grahamhttp://hdl.handle.net/2262/792522017-02-10T11:06:56Z2013-01-01T00:00:00ZSpectroscopy and scattering of mesons containing charm quarks from lattice QCD
Moir, Graham
We present excited spectra of mesons containing charm-light (D), charm-strange (Ds) and charm-charm (charmoninm) combinations. We perform these spectroscopic calculations on two volumes. 16(3) X 128 and 24(3) x 128, of dynamical Nf = 2 + 1 configurations generated by the Hadron Spectrum Collaboration. These ensembles have unphysically-heavy degenerate up and down quarks, resulting in a pion mass of ~ 391 MeV. Our use of distillation and the variational method combined with a large basis of carefully constructed interpolators allows us to extract and reliably identify the continuum spin of an extensive set of states up to J ≤ 4, while also allowing access to explicit gluonic degrees of freedom. For the first time in a lattice QCD calculation, we extract charmoninm states with exotic quantum nmnbers 0+-, 1-+ and 2+-, and in all three sectors, we identify the lightest hybrid supermultiplet and evidence for an excited hybrid supermultiplet. Using a non-relativistic interpretation of some of our interpolators in the open-charm sectors, we calculate mixing angles for P-wave, D-wave and the hybrid 1-, spin-singlet triplet states. We also present preliminary results for the isospin. I = 3/2. Dπ multi-particle spectrum and map out. via the Lüscher formalism, the l = 0 elastic scattering phase shift. As expected we do not find a resonance in this channel.
2013-01-01T00:00:00ZStatic-light-light baryons : a spectroscopic study using distillationMc Elroy, Finnianhttp://hdl.handle.net/2262/791132017-01-20T03:44:22Z2013-01-01T00:00:00ZStatic-light-light baryons : a spectroscopic study using distillation
Mc Elroy, Finnian
Over the last decade, hadron spectroscopy in lattice QCD has graduated from calculating single rows of the quark propagation matrix to calculating all elements of the quark propagation matrix - the so-called all-to-all propagator. On a spatially symmetric anisotropic lattice of spatial extent and temporal extent Nx the quark propagation matrix has rank 4 x 3 x N3x x Nt, where 4 represents the number of components in a Dirac field and 3 represents the number of colours. Calculating all elements of this matrix requires 144 x N6x x N2t matrix inversions - a formidable task. The relatively new method of distillation enables access to all elements of the quark propagation matrix at a much more affordable cost.
2013-01-01T00:00:00ZCFTs on Riemann surfaces of genus g ≥ 1Leitner, Mariannehttp://hdl.handle.net/2262/790942017-01-20T03:42:55Z2014-01-01T00:00:00ZCFTs on Riemann surfaces of genus g ≥ 1
Leitner, Marianne
The purpose of this thesis is to argue that N-point functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus g≥ 1. N-point functions for higher N are obtained inductively, and we show that they have a nice graphical representation. We discuss the Virasoro 3-point function with application to the Virasoro (2,5) minimal model.
2014-01-01T00:00:00Z