arXiv subjects
Publications and source records attributed to Joshua Squires.
The conformal bootstrap is applied to percolation and dilute self-avoiding polymers, two theories with Virasoro central charge $c=0$ in two dimensions. In both cases we propose a spectrum of operators motivated by Virasoro symmetry which is devoid of a stress energy tensor as an approximate means of enforcing $c=0$. Percolation is treated in $2\leq D \leq 6$ dimensions, and the self-avoiding walk in $2 \leq D \leq 4$.
Using a formalism based on the two-body S-matrix we study two-dimensional Bose and Fermi gases with both attractive and repulsive interactions. Approximate analytic expressions, valid at weak coupling and beyond, are developed and applied to the Berezinskii-Kosterlitz-Thouless (BKT) transition. We successfully recover the correct logarithmic functional form of the critical chemical potential and density for the Bose gas. For fermions, the BKT critical temperature is calculated in BCS and BEC regimes through consideration of Tan's contact.
We study three dimensional Bose and Fermi gases in the upper branch, a phase defined by the absence of bound states in the repulsive interaction regime, within an approximation that considers only two-body interactions. Employing a formalism based on the S-matrix, we derive useful analytic expressions that hold on the upper branch in the weak coupling limit. We determine upper branch phase diagrams for both bosons and fermions with techniques valid for arbitrary positive scattering length.