Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions

We implement the universal wave function overlap (UWFO) method to extract modular $S$ and $T$ matrices for topological orders in Gutzwiller-projected parton wave functions (GPWFs). The modular $S$ and $T$ matrices generate a projective representation of $SL(2,\mathbb{Z})$ on the degenerate-ground-state Hilbert space on a torus and may fully characterize the 2+1D topological orders, i.e. the quasi-particle statistics and chiral central charge (up to $E_8$ bosonic quantum Hall states). We used the variational Monte Carlo method to computed the $S$ and $T$ matrices of the chiral spin liquid (CSL) constructed by the GPWF on the square lattice, and confirm that the CSL carries the same topological order as the $\nu=\frac{1}{2}$ bosonic Laughlin state. We find that the non-universal exponents in UWFO can be small and direct numerical computation is able to be applied on relatively large systems. We also discuss the UWFO method for GPWFs on other Bravais lattices in two and three dimensions by using the Monte Carlo method. UWFO may be a powerful method to calculate the topological order in GPWFs.Comment: 5 pages with 3 figure

Summary of lecture recital: Bright Sheng\u27s selected chamber music for strings: two violin solos, and two string quartets

Bright Sheng was born in Shanghai, China, in 1955, and became one of America’s leading composers in the twentieth-century. Bright Sheng’s orchestral music, opera and chamber music is frequently performed throughout the world. His musical language combines Chinese folk music and Western techniques--the meeting of East and West. This essay will discuss Bright Sheng’s The Stream Flows for solo violin (1990), Three Fantasies for Violin and Piano (2006), String Quartet No.3 (1993), and String Quartet No.4 Silent Tempo (2000). These works represent Sheng’s chamber music for strings. This essay will be organized as follows: Chapter 1 will provide Bright Sheng’s biography and compositional style. Chapter 2 will discuss an overview of Chinese folk music. Chapter 3 is an analysis of Sheng’s The Stream Flows for solo violin. Chapter 4 will introduce Sheng’s Three Fantasies for Violin and Piano. Chapters 5 and 6 will present Sheng’s String Quartets No.3 and No.4