Work

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

Year: 2015

Type: article

Abstract: 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 quasiparticle statistics and chiral central charge (up to ${E}_{8}$ bosonic quantum Hall states). We use 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 we confirm that the CSL carries the same topological order as the $\ensuremath{\nu}=\frac{1}{2}$ bosonic Laughlin state. We find that the nonuniversal exponents in the UWFO can be small, and direct numerical computation can be applied on relatively large systems. The UWFO may be a powerful method to calculate the topological order in GPWFs.

Source: Physical Review B

DOI: 10.1103/physrevb.91.125123

Authors: Jia-Wei Mei, Xiao-Gang Wen

Institutions: Perimeter Institute, Massachusetts Institute of Technology

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze