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

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 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.

5 pages with 3 figures

References in corpus (5)

• An exact chiral spin liquid with non-Abelian anyons
• Characterizing topological order by studying the ground states of an infinite cylinder
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions