Precise estimation of critical exponents from real-space renormalization group analysis

Understand

We develop a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponent $\nu$ near criticality of higher-dimensional quantum Ising and Potts models in a transverse field.

• Our method is remarkably simple (often analytical), grouping only a few spins into a block spin so that renormalized Hamiltonian has a closed form.
• A previous difficulty of spatial anisotropy and unwanted terms is avoided by incorporating rotational invariance and internal $\mathbb{Z}_q$ symmetries of the Hamiltonian.
• By applying this scheme to the (2+1)-dim Ising model on a triangular lattice and solving an analytical RG equation, we obtain $\nu\approx 0.6300$.