Density matrix renormalization group approach to a two-dimensional bosonic model

TL;DR

This paper applies the density matrix renormalization group method to a (1+1)-dimensional bosonic model to accurately determine critical parameters and demonstrate the method's effectiveness in approaching the continuum limit.

Contribution

The study extends DMRG techniques to a bosonic field theory, providing precise numerical estimates of critical coupling and exponents consistent with known results.

Findings

Critical coupling $(rac{}{^2})_c=59.89\u00b1 0.01$

Critical exponent $eta=0.1264\u00b1 0.0073$

Lattice size $L=500$ suffices for continuum limit approximation

Abstract

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $\lambda\phi^4$ model to study spontaneous breakdown of discrete $Z_2$ symmetry numerically. We obtain the critical coupling $(\lambda/\mu^2)_{\rm c}=59.89\pm 0.01$ and the critical exponent $\beta=0.1264\pm 0.0073$, which are consistent with the Monte Carlo and the exact results, respectively. The results are based on extrapolation to the continuum limit with lattice sizes $L=250,500$, and 1000. We show that the lattice size L=500 is sufficiently close to the the limit $L\to\infty$ \cite{Sugihara:2004qr}.