Density matrix renormalization group in a two-dimensional $\lambda {\varphi }^4$ Hamiltonian lattice model

Abstract

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $\lambda {\varphi }^4$ model. Spontaneous breakdown of discrete $Z_2$ symmetry is studied numerically using vacuum wavefunctions. We obtain the critical coupling $(\lambda /{\mu }^2{)}_{\mathrm{c}}=59.89\pm 0.01$ 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 $L\to \infty$.

16 pages, 10 figures, minor corrections, accepted for publication in JHEP