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

TL;DR

This paper applies the density matrix renormalization group method to a two-dimensional $\u0005$ lattice model, accurately determining critical parameters and demonstrating the method's effectiveness in studying phase transitions.

Contribution

The study introduces the application of DMRG to a 2D $\u0005$ lattice model, providing precise critical coupling and exponent estimates consistent with other methods.

Findings

Critical coupling $(/^2)_{c}=59.89\u00b1 0.01$

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. Spontaneous breakdown of discrete $Z_2$ symmetry is studied numerically using vacuum wavefunctions. 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 $L\to\infty$.