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

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}.Comment: 3 pages, 2 figures, parallel talk given at LATTICE 2004, Fermilab, June 21-26, 200

Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory

The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian.Comment: 15 pages, 6 figures, minor corrections, accepted for publication in JHE

Chiral symmetry on a lattice with hopping interactions

The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation of the fermion propagator from the continuum one is small.Comment: 3 pages, 2 figures, talk presented at Lattice2003 (chiral fermions

Manifestation of a nontrivial vacuum in discrete light cone quantization

We study a (1+1)-dimensional $\lambda\phi^4$ model with a light-cone zero mode and constant external source to describe spontaneous symmetry breaking. In the broken phase, we find degenerate vacua and discuss their stability based on effective-potential analysis. The vacuum triviality is spurious in the broken phase because these states have lower energy than Fock vacuum. Our results are based on the variational principle.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let