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

Abstract

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $\lambda {\varphi }^4$ model to study spontaneous breakdown of discrete $Z_2$ symmetry numerically. 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 $L\to \infty$ \cite{Sugihara:2004qr}.

3 pages, 2 figures, parallel talk given at LATTICE 2004, Fermilab, June 21-26, 2004

References in corpus (17)

• Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
• Density-matrix renormalization-group method in momentum space
• Density matrix renormalisation group for a quantum spin chain at non-zero temperature
• Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method
• Thermodynamics of quantum Heisenberg spin chains
• Self-Consistent Tensor Product Variational Approximation for 3D Classical Models
• A two-dimensional algorithm of the density matrix renormalization group
• Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum ϕ^4_2
• The massive Schwinger model with $SU(2{)}_f$ on the light cone
• Density matrix renormalization group in a two-dimensional $\lambda {\varphi }^4$ Hamiltonian lattice model
• Kramers-Wannier Approximation for 3D Ising Model
• Two-dimensional SU(N) Gauge Theory on the Light Cone
• Connected Green function approach to ground state symmetry breaking in ${\Phi }_{1+1}^4$-theory
• Variational Calculation of the Effective Action
• Manifestation of a nontrivial vacuum in discrete light cone quantization
• Lattice chiral symmetry with hopping interactions
• Basis Optimization Renormalization Group for Quantum Hamiltonian

Cited by in corpus (3)

• Full characterization of the quantum linear-zigzag transition in atomic chains
• Ab-initio characterization of the quantum linear-zigzag transition using DMRG
• Studying a relativistic field theory at finite chemical potential with the density matrix renormalization group