A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm

Abstract

It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it possible to use an infinite system method, and for the first time the fixed point in two dimensions is studied. By analyzing several related blocking schemes I find that there exists an algorithm for which the local energy decreases monotonically as the system size increases, thereby showing the potential feasibility of this method.

5 pages, 6 figures

References in corpus (2)

• The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
• A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site

Cited by in corpus (11)

• The density-matrix renormalization group
• New Trends in Density Matrix Renormalization
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• A two-dimensional algorithm of the density matrix renormalization group
• Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz
• The N-Leg spin-S Heisenberg ladders: A DMRG study
• DMRG and the Two Dimensional t-J Model
• Density Matrix Renormalisation Group Calculations for Two-Dimensional Lattices: An Application to the Spin-Half and Spin-One Square-Lattice Heisenberg Models
• Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice
• The Stochastic State Selection Method Combined with the Lanczos Approach to Eigenvalues in Quantum Spin Systems
• A constrained stochastic state selection method applied to quantum spin systems