Scale-renormalized matrix-product states for correlated quantum systems

Abstract

A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining of the lattice in which the blocks at each level are associated with matrix products that are further transformed (scale renormalized) with other matrices before they are assembled to form blocks at the next level. Using variational Monte Carlo simulations of the two-dimensional transverse-field Ising model as a test, it is shown that the SR-MPS converge much more rapidly with the matrix size than a standard MPS. It is also shown that the use of lattice-symmetries speeds up the convergence very significantly.

4+ pages, 5 figures

References in corpus (6)

• DMRG and periodic boundary conditions: a quantum information perspective
• Criticality, the area law, and the computational power of PEPS
• Scaling of entanglement support for Matrix Product States
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods

Cited by in corpus (8)

• Monte Carlo simulation with Tensor Network States
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Accurate simulation for finite projected entangled pair states in two dimensions
• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Direct sampling of projected entangled-pair states
• Plaquette Renormalization Scheme for Tensor Network States
• Variational Monte Carlo simulations using tensor-product projected states
• Matrix-Product based Projected Wave Functions Ansatz for Quantum Many-Body Ground States