Scale-Renormalized Matrix-Product States for Correlated Quantum Systems

2007/10/17 by Anders W. Sandvik · 2 citations
Physics and Astronomy · #Opinion Dynamics and Social Influence #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.101.140603

published as Phys. Rev. Lett. 101, 140603 (2008) · 4+ pages, 5 figures

arxiv created 2007/10/17 · openalex publication_date 2008/10/03 · arxiv updated 2010/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A generalization of matrix product states (MPS) for interacting quantum systems in two and three dimensions is introduced. These scale-renormalized matrix-product states (SR-MPS) are based on a coarse 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 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.

Citations

• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Criticality, the area law, and the computational power of PEPS
• The renormalization group: Critical phenomena and the Kondo problem
• Scaling of entanglement support for matrix product states

Cited by

• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Variational Monte Carlo simulations using tensor-product projected states

Related

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• Renormalization-group-based preparation of matrix product states on up to 80 qubits
• Space Reduction in Matrix Product State
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Infinite size density matrix renormalization group, revisited