Applying matrix product operators to model systems with long-range interactions

2008/04/30 by Gregory M. Crosswhite, Andrew C. Doherty, Guifre Vidal +1 · 6 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.other #quant-ph

paper · pdf · doi:10.1103/physrevb.78.035116

published as Phys. Rev. B 78, 035116 (2008) · 7 pages, 3 figures; manuscript has been expanded and restructured in order to improve presentation of the algorithm

arxiv created 2008/07/07 · openalex publication_date 2008/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite one-dimensional (1D) system. It does this by embedding sites into an approximation of the infinite ``environment'' of the chain, allowing the sites to relax and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply these techniques to compute the ground state of the Haldane-Shastry model [Phys. Rev. Lett. 60, 635 (1988) and Phys. Rev. Lett. 60, 639 (1988)] and present the results.

Citations

• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• The renormalization group: Critical phenomena and the Kondo problem

Cited by

• Out-of-equilibrium dynamics with matrix product states
• Generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions
• Simulating fermions in spin-dependent potentials with spin models on an energy lattice
• Spread of Correlations in Long-Range Interacting Quantum Systems
• Continuous Matrix Product Operator Approach to Finite Temperature Quantum States
• Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder

Related

• Matrix product operator representations
• Matrix Product Operator Constructions for Gauge Theories in the Thermodynamic Limit
• Matrix product state approximations for infinite systems
• Finite-Element Matrix Product States for Continuum Models in One Dimension
• Environment-matrix-product operator for boundary-free large-scale quantum many-body simulations