Efficient MPS algorithm for periodic boundary conditions and applications

Abstract

We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS), and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of about 100 sites and more than for small quantum systems. We apply the formalism to calculate the ground state and first excited state of a spin-1 Heisenberg ring and deduce the size of the Haldane gap. The results are compared to previous high-precision DMRG calculations. Furthermore, we study spin-1 systems with a biquadratic nearest-neighbor interaction and show first results of an application to a mesoscopic Hubbard ring of spinless Fermions which carries a persistent current.

7 pages, 3 figures, 3 tables, the article was accepted for Ukrainian Journal of Physics

References in corpus (3)

• DMRG and periodic boundary conditions: a quantum information perspective
• Efficient Matrix Product State Method for periodic boundary conditions
• The large system asymptotics of persistent currents in mesoscopic quantum rings

Cited by in corpus (9)

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• Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions
• Symmetries and entanglement in the one-dimensional spin-1/2 XXZ model
• Dimerization in ultracold spinor gases with Zeeman splitting
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• Quantum Coherence of Topologically Frustrated Spin Chains
• Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems