Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

Abstract

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.

5 pages, 4 figures

References in corpus (9)

• The density-matrix renormalization group
• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• DMRG and periodic boundary conditions: a quantum information perspective
• From density-matrix renormalization group to matrix product states
• Quantum phases of bosons in double-well optical lattices
• Numerical Analysis of Coherent Many-Body Currents in a Single Atom Transistor
• Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function
• Density Matrix Renormalization Group and the Nuclear Shell Model

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