A J Daley et al J. Stat. Mech. (2004) P04005 doi:10.1088/1742-5468/2004/04/P04005
A J Daley1,2, C Kollath3, U Schollwöck4 and G Vidal5
Show affiliationsAn algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure to identify and dynamically update the relevant, conveniently small, subregion of the otherwise exponentially large Hilbert space. Potential applications of the TEBD algorithm are the simulation of time-dependent Hamiltonians, transport in quantum systems far from equilibrium and dissipative quantum mechanics. In this paper we translate the TEBD algorithm into the language of matrix product states in order to both highlight and exploit its resemblances to the widely used density-matrix renormalization-group (DMRG) algorithms. The TEBD algorithm, being based on updating a matrix product state in time, is very accessible to the DMRG community and it can be enhanced by using well-known DMRG techniques, for instance in the event of good quantum numbers. More importantly, we show how it can be simply incorporated into existing DMRG implementations to produce a remarkably effective and versatile 'adaptive time-dependent DMRG' variant, that we also test and compare to previous proposals.
03.65.Yz Decoherence; open systems; quantum statistical methods
05.10.Cc Renormalization group methods
03.67.Mn Entanglement measures, witnesses, and other characterizations
81T17 Renormalization group methods
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
Issue 04 (April 2004)
Received 17 March 2004, accepted for publication 6 April 2004
Published 21 April 2004
A J Daley et al J. Stat. Mech. (2004) P04005
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