Abstract
An algorithm for the simulation of the evolution of slightly entangled quantum states hasbeen recently proposed as a tool to study time-dependent phenomena in one-dimensionalquantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure toidentify and dynamically update the relevant, conveniently small, subregion of theotherwise exponentially large Hilbert space. Potential applications of the TEBD algorithmare the simulation of time-dependent Hamiltonians, transport in quantum systems far fromequilibrium and dissipative quantum mechanics. In this paper we translate the TEBDalgorithm into the language of matrix product states in order to both highlight and exploitits resemblances to the widely used density-matrix renormalization-group (DMRG)algorithms. The TEBD algorithm, being based on updating a matrix product state intime, is very accessible to the DMRG community and it can be enhanced byusing well-known DMRG techniques, for instance in the event of good quantumnumbers. More importantly, we show how it can be simply incorporated into existingDMRG implementations to produce a remarkably effective and versatile ‘adaptivetime-dependent DMRG’ variant, that we also test and compare to previous proposals.
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