Unifying time evolution and optimization with matrix product states
Abstract
We show that the timedependent variational principle provides a unifying framework for timeevolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying timeevolution, which can cope with arbitrary Hamiltonians, including those with longrange interactions. Rather than a SuzukiTrotter splitting of the Hamiltonian, which is the idea behind the adaptive timedependent density matrix renormalization group method or timeevolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the DiracFrenkel timedependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which DMRG can be implemented efficiently and DMRG is obtained as a special case of imaginary time evolution with infinite time step.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 arXiv:
 arXiv:1408.5056
 Bibcode:
 2014arXiv1408.5056H
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 5 pages + 5 pages supplementary material (6 figures) (updated example, small corrections)