Abstract
We present a detailed analysis of various tensor network parameterizations within the complete graph tensor network states (CGTNS) approach. We extend our 2-site CGTNS scheme by introducing 3-site correlators. For this we devise three different strategies. The first relies solely on 3-site correlators and the second on 3-site correlators added on top of the 2-site correlator ansatz. To avoid an inflation of the variational space introduced by higher-order correlators, we limit the number of higher-order correlators to the most significant ones in the third strategy. Approaches for the selection of these most significant correlators are discussed. The sextet and doublet spin states of the spin-crossover complex manganocene serve as a numerical test case. In general, the CGTNS scheme achieves a remarkable accuracy for a significantly reduced size of the variational space. The advantages, drawbacks, and limitations of all CGTNS parameterizations investigated are rigorously discussed.
Highlights
Electronic structure theory aims at providing accurate properties of molecules in their electronic ground and excited states
We presented a rigorous analysis of various n-site correlators schemes for tensor network states (TNS) at the example of manganocene
We demonstrated that the 2-site correlator content from this graph tensor network states (CGTNS) scheme achieves an efficient parameter reduction for the systems with a configurational space spanned by about 15 000 occupation number vector (ONV)
Summary
Electronic structure theory aims at providing accurate properties of molecules in their electronic ground and excited states. In contrast to one-dimensional spin chains in solid-state physics, molecular systems governed by the full Coulomb interaction in general feature multidimensional entanglement for which the linear MPS ansatz is not well suited (note that we will refer to general quantum correlations of subsystems as ‘entanglement’ in order to distinguish them from ordinary electron-correlation effects discussed for molecules on the basis of orbital spectra in quantum chemistry). This in turn may lead to convergence problems. We explore different optimization strategies to assess its potential for actual applications in molecular physics and chemistry
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