Adaptive mode transformations in fermionic tensor networks

C. Krumnow, O. Legeza, R. Schneider, J. Eisert

Non-local fermionic models are frequently encountered in physics, most prominently in quantum 
chemistry, but also when capturing quantum lattice systems. If strong correlations are present in 
the system, traditional numerical methods such as HF, CI or CC reach in some instances their 
limits. In these cases tensor-network methods provide a new way forward at the cost of being more 
expensive. The long-range nature of the interaction of such systems, however, renders their 
straightforward numerical simulation using tensor-network methods difficult. When using a 
DMRG-based method, a suitable reordering of the orbitals will already reduce the computational 
effort. Still, one has more freedom to preprocess the Hamiltonian by means of unitary 
transformations from one set of fermionic modes to another, aiming at minimising the entanglement 
present in the system. Here, we present an adaptive method that aims at combining advantages 
arising from suitable local mode transformations and matrix-product updates ``on the fly'' in an 
iterative fashion. Our results - both for lattice models and for systems in quantum chemistry - 
show that by including such local mode transformations and applying known reordering techniques, 
one finds good approximations of the ground state already for low bond dimensions and optimises the 
entanglement structure present in the ground. In addition, in cases where they can be identified in 
advance, we are able to approximately recover optimal global mode transformations from the local 
ones for medium sized systems.