TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.2.036
TI  - State diagrams to determine tree tensor network operators
PY  - 2024/06/19
UR  - https://scipost.org/SciPostPhysCore.7.2.036
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 2
SP  - 036
A1  - Milbradt, Richard M.
AU  - Huang, Qunsheng
AU  - Mendl, Christian B.
AB  - This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for constructing a TTNO given a Hamiltonian. The algorithm exploits the tensor product structure of the Hamiltonian to add paths to a state diagram, while combining local operators if possible. We test the capabilities of our algorithm on random Hamiltonians for a given tree structure. Additionally, we construct explicit TTNOs for nearest neighbour interactions on a tree topology. Furthermore, we derive a bound on the bond dimension of tensor operators representing arbitrary interactions on trees. Finally, we consider an open quantum system in the form of a Heisenberg spin chain coupled to bosonic bath sites as a concrete example. We find that tree structures allow for lower bond dimensions of the Hamiltonian tensor network representation compared to a matrix product operator structure. This reduction is large enough to reduce the number of total tensor elements required as soon as the number of baths per spin reaches 3.
ER  -

@Article{10.21468/SciPostPhysCore.7.2.036,
	title={{State diagrams to determine tree tensor network operators}},
	author={Richard M. Milbradt and Qunsheng Huang and Christian B. Mendl},
	journal={SciPost Phys. Core},
	volume={7},
	pages={036},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.2.036},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.2.036},
}