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State Diagrams to determine Tree Tensor Network Operators
by Richard M. Milbradt, Qunsheng Huang, Christian B. Mendl
Submission summary
| Authors (as registered SciPost users): | Richard Milbradt |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2311.13433v3 (pdf) |
| Code repository: | https://github.com/Drachier/state_diagrams_for_ttno |
| Date submitted: | 2024-03-07 17:09 |
| Submitted by: | Milbradt, Richard |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.