State diagrams to determine tree tensor network operators
Richard M. Milbradt, Qunsheng Huang, Christian B. Mendl
SciPost Phys. Core 7, 036 (2024) · published 19 June 2024
- doi: 10.21468/SciPostPhysCore.7.2.036
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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.
Cited by 1
Authors / Affiliation: mappings to Contributors and Organizations
See all Organizations.- 1 Richard M. Milbradt,
- 1 Qunsheng Huang,
- 1 Christian B. Mendl