TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.8.4.067
TI  - Fractal decompositions and tensor network representations of Bethe wavefunctions
PY  - 2025/10/10
UR  - https://www.scipost.org/SciPostPhysCore.8.4.067
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 8
IS  - 4
SP  - 067
A1  - Sahu, Subhayan
AU  - Vidal, Guifre
AB  - We investigate the entanglement structure of a generic $M$-particle Bethe wavefunction (not necessarily an eigenstate of an integrable model) on a 1d lattice by dividing the lattice into $L$ parts and decomposing the wavefunction into a sum of products of $L$ local wavefunctions. Using the fact that a Bethe wavefunction accepts a fractal multipartite decomposition – it can always be written as a linear combination of $L^M$ products of $L$ local wavefunctions, where each local wavefunction is in turn also a Bethe wavefunction – we then build exact, analytical tensor network representations with finite bond dimension $\chi=2^M$, for a generic planar tree tensor network (TTN), which includes a matrix product states (MPS) and a regular binary TTN as prominent particular cases. For a regular binary tree, the network has depth $\log_{2}(N/M)$ and can be transformed into an adaptive quantum circuit of the same depth, composed of unitary gates acting on $2^M$-dimensional qudits and mid-circuit measurements, that deterministically prepares the Bethe wavefunction. Finally, we put forward a much larger class of generalized Bethe wavefunctions, for which the above decompositions, tensor network and quantum circuit representations are also possible.
ER  -

@Article{10.21468/SciPostPhysCore.8.4.067,
	title={{Fractal decompositions and tensor network representations of Bethe wavefunctions}},
	author={Subhayan Sahu and Guifre Vidal},
	journal={SciPost Phys. Core},
	volume={8},
	pages={067},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.8.4.067},
	url={https://scipost.org/10.21468/SciPostPhysCore.8.4.067},
}