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PreprintarXiv licencearXiv

Leg-Tied Tensor Network States: Entanglement Beyond Virtual Bonds

  • Shuoyi Hu
  • Bing Gu
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Abstract

We introduce a class of tensor-network states in which physical legs are shared among local tensors, termed leg-tied tensor ansätze (LETTA). Physical leg ties encode long-range correlations directly, while a virtual matrix product state (MPS) backbone retains short-range multipartite entanglement. The linear virtual backbone allows us to develop a deterministic density matrix renormalization group-like variational optimization algorithm using exact contractions over the active tie-boundary sets and local minimization. We demonstrate the advantages of LETTA for the two-dimensional frustrated J1--J2 Heisenberg model and the three-dimensional transverse-field Ising model. Our results show that LETTA is substantially more accurate than same-bond-dimension MPS calculations and can typically reach the accuracy of much larger MPS calculations using one order of magnitude fewer variational parameters. LETTA thus opens the door for explicitly correlated tensor-network states that can encode long-range correlation beyond virtual bonds.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026legtied,
  title = {{Leg-Tied Tensor Network States: Entanglement Beyond Virtual Bonds}},
  author = {Shuoyi Hu and Bing Gu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30101},
  eprint = {2609.30101},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30101},
}
RIS
TY  - UNPB
TI  - Leg-Tied Tensor Network States: Entanglement Beyond Virtual Bonds
AU  - Shuoyi Hu
AU  - Bing Gu
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30101
UR  - https://arxiv.org/abs/2609.30101
AB  - We introduce a class of tensor-network states in which physical legs are shared among local tensors, termed leg-tied tensor ansätze (LETTA). Physical leg ties encode long-range correlations directly, while a virtual matrix product state (MPS) backbone retains short-range multipartite entanglement. The linear virtual backbone allows us to develop a deterministic density matrix renormalization group-like variational optimization algorithm using exact contractions over the active tie-boundary sets and local minimization. We demonstrate the advantages of LETTA for the two-dimensional frustrated J_1--J_2 Heisenberg model and the three-dimensional transverse-field Ising model. Our results show that LETTA is substantially more accurate than same-bond-dimension MPS calculations and can typically reach the accuracy of much larger MPS calculations using one order of magnitude fewer variational parameters. LETTA thus opens the door for explicitly correlated tensor-network states that can encode long-range correlation beyond virtual bonds.
ER  -