Bypassing the Chiral Obstruction in Two-Dimensional Tensor Networks
Abstract
Gapped chiral phases pose an intrinsic obstruction to projected entangled pair state (PEPS) representations with finite bond dimension D, which generically develop spurious long-range correlations despite the gapped nature of the target state. To address this long-standing problem, we take a qualitatively different route by considering the target chiral system together with a completely decoupled time-reversed auxiliary copy. Constraining the finite-D PEPS to the factorized form would simply reduce the problem to representing each chiral layer independently, leaving the original finite-D obstruction unchanged. Unexpectedly, however, we find that finite-D variational optimization generates an \emph{emergent} residual interlayer entanglement, despite the absence of any explicit interlayer coupling in the Hamiltonian. This emergent entanglement is the key mechanism that bypasses the obstruction, qualitatively changing the PEPS from an effectively gapless representation with long-range correlation tails to one with a finite correlation length. We demonstrate this mechanism for both a free-fermion Chern insulator and an interacting chiral spin liquid. The residual entanglement is systematically suppressed with increasing D, approaching the decoupled limit, while the chiral topological information remains accessible through layer-resolved entanglement spectra. Our results thus uncover a previously unrecognized mechanism for bypassing the chiral obstruction through variationally generated auxiliary entanglement.
Related
- Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
- Real-space spectral functions of three-dimensional billion-size topological non-Hermitian matter with tensor networks
- Non-stabilizerness and entanglement in (2+1)-dimensional SU(2) lattice gauge theory using tensor networks
- Chiral-odd structure of the N → Δ transition: tensor form factors from QCD light-cone sum rules
- Obstruction to local entropy laws on arbitrary black-hole cuts in five-dimensional Einstein--Gauss--Bonnet gravity
BibTeX
@misc{niu2026bypassing,
title = {{Bypassing the Chiral Obstruction in Two-Dimensional Tensor Networks}},
author = {Sen Niu and Rui-Zhen Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.15732},
eprint = {2608.15732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15732},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bypassing the Chiral Obstruction in Two-Dimensional Tensor Networks
AU - Sen Niu
AU - Rui-Zhen Huang
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2608.15732
UR - https://arxiv.org/abs/2608.15732
AB - Gapped chiral phases pose an intrinsic obstruction to projected entangled pair state (PEPS) representations with finite bond dimension D, which generically develop spurious long-range correlations despite the gapped nature of the target state. To address this long-standing problem, we take a qualitatively different route by considering the target chiral system together with a completely decoupled time-reversed auxiliary copy. Constraining the finite-D PEPS to the factorized form would simply reduce the problem to representing each chiral layer independently, leaving the original finite-D obstruction unchanged. Unexpectedly, however, we find that finite-D variational optimization generates an \emph{emergent} residual interlayer entanglement, despite the absence of any explicit interlayer coupling in the Hamiltonian. This emergent entanglement is the key mechanism that bypasses the obstruction, qualitatively changing the PEPS from an effectively gapless representation with long-range correlation tails to one with a finite correlation length. We demonstrate this mechanism for both a free-fermion Chern insulator and an interacting chiral spin liquid. The residual entanglement is systematically suppressed with increasing D, approaching the decoupled limit, while the chiral topological information remains accessible through layer-resolved entanglement spectra. Our results thus uncover a previously unrecognized mechanism for bypassing the chiral obstruction through variationally generated auxiliary entanglement.
ER -