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.