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abstract = {The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are nonanalytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of SU({$n$}) models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.}
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@article{jeckelmann2002,
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title = {Dynamical Density-Matrix Renormalization-Group Method},
title = {Spiral Renormalization Group Flow and Universal Entanglement Spectrum of the Non-{{Hermitian}} 5-State {{Potts}} Model},
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author = {Linden, Vic Vander and Vos, Boris De and Vervoort, Kevin and Verstraete, Frank and Ueda, Atsushi},
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year = 2025,
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month = jul,
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number = {arXiv:2507.14732},
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eprint = {2507.14732},
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primaryclass = {cond-mat},
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publisher = {arXiv},
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doi = {10.48550/arXiv.2507.14732},
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url = {http://arxiv.org/abs/2507.14732},
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abstract = {The quantum \$5\$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on the lattice, the model must be deformed by an additional non-Hermitian term due to its complex coefficient \$\textbackslash lambda\$. Although the variational principle breaks down in this case, we demonstrate that tensor network algorithms are still capable of simulating these non-Hermitian theories. We access system sizes up to \$L = 28\$, which enable the observation of the theoretically predicted spiral flow of the running couplings. Moreover, we reconstruct the full boundary CCFT spectrum through the entanglement Hamiltonian encoded in the ground state. Our work demonstrates how tensor networks are the correct approach to capturing the approximate conformal invariance of weakly first-order phase transitions.},
author = {Mortier, Quinten and Devos, Lukas and Burgelman, Lander and Vanhecke, Bram and Bultinck, Nick and Verstraete, Frank and Haegeman, Jutho and Vanderstraeten, Laurens},
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