Dissociation of bulk and entanglement phase transitions in the Haldane phase

Abstract:Quantum entanglement provides a sensitive probe of topological phases and strong correlations in quantum many-body systems. We revisit the momentum-resolved entanglement spectrum (ES) of the spin-$\frac12$ XXZ ladder in the Haldane phase, whose SU(2)-symmetric spectrum has for over fifteen years been interpreted as a single des Cloizeaux--Pearson mode. Using momentum-resolved entanglement spectroscopy based on exact diagonalization of ladders with up to 40 spins, we instead resolve two distinct modes crossing at $k=\pi/2$ and forming a sharp cusp rather than a single $\sin|k|$ branch, revising the SU(2)-symmetric ES. We then introduce explicit SU(2) symmetry breaking through an XXZ anisotropy. The ES undergoes a phase transition at the isotropic point, while the physical ladder remains in the Haldane phase until a distinct bulk transition at larger anisotropy, establishing a dissociation between bulk and entanglement phase transitions. Between the entanglement and bulk critical points, no gapless entanglement branch remains that can be interpreted as a Haldane-edge excitation, signalling breakdown of the Li--Haldane correspondence. In the easy-plane regime, the ES develops an Anderson tower of states, and the entanglement ground state exhibits long-ranged spin correlations on the finite chains studied, consistent with emergent U(1)-broken order and incompatible with conventional short-range one-dimensional Hamiltonians satisfying the assumptions underlying the Lieb--Schultz--Mattis and Mermin--Wagner--Hohenberg--Coleman theorems. Together, these results establish entanglement-only quantum criticality as a distinct manifestation of critical behaviour encoded in the entanglement description.

Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2509.03588 [cond-mat.str-el]

(or arXiv:2509.03588v2 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2509.03588 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.