Work

Unconventional entanglement scaling and quantum criticality in the long-range spin-one Heisenberg chain with single-ion anisotropy

Year: 2026

Type: article

Abstract: Long-range interactions can fundamentally reshape the low-energy properties of low-dimensional quantum matter, altering both continuous-symmetry breaking (CSB) and topological phenomena. However, their impact on the quantum criticality separating these regimes remains poorly understood. We determine the ground-state phase diagram and critical properties of the spin-one Heisenberg chain with single-ion anisotropy and staggered antiferromagnetic power-law interactions, using matrix-product state calculations complemented by high-order series expansions (perturbative continuous unitary transformations + Monte Carlo). Such long-range, nonfrustrated interactions circumvent the Hohenberg-Mermin-Wagner theorem, thereby stabilizing CSB phases in direct competition with the Haldane phase. We map out the resulting phase diagram and analyze the entanglement entropy scaling behavior in the U(1) and SU(2) CSB phases, finding logarithmic corrections beyond the short-range, universal contributions expected from linearly dispersed Goldstone modes. We further characterize all critical boundaries through finite-size scaling of either the entanglement entropy or the staggered magnetization. In particular, the large- D -to-U(1)-CSB transition exhibits unconventional, continuously varying critical exponents as a function of the long-range decay exponent with a strong dependence on the imposed boundary conditions leading to distinct finite-size scalings for sufficiently long-range potentials. Remarkably, the Haldane-to-U(1)-CSB transition likewise displays unconventional quantum criticality with distinct continuously varying critical exponents. Our work positions this model as a target for near-term atomic platforms with tunable long-range couplings and exhibiting natural single-ion anisotropy, offering a minimal playground for exploring the interplay between long-range interactions, continuous symmetry breaking, and topology.

Source: Physical Review Research

DOI: 10.1103/3cyg-8wsw

Authors: Patrick Adelhardt, Sean R. Muleady, Kai P. Schmidt, Alexey V. Gorshkov

Institutions: Friedrich-Alexander-Universität Erlangen-Nürnberg, Joint Center for Quantum Information and Computer Science, Joint Quantum Institute

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625