Related Experiment Video
Updated: Aug 9, 2025

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
Published on: July 27, 2022
Contrasting pseudocriticality in the classical two-dimensional Heisenberg and RP^{2} models: Zero-temperature phase
Lander Burgelman1, Lukas Devos1, Bram Vanhecke1,2
1Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium.
Abstract:
Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and RP^{2} models. We demonstrate that uniform matrix product states (MPSs) with explicit SO(3) symmetry can probe correlation lengths up to O(10^{3}) sites accurately, and we study the scaling of entanglement entropy and universal features of MPS entanglement spectra. For the Heisenberg model, we find no signs of a finite-temperature phase transition, supporting the scenario of asymptotic freedom. For the RP^{2} model we observe an abrupt onset of scaling behavior, consistent with hints of a finite-temperature phase transition reported in previous studies. A careful analysis of the softening of the correlation length divergence, the scaling of the entanglement entropy, and the MPS entanglement spectra shows that our results are inconsistent with true criticality, but are rather in agreement with the scenario of a crossover to a pseudocritical region which exhibits strong signatures of nematic quasi-long-range order at length scales below the true correlation length. Our results reveal a fundamental difference in scaling behavior between the Heisenberg and RP^{2} models: Whereas the emergence of scaling in the former shifts to zero temperature if the bond dimension is increased, it occurs at a finite bond-dimension independent crossover temperature in the latter.
Related Concept Videos
The Uncertainty Principle
The Pauli Exclusion Principle
The Quantum-Mechanical Model of an Atom
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
Reduced Mass Coordinates: Isolated Two-body Problem
The Bohr Model

