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Mixed permutation symmetry quantum phase transitions of critical three-level atom models

by A. Mayorgas, J. Guerrero, and M. Calixto

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Submission summary

Authors (as registered SciPost users): Manuel Calixto · Julio Guerrero · Alberto Mayorgas
Submission information
Preprint Link: scipost_202212_00060v2  (pdf)
Date accepted: 2023-08-11
Date submitted: 2023-02-17 12:12
Submitted by: Mayorgas, Alberto
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approaches: Theoretical, Computational


We define the concept of Mixed Symmetry Quantum Phase Transition (MSQPT), considering each permutation symmetry sector $\mu$ of an identical particles system, as singularities in the properties of the lowest-energy state into each $\mu$ when shifting a Hamiltonian control parameter $\lambda$. A three-level Lipkin-Meshkov-Glick (LMG) model is chosen to typify our construction. Firstly, we analyze the finite number $N$ of particles case, proving the presence of MSQPT precursors. Then, in the thermodynamic limit $N\to\infty$, we calculate the lowest-energy density inside each sector $\mu$, augmenting the control parameter space by $\mu$, and showing a phase diagram with four different quantum phases.

Published as SciPost Phys. Proc. 14, 036 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-3-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202212_00060v2, delivered 2023-03-22, doi: 10.21468/SciPost.Report.6943


The content of the submitted work shows a real expertise of the authors in managing permutational symmetries and the study of phase transitions for systems at large number of particles with mixed permutational symmetries. The model considered by the authors is described by the Lipkin-Meshkov-Glick Hamiltonian.
The mathematical aspects are clearly exposed and justified. The numerical explorations are convincing.


There is no weakness but the fact that the content is quite condensed.


All criteria of the Journal are met in a satisfactory way. The submission excellently proves the strength of symmetry methods in facing with non-trivial questions pertaining with quantum phase transitions.

Requested changes

No change

  • validity: high
  • significance: high
  • originality: high
  • clarity: good
  • formatting: excellent
  • grammar: good

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