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Topological Frustration can modify the nature of a Quantum Phase Transition

by Vanja Marić, Gianpaolo Torre, Fabio Franchini, Salvatore Marco Giampaolo

This is not the current version.

Submission summary

As Contributors: Fabio Franchini · Salvatore Marco Giampaolo · Vanja Marić
Arxiv Link: (pdf)
Date submitted: 2021-05-14 09:23
Submitted by: Franchini, Fabio
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2021-8-16 (Invited Report)


The paper is well written, rigorous, presents interesting results which can be highly relevant to researchers working on phase transitions.


The authors derive all the results for a specific model, given by Eq. (1). However, the authors claim that the results are more general, and refer to reference [18] for the proof. I suggest the authors elaborate more on an intuitive / hand waiving argument regarding why these behaviors can be expected in models other than the one described by Eq. (1).


The authors show that topological frustration in finite size spin systems, arising due to frustrated boundary conditions, can lead to a critical point separating two phases with zero local order parameters. This is in contrast to conventional phase transitions, where a critical point is separated by two phases with different local order parameters. However, here the phases on either side of the critical point are characterized by distinct topological order parameters.
This work is very interesting and revisits the problem of quantum phase transitions from a new perspective. It shows that since in practice all systems are finite sized, so frustrated boundary conditions may become highly relevant close to phase transitions.

Requested changes

I suggest the authors elaborate more on an intuitive / hand waiving argument regarding why these behaviors can be expected in models other than the one described by Eq. (1). For example, what are the general characteristics of the models in which these kind of behaviors can be expected?

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

Anonymous Report 1 on 2021-7-14 (Invited Report)


1) Interesting results
2) High scientific standards
3) Well written


1) I personally could not estrapolate a general concept. I think that a hand waving argument from 'the more mathematical companion article' would improve the present paper. In other words, which are the models that are 'dangerous'? I understand that to answer this question some rigor could be lost, but I think that even a qualitative answer would make the article more fruitful in terms of stimulating further investigations.


The Authors challenge some general principles behind the Ginzburg Landau theory. More specifically, they show that the order parameter can change from local to string-like for an appropriate choice of the boundary conditions. The model that they employ is solvable via a Wigner Jordan transformation , and a machinery similar to the one of the xy chain can be employed. The key ingredient is the adoption of 'frustrated boundary conditions'.
The results are interesting, well supported, and well explained.

Requested changes

I would appreciate the inclusion of a simple intuitive argument, if available.

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

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