SciPost Submission Page
Replica Field Theory of Quantum Jumps Monitoring: Application to the Ising Chain
by Youenn Le Gal, Marco Schirò
Submission summary
| Authors (as registered SciPost users): | Marco Schirò |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2511.22506v1 (pdf) |
| Date submitted: | Dec. 19, 2025, 12:45 a.m. |
| Submitted by: | Marco Schirò |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this work we derive the replica field theory for monitored quantum many-body systems evolving under the quantum jumps protocol, corresponding to a non-Hermitian evolution interspersed with random quantum jumps whose distribution is state-dependent. We show that the density matrix of $R$ replicas evolves according to a master equation where the non-Hermitian term is replica-diagonal while coupling among replicas are due to quantum jumps. We write down the associated Keldysh action and study its behavior for the specific case of the Ising Chain with monitoring of particle density and tunable anisotropy, interpolating between free fermions with strong U(1) symmetry and the Ising chain with Z$_2$ symmetry. We derive the effective field theory in terms of slowly varying fields and obtain the replica-diagonal saddle point, which we show to describe the average state. We then go beyond saddle point and derive the effective field theory describing the replica off-diagonal sector, which takes the form of a Non-Linear Sigma Model. The symmetry class is either DIII or D, depending on the parameters of the Ising chain, except at a special symmetric point, where we recover the results for free fermions. We discuss the implications of these findings for the entangling phase observed numerically for the monitored Ising chain.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2026-1-19 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
ChatGPT (GPT-5.2 Thinking) was used to edit and reorganize the referee’s draft and to suggest phrasing and references. All scientific judgments, assessment, and final wording choices remain the referee’s responsibility.
Strengths
1) Clean QJ-specific derivation step: The replicated master equation explicitly displays the structural feature “replica-diagonal non-Hermitian part + replica-coupling only via the jump term.” 2) Technically competent construction: The paper provides a full route from the replicated stochastic dynamics → replicated Keldysh action → saddle point → replicon NLσM. 3) Useful synthesis for readers coming from spin-chain monitoring: The Ising/Majorana chain is a natural and widely studied example; the manuscript gives a self-contained symmetry-class identification across the phase diagram.
Weaknesses
1) Novelty and added value relative to existing NLσM literature are not clearly established. The key physics outcomes (NLσM; symmetry classes including D/DIII; using the known beta functions to infer stability; recovery of a higher-symmetry structure on special lines; etc.) appear already present in the monitored-free-fermion NLσM literature, notably: 1.1) Fava et al., PRX 13, 041045 (2023). 1.2) Poboiko et al., PRX 13, 041046 (2023). 1.3) Starchl, Fischer, Sieberer, PRX Quantum 6, 030302 (2024), which develops a replica-Keldysh/NLσM viewpoint for generalized measurements and explicitly discusses/uses quantum-jump trajectory numerics. 1.4) Fava et al., PRR 6, 043246 (2024) relevant to the U(1)/AIII sector and the “no true transition but sharp crossover” narrative.
2) Main claims are largely symmetry-class statements without new quantitative predictions. The Ising application largely culminates in identifying DIII/D/AIII and then importing the known RG flow to argue weak-monitoring stability. This is plausible, but it is not clear what new universal content is obtained beyond the classification that has been established in the literature.
3) Protocol dependence / unraveling dependence is not clarified. Given the emphasis in the literature that different measurement implementations can share the same IR NLσM description, the authors should state clearly whether QJ monitoring is expected to yield anything different (at the level of universal long-distance physics) compared to generalized-measurement/QSD/projective protocols in the same symmetry class.
Report
Requested changes
1) Add a dedicated “Relation to previous work” section that directly compares to the works above (and maybe others from the monitored free fermion community). The authors should clearly state: 1.1) Which steps/results are genuinely new and depend essentially on QJ state-dependent jump statistics. 1.2) Which results are universal symmetry-class consequences already implied by the existing NLσM framework.
2) Clarify the relation to generalized-measurement formalisms. If the present QJ protocol can be reformulated within the generalized-measurement framework of PRX Quantum 6, 030302 (2024), the novelty claim should be reframed accordingly; if not, the obstruction should be stated precisely.
3) Strengthen the Ising-chain “application” beyond classification. At least one nontrivial output would be needed to make the application more than an expected symmetry check (e.g., an explicit mapping of microscopic parameters to NLσM coupling/defect content with a testable scaling implication, discussion of possible topological terms/defects on special lines, or a comparison with numerics specific to the QJ protocol).
Recommendation
Accept in alternative Journal (see Report)