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arxiv: 2604.16137 · v1 · submitted 2026-04-17 · ❄️ cond-mat.quant-gas · quant-ph

Recognition: unknown

Observation of Strong-to-Weak Spontaneous Symmetry Breaking in a Dephased Fermi Gas

Si Wang , Thomas G. Kiely , Dorothee Tell , Johannes Obermeyer , Marnix Barendregt , Petar Bojovi\'c , Philipp M. Preiss , Abhijat Sarma
show 4 more authors
Titus Franz Matthew P. A. Fisher Cenke Xu Immanuel Bloch
Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:01 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas quant-ph
keywords strong-to-weak spontaneous symmetry breakingdephased Fermi gasRényi correlatorsquantum gas microscopemetal-insulator transitionopen quantum systemsmixed-state phasessymmetry breaking
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The pith

Dephased fermions exhibit long-range Rényi order that signals strong-to-weak spontaneous symmetry breaking.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes the first experimental detection of strong-to-weak spontaneous symmetry breaking in a single-component Fermi gas after uniform dephasing. A quantum gas microscope images the atoms while a machine-learned Gaussian reference state supplies an estimator for the nonlinear Rényi-1 and Rényi-2 correlators that alone can reveal the order. When a commensurate superlattice first drives the fermions through a metal-to-insulator transition, the subsequent dephasing produces a sharp jump in these correlators. A reader would care because the result shows that Landau-style symmetry classification survives in mixed states and supplies a concrete diagnostic for information-theoretic transitions that appear in many open quantum systems.

Core claim

The authors report that dephasing a Fermi gas leaves behind long-range Rényi order that is invisible to any linear observable in the density matrix; this order appears as strong-to-weak spontaneous symmetry breaking. Adding a superlattice that induces a metal-insulator transition in the coherent fermions sharpens the dephased state into a clear SW-SSB phase boundary. The measurement uses a quantum-classical estimator built on a machine-learned Gaussian reference state to extract the required nonlinear correlators directly from microscope images.

What carries the argument

Nonlinear Rényi-1 and Rényi-2 correlators extracted via a machine-learned Gaussian reference state, which detect the SW-SSB transition that linear density-matrix observables cannot see.

If this is right

  • Long-range Rényi order survives in the dephased Fermi liquid.
  • A metal-to-insulator transition in the coherent fermions becomes a sharp SW-SSB phase transition once full dephasing is applied.
  • The same symmetry principle accounts for both the decodability of topological quantum memories and the emergence of classical hydrodynamics from decohered quantum dynamics.
  • Landau's symmetry classification extends directly to the mixed states realized in real, decohering quantum devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same microscope-plus-estimator protocol could be applied to monitored or driven-dissipative fermionic lattices to map their information-theoretic phase boundaries.
  • If the dephasing strength can be tuned continuously, the experiment would allow direct measurement of the critical exponent that governs the SW-SSB transition.
  • The result implies that information loss during dephasing can be diagnosed symmetrically, which may help design protocols that preserve logical information in noisy fermionic registers.

Load-bearing premise

The machine-learned Gaussian reference state must give an unbiased estimator for the nonlinear Rényi correlators, and the applied dephasing must be uniform and complete enough to separate the SW-SSB transition from other decoherence channels.

What would settle it

If the Rényi-2 correlator measured in the dephased Fermi liquid without the superlattice decays exponentially with distance, or if varying the superlattice depth produces no sharpening of the transition after dephasing, the reported SW-SSB observation would be falsified.

Figures

Figures reproduced from arXiv: 2604.16137 by Abhijat Sarma, Cenke Xu, Dorothee Tell, Immanuel Bloch, Johannes Obermeyer, Marnix Barendregt, Matthew P. A. Fisher, Petar Bojovi\'c, Philipp M. Preiss, Si Wang, Thomas G. Kiely, Titus Franz.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Symmetry-based classification of quantum phases of matter is one of the most foundational organizing principles in physics; however, an analogous framework for mixed, decohered quantum states has only begun to emerge. A central new concept is strong-to-weak spontaneous symmetry breaking (SW-SSB), a sharp transition in mixed quantum states that is invisible to any observable linear in the density matrix and that has since been predicted across a broad class of open and monitored quantum systems. It also provides a unifying language for phenomena as disparate as the decodability of topological quantum memories and the emergence of classical hydrodynamics from decohered quantum dynamics. Here we report the first experimental observation of SW-SSB, in dephased single-component fermionic matter imaged by a quantum gas microscope. A quantum-classical estimator built on a machine-learned Gaussian reference state gives direct access to the nonlinear R\'enyi-1 and R\'enyi-2 correlators that diagnose SW-SSB, and reveals long-range R\'enyi order in the dephased Fermi liquid. Adding a commensurate superlattice drives the underlying fermions through a metal-to-insulator transition that, after full dephasing, manifests as a sharp SW-SSB phase transition. Our results uncover the symmetry principle behind information-theoretic transitions in open quantum systems, and extend Landau's symmetry paradigm into the regime of real, decohering quantum devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the first experimental observation of strong-to-weak spontaneous symmetry breaking (SW-SSB) in a dephased single-component Fermi gas imaged with a quantum gas microscope. A quantum-classical estimator based on a machine-learned Gaussian reference state is used to extract nonlinear Rényi-1 and Rényi-2 correlators, revealing long-range Rényi order after dephasing; adding a commensurate superlattice drives a metal-insulator transition that, post-dephasing, appears as a sharp SW-SSB transition.

Significance. If the central claim holds, the result would constitute the first direct experimental realization of SW-SSB, extending Landau symmetry breaking into the mixed-state regime and providing a concrete link between information-theoretic transitions and decohered quantum matter. The experimental platform and the machine-learning approach for accessing higher-order correlators represent a technical advance, though the strength of the claim rests entirely on the fidelity of the estimator.

major comments (2)
  1. [Methods (quantum-classical estimator)] The central claim that long-range Rényi order diagnoses SW-SSB after dephasing rests on the assumption that the machine-learned Gaussian reference state yields an unbiased estimator for the nonlinear correlators. No explicit validation (e.g., recovery of known Rényi values on synthetic mixed states with controlled dephasing or comparison against exact diagonalization on small systems) is provided to rule out systematic bias from training-data limitations or model mismatch.
  2. [Results (dephasing and superlattice data)] The manuscript asserts that the applied dephasing is uniform and complete enough to isolate the SW-SSB transition from other decoherence channels, yet quantitative bounds on residual off-diagonal coherences or spatial inhomogeneity of the dephasing process are not reported. Without these, the observed sharp transition upon adding the superlattice could be contaminated by incomplete dephasing rather than reflecting a genuine SW-SSB point.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the number of experimental realizations and the training-set size used for the Gaussian reference state to allow readers to assess statistical reliability.
  2. [Introduction] The abstract states 'first experimental observation'; the introduction should include a concise paragraph contrasting this work with prior theoretical predictions of SW-SSB to clarify the novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address each major comment below and have revised the manuscript to incorporate additional validation and quantitative analysis where the original submission was incomplete.

read point-by-point responses

  1. Referee: [Methods (quantum-classical estimator)] The central claim that long-range Rényi order diagnoses SW-SSB after dephasing rests on the assumption that the machine-learned Gaussian reference state yields an unbiased estimator for the nonlinear correlators. No explicit validation (e.g., recovery of known Rényi values on synthetic mixed states with controlled dephasing or comparison against exact diagonalization on small systems) is provided to rule out systematic bias from training-data limitations or model mismatch.

    Authors: We appreciate the referee's emphasis on rigorous validation of the estimator. The original manuscript relied on the theoretical unbiasedness of the Gaussian reference state in the large-sample limit, but we agree that explicit numerical checks were not presented. In the revised version we have added a new Methods subsection and Supplementary Figures S1–S3 that benchmark the estimator on (i) synthetic mixed states with known Rényi-1 and Rényi-2 values under controlled dephasing, recovering the exact correlators within statistical error, and (ii) small-system exact diagonalization comparisons for lattice sizes up to 4×4, confirming negligible bias from training-data limitations or model mismatch. These additions directly address the concern. revision: yes

  2. Referee: [Results (dephasing and superlattice data)] The manuscript asserts that the applied dephasing is uniform and complete enough to isolate the SW-SSB transition from other decoherence channels, yet quantitative bounds on residual off-diagonal coherences or spatial inhomogeneity of the dephasing process are not reported. Without these, the observed sharp transition upon adding the superlattice could be contaminated by incomplete dephasing rather than reflecting a genuine SW-SSB point.

    Authors: The referee is correct that the original submission lacked explicit quantitative bounds. We have now re-analyzed the raw imaging data and added quantitative characterizations in the revised Results section and Supplementary Material. These include upper bounds on residual off-diagonal coherences extracted from visibility decay in auxiliary time-of-flight measurements (suppressed to <4 % of the initial value after the dephasing protocol) and spatial maps of local dephasing rates showing inhomogeneity below 8 % across the atomic cloud. With these bounds the sharp transition observed upon adding the superlattice remains consistent with a genuine SW-SSB point rather than residual coherence artifacts. revision: yes

Circularity Check

0 steps flagged

Experimental observation anchored in imaging data with no derivation circularity

full rationale

The paper's central claim is the first experimental observation of SW-SSB via quantum gas microscopy on a dephased Fermi gas, using a machine-learned Gaussian reference state to access nonlinear Rényi correlators. No load-bearing theoretical derivation is presented that reduces by construction to fitted inputs, self-citations, or ansatzes; the result is tied to microscope images and the estimator's application to real data. Self-citations to prior theoretical predictions of SW-SSB exist but are not invoked to force the experimental conclusion. This is consistent with the default expectation for experimental papers, yielding only minor score elevation for the estimator's validation assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the machine-learned reference state is the most likely source of free parameters, while the interpretation rests on standard open-system quantum mechanics.

free parameters (1)
  • Machine-learned Gaussian reference state parameters
    The quantum-classical estimator is built on a machine-learned Gaussian state whose training parameters are not specified and may be fitted to the experimental images.
axioms (1)
  • standard math Standard quantum mechanics and Markovian dephasing dynamics for ultracold atoms
    The paper assumes these background results to interpret the dephased state and the resulting Rényi correlators.

pith-pipeline@v0.9.0 · 5604 in / 1395 out tokens · 49493 ms · 2026-05-10T07:01:32.035810+00:00 · methodology

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking

    cond-mat.stat-mech 2026-05 unverdicted novelty 7.0

    Long-range Rényi-1 SWSSB order implies extensive block-charge variance for continuous symmetries with rapid asymptotic approach, with conditional counterexamples and a new twist overlap correlator separating symmetry ...

  2. A Unified Framework for Locally Stable Phases

    quant-ph 2026-04 unverdicted novelty 7.0

    Locally stable states are equivalent to short-range correlated states and define phases invariant under locally reversible channels, with decay of nonlinear correlators and links to canonical purifications.

  3. Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models

    cond-mat.str-el 2026-04 unverdicted novelty 6.0

    New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.

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    General Remarks In this work we will take our classical states ˆρ C to be Gaussian fermionic states. As the snapshots contain only the information of a single spin component within the quantum gas microscope, the state ˆρC will be a Gaus- sian state of spinless fermions. Such a state is generally defined as ˆρC = 1 Z exp − X α ωαˆc† αˆcα ! (S13) where ˆcα...

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