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arxiv: 2411.03953 · v1 · submitted 2024-11-06 · ❄️ cond-mat.stat-mech · quant-ph

Emergent dynamical quantum phase transition in a Z₃ symmetric chiral clock model

Ling-Feng Yu , Wei-Lin Li , Xue-Jia Yu , Zhi Li This is my paper

Pith reviewed 2026-05-23 17:45 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords chiral clock modeldynamical quantum phase transitionLee-Yang-Fisher zerosLoschmidt echoZ3 symmetryquench dynamicsdynamical partition function
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The pith

In the Z3 chiral clock model only certain angles in the chiral phase produce dynamical quantum phase transitions after a quench.

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

The paper examines quench dynamics in a Z3 symmetric chiral clock model and shows that dynamical quantum phase transitions arise only when the chiral angle takes particular discrete values. It links this selectivity to the way Lee-Yang-Fisher zeros are distributed in the complex plane for the chosen quench protocol. Non-analytic points appear in the Loschmidt echo return rate precisely when those zeros cross the imaginary axis. An exact expression for the zero locations is derived from the dynamical partition function, allowing all inducing angles to be listed in advance.

Core claim

Chiral phases in the Z3 clock model induce dynamical quantum phase transitions only at special angles; the emergence is controlled by the distribution of Lee-Yang-Fisher zeros of the dynamical partition function, which cross the imaginary axis solely for those angles, producing non-analyticities in the Loschmidt echo return rate whose coordinates are given by a closed-form expression.

What carries the argument

Distribution of Lee-Yang-Fisher zeros of the dynamical partition function, which determines whether the Loschmidt echo return rate develops non-analytic points after the quench.

If this is right

  • All angles that trigger DQPT can be obtained directly from the analytic zero-coordinate expression without further numerical diagonalization.
  • The same zero-crossing criterion predicts additional DQPTs in larger parameter regions of the model.
  • The mapping between chiral phase and DQPT is specific to the quench protocol; different initial states may shift the active angles.
  • The mechanism explains why generic angles in the chiral phase do not produce DQPTs while discrete special angles do.

Where Pith is reading between the lines

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

  • The zero-crossing condition may generalize to other clock models with higher Z_n symmetry if the dynamical partition function admits a similar closed form.
  • Experimental platforms realizing the chiral clock Hamiltonian could test the predicted angles by measuring Loschmidt echoes in cold-atom or ion-trap quenches.
  • If the zeros control the dynamics for generic initial states, the result supplies a diagnostic for the presence of chiral order via quench spectroscopy.

Load-bearing premise

The singularities in the Loschmidt echo are assumed to be fully determined by whether Lee-Yang-Fisher zeros cross the imaginary axis for the specific quench protocol and initial state examined.

What would settle it

Compute the Loschmidt echo return rate for a quench to a chiral angle not listed by the derived zero-coordinate formula and check whether non-analytic points are absent, or appear for an angle the formula predicts should be inactive.

Figures

Figures reproduced from arXiv: 2411.03953 by Ling-Feng Yu, Wei-Lin Li, Xue-Jia Yu, Zhi Li.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The schematic representation of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The rate functions over time under the quench condi [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Panoramic rate function (a) and the corresponding [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Subcomponents’ arguments arg[ [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

We study the quench dynamics in a $Z_3$ symmetric chiral clock model (CCM). The results reveal that chiral phases can lead to the emergence of dynamical quantum phase transition (DQPT). By analyzing Lee-Yang-Fisher zeros' distribution in the complex plane, we uncover the relation between the chiral phase and the emergence of DQPT. In concrete terms, only by taking some special angles can DQPT be induced. We confirm the above relation by computing the non-analytic points in Loschmidt echo return rate function. Furthermore, through the analysis of the corresponding dynamical partition function, we reveal the mechanism of the emergent DQPT and deduce the analytical expression of dynamical partition function's zero points' coordinates. Based on the analytic expression, one can obtain all the angles that induce DQPT's emergence and predict more possible DQPT in the system.

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

1 major / 2 minor

Summary. The manuscript examines quench dynamics in the Z_3-symmetric chiral clock model and claims that dynamical quantum phase transitions (DQPTs) emerge exclusively for certain special angles within the chiral phase. This relation is established by analyzing the distribution of Lee-Yang-Fisher zeros in the complex plane, numerically locating non-analytic points in the Loschmidt-echo return rate, and deriving an analytic expression for the coordinates of the zeros of the dynamical partition function, from which all inducing angles can be obtained and additional DQPTs predicted.

Significance. If the central mapping holds, the work supplies an analytic route from the chiral phase parameters to the locations of DQPTs via the zeros of the dynamical partition function, together with direct numerical confirmation on the Loschmidt echo. The explicit analytic expression for zero coordinates is a concrete strength that permits systematic prediction beyond the numerically studied cases.

major comments (1)
  1. [section deriving the analytic expression for zero coordinates (likely §4 or equivalent)] The central claim that only special angles induce DQPT rests on the assertion that the derived zeros of the dynamical partition function account for all observed non-analyticities in the return rate. The manuscript should explicitly verify, for the quench protocol employed, that no additional singularities arise from the Z_3 chiral terms or from the choice of initial state (e.g., by comparing the analytic zero loci directly against the full set of numerically detected non-analytic points without post-selection).
minor comments (2)
  1. Notation for the dynamical partition function and its zeros should be introduced with a clear equation number at first appearance to avoid ambiguity when the analytic expression is later invoked.
  2. Figure captions for the Loschmidt-echo return-rate plots should state the precise quench parameters and initial state used, so that the numerical confirmation can be reproduced from the text alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the major point below and will incorporate the requested verification in the revised version.

read point-by-point responses

  1. Referee: [section deriving the analytic expression for zero coordinates (likely §4 or equivalent)] The central claim that only special angles induce DQPT rests on the assertion that the derived zeros of the dynamical partition function account for all observed non-analyticities in the return rate. The manuscript should explicitly verify, for the quench protocol employed, that no additional singularities arise from the Z_3 chiral terms or from the choice of initial state (e.g., by comparing the analytic zero loci directly against the full set of numerically detected non-analytic points without post-selection).

    Authors: We agree that an explicit, unfiltered comparison strengthens the central claim. The analytic zeros are obtained from the exact dynamical partition function of the full Z_3 chiral clock Hamiltonian under the chosen quench protocol and initial state; the derivation therefore already incorporates all chiral terms. To make this verification fully transparent, the revised manuscript will include a new figure (or panel) that overlays the analytic zero loci directly onto the complete set of numerically located non-analytic points in the Loschmidt return rate for several representative quenches. No post-selection or filtering will be applied to the numerical data, allowing direct visual confirmation that every detected singularity coincides with a predicted zero and that no extraneous singularities appear. revision: yes

Circularity Check

0 steps flagged

No circularity: analytic zeros derived from dynamical partition function, then used to identify angles

full rationale

The paper derives the coordinates of dynamical partition function zeros directly from the model and quench protocol, then applies that expression to locate the special angles inducing DQPT. This is a standard forward derivation confirmed by separate numerical computation of Loschmidt return-rate non-analyticities. No self-citation chains, no fitted parameters renamed as predictions, and no self-definitional steps are present in the abstract or described workflow. The mapping from zeros to DQPT is presented as an independent analytic result rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract invokes standard complex analysis for locating zeros and the definition of the Loschmidt echo; no new free parameters, ad-hoc axioms, or invented entities are introduced. The central claim rests on the assumption that the dynamical partition function fully encodes the non-analyticities of the return rate.

axioms (2)
  • domain assumption Lee-Yang-Fisher zeros in the complex plane determine the non-analytic points of the Loschmidt echo return rate
    Invoked when relating zero distribution to DQPT emergence
  • domain assumption The quench protocol and initial state are such that the dynamical partition function captures all relevant singularities
    Required for the analytic expression to predict all inducing angles

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