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arxiv: 2512.17333 · v2 · submitted 2025-12-19 · ❄️ cond-mat.stat-mech · quant-ph

Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models

Andrea Pelissetto , Davide Rossini , Ettore Vicari This is my paper

Pith reviewed 2026-05-16 21:06 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords quantum quenchesIsing chaincontinuous quantum transitionfirst-order quantum transitionout-of-equilibrium dynamicsthermalizationmany-body chaos
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The pith

Quantum quenches in the Ising chain produce qualitatively different dynamics when crossing a continuous transition versus a first-order transition.

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

This paper studies sudden changes in the longitudinal magnetic field of the one-dimensional quantum Ising model, from a negative initial value to a positive final value. The quenches cross the line h=0 where the system undergoes either a continuous quantum transition or first-order quantum transitions, depending on the fixed value of the transverse field g. The authors find distinct out-of-equilibrium behaviors in the disordered phase above the critical g, exactly at the continuous transition, and below g_c in the first-order regime. They restrict attention to final Hamiltonians whose spectra are chaotic, so that thermalization can set in at long times. The results clarify how the character of the underlying quantum transition shapes relaxation in non-integrable many-body systems.

Core claim

We investigate the quantum dynamics generated by quenches of the Hamiltonian parameters in the quantum Ising chain with transverse field g and longitudinal field h. We focus on protocols that change h from a negative value h_i < 0 to a positive value h_f > 0, crossing the line of quantum transitions at h=0. For g > g_c the chain remains in the disordered phase; at g = g_c the quench crosses the continuous quantum transition; for g < g_c it crosses the first-order quantum transition line. In the integrable limit h=0 the model maps to free fermions, but any nonzero h_f breaks integrability and places the post-quench spectrum in the chaotic regime where thermalization may occur at long times.We

What carries the argument

The one-dimensional Ising chain with transverse field g and longitudinal field h, subjected to a sudden quench in h across zero at fixed g, analyzed in the chaotic regime of the post-quench Hamiltonian.

If this is right

  • Dynamics in the disordered phase g > g_c remain qualitatively separate from any quench that crosses a transition.
  • Quenches exactly at g = g_c cross the continuous quantum transition and produce a distinct relaxation pattern.
  • Quenches for g < g_c cross the first-order transition line and yield yet another long-time behavior.
  • Because the post-quench spectrum is chaotic, thermalization is expected to appear at late times in all three regimes, but with different transient signatures.

Where Pith is reading between the lines

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

  • The distinction between continuous and first-order crossings may survive in the thermodynamic limit and produce different steady-state properties.
  • Similar quench protocols could be applied to other non-integrable spin chains to test whether the type of transition crossed universally controls relaxation.
  • The results suggest that integrability breaking alone is insufficient to erase memory of the underlying quantum transition in the approach to equilibrium.

Load-bearing premise

The spectrum of the post-quench Hamiltonian lies in the chaotic regime so that thermalization can emerge at asymptotically long times.

What would settle it

Numerical or experimental observation that the long-time dynamics become indistinguishable for g > g_c, g = g_c and g < g_c, or that no thermalization occurs despite the assumed chaotic spectrum.

Figures

Figures reproduced from arXiv: 2512.17333 by Andrea Pelissetto, Davide Rossini, Ettore Vicari.

Figure 1
Figure 1. Figure 1: FIG. 1: The distribution of the level spacings [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The average value [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The ratio [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The magnetization [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The post-QQ mean energy per site ¯e [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The overlap among the initial ground state of [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The diagonal-ensemble magnetization [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: The overlap between the ground state of the Hamil [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: The magnetization (top) and excess bond energy [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Time dependence of the magnetization, compared [PITH_FULL_IMAGE:figures/full_fig_p016_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: The ratio [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: The rescaled normalized distribution of the energy [PITH_FULL_IMAGE:figures/full_fig_p020_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: (Top): The time evolution of the largest eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p020_22.png] view at source ↗
read the original abstract

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse ($g$) and longitudinal ($h$) magnetic fields. This model exhibits a continuous quantum transition (CQT) at $g=g_c$ and $h=0$, and first-order quantum transitions (FOQTs) driven by $h$ along the line $h=0$ ($g<g_c$). In the integrable limit $h=0$, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value $h_i < 0$ to a positive value $h_f>0$. We focus on values of $h_f$ such that the spectrum of the post-QQ Hamiltonian $H(g,h_f)$ lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of $g$, finding qualitatively distinct behaviors for $g > g_c$ (where the chain is in the disordered phase), for $g = g_c$ (QQ across the CQT), and for $g<g_c$ (QQ across the FOQT line).

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 / 1 minor

Summary. The manuscript investigates quantum quenches in the one-dimensional quantum Ising chain with transverse field g and longitudinal field h. It considers protocols that suddenly change h from a negative initial value to a positive final value h_f, crossing either the continuous quantum transition at g = g_c (h=0) or first-order transitions along h=0 for g < g_c. The authors report qualitatively distinct out-of-equilibrium dynamics in three regimes: g > g_c (disordered phase), g = g_c (across the CQT), and g < g_c (across the FOQT line), attributing the distinctions to the post-quench Hamiltonian H(g, h_f) entering a chaotic regime where thermalization can occur at long times. The analysis builds on the exact mapping to free fermions when h=0 and numerical or approximate methods otherwise.

Significance. If the central claims hold after verification, the work would advance understanding of how the type of quantum transition crossed during a quench influences relaxation and thermalization in many-body systems. A strength is the systematic comparison across integrable and non-integrable cases using the model's exact solvability at h=0. The results could inform studies of non-equilibrium dynamics near quantum critical points, provided the chaotic regime is explicitly confirmed.

major comments (1)
  1. [Abstract and model Hamiltonian section] Abstract and the section introducing the post-quench Hamiltonian: The assertion that the spectrum of H(g, h_f) lies in the chaotic regime for the selected finite h_f (allowing thermalization at long times) is not supported by any reported diagnostics such as level-spacing ratio distributions, spectral form factors, or participation ratios. This assumption underpins the interpretation of qualitatively distinct behaviors across the three g regimes, yet near g = g_c or the FOQT line the integrability-breaking effect of h_f may be weak, potentially leading to intermediate statistics rather than full GOE chaos. Without such evidence, the central claim of regime-dependent dynamics risks being under-supported.
minor comments (1)
  1. Figure captions should explicitly list all parameter values (system size L, specific g, h_i, h_f) and the observable plotted to improve reproducibility and clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: The assertion that the spectrum of H(g, h_f) lies in the chaotic regime for the selected finite h_f (allowing thermalization at long times) is not supported by any reported diagnostics such as level-spacing ratio distributions, spectral form factors, or participation ratios. This assumption underpins the interpretation of qualitatively distinct behaviors across the three g regimes, yet near g = g_c or the FOQT line the integrability-breaking effect of h_f may be weak, potentially leading to intermediate statistics rather than full GOE chaos. Without such evidence, the central claim of regime-dependent dynamics risks being under-supported.

    Authors: We agree that the original manuscript did not include explicit diagnostics confirming the chaotic character of the post-quench spectra. The statement in the abstract and model section relies on the general expectation that a finite longitudinal field h_f breaks integrability in the Ising chain, leading to chaotic behavior for the chosen parameters (as supported by prior studies of this model). However, we acknowledge the referee's valid point that this may need verification near g = g_c or along the FOQT line. In the revised manuscript we will add level-spacing ratio distributions (and, where feasible, spectral form factors) computed for representative post-quench Hamiltonians H(g, h_f) in each of the three regimes. These diagnostics will be used to confirm the approach to GOE statistics and thereby strengthen the interpretation of the observed dynamical distinctions. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's analysis proceeds from the standard Jordan-Wigner mapping of the h=0 Ising chain to free fermions, followed by direct numerical or perturbative study of the time evolution after a quench to h_f>0. The statement that non-zero h_f breaks integrability and places the spectrum in a chaotic regime is presented as a general expectation rather than a fitted or self-derived input; the distinct dynamical behaviors for g>gc, g=gc, and g<gc are then extracted from the resulting equations of motion or spectra without reducing any central prediction to a tautological re-expression of the inputs. No load-bearing self-citations, ansatze smuggled via prior work, or renaming of known results appear in the derivation. The chain remains self-contained against the model's Hamiltonian and established many-body techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Relies on standard properties of the Ising model without introducing new free parameters or entities in the abstract.

axioms (2)
  • standard math The quantum Ising chain with h=0 is integrable and mappable to quadratic fermionic theory.
    Stated directly in the abstract as a known fact.
  • domain assumption Nonzero longitudinal field h breaks integrability and places the spectrum in a chaotic regime.
    Invoked to justify expectation of thermalization at long times.

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Forward citations

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