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arxiv: 2103.02626 · v6 · submitted 2021-03-03 · ❄️ cond-mat.stat-mech · hep-lat· quant-ph

Coherent and dissipative dynamics at quantum phase transitions

Davide Rossini , Ettore Vicari This is my paper

Pith reviewed 2026-05-24 13:26 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech hep-latquant-ph
keywords quantum phase transitionsdynamic scalingquantum quenchesdissipative dynamicsrenormalization groupcritical phenomenamany-body systems
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The pith

Dynamic scaling laws extend equilibrium descriptions to quenches, passages, and dissipation at quantum phase transitions.

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

This review establishes how the scaling framework for equilibrium quantum phase transitions, based on the quantum-to-classical mapping and renormalization-group theory, can be extended to out-of-equilibrium settings. It shows that dynamic scaling laws describe instantaneous quenches and slow passages across the transitions. The paper also covers the scaling at first-order quantum transitions, which depends strongly on boundary conditions, and treats dissipation as a perturbation that affects only low-energy modes. Readers would care because these extensions allow predictions for the behavior of quantum many-body systems under realistic conditions involving time-dependent protocols and environmental interactions.

Core claim

The paper claims that coherent and dissipative dynamics at quantum phase transitions are governed by dynamic scaling frameworks obtained by extending the equilibrium scaling laws from the quantum-to-classical mapping and renormalization-group theory, with dissipation acting as a perturbation when it excites only low-energy critical modes.

What carries the argument

Dynamic scaling frameworks derived by extending equilibrium scaling laws using the quantum-to-classical mapping and renormalization-group theory of critical phenomena.

If this is right

  • Quenches across quantum transitions exhibit scaling behaviors predictable from equilibrium exponents.
  • Slow passages through the transition follow dynamic scaling relations.
  • Weak dissipation leads to specific modifications of the critical dynamics when limited to low-energy modes.
  • First-order quantum transitions show exponential or power-law scaling depending on boundary conditions.
  • The interplay between critical modes and dissipative mechanisms is nontrivial only under certain physical conditions.

Where Pith is reading between the lines

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

  • These scaling approaches could guide the design of experiments in quantum simulators to test dynamic critical behavior.
  • Connections may exist to classical dissipative phase transitions in other contexts.
  • Further work might explore cases where dissipation excites higher-energy modes beyond the perturbative regime.
  • Applications to specific models like the Ising chain could yield testable predictions for real systems.

Load-bearing premise

The quantum-to-classical mapping and renormalization-group scaling laws from equilibrium continuous transitions remain valid in the dynamic and weakly dissipative regimes.

What would settle it

An experiment on a quantum many-body system near a phase transition where the observed scaling of relaxation times or correlation lengths during a quench deviates from the predicted dynamic scaling exponents.

Figures

Figures reproduced from arXiv: 2103.02626 by Davide Rossini, Ettore Vicari.

Figure 1
Figure 1. Figure 1: Sketch of the phase diagram, in the T-g plane, for quantum Ising systems (6). Panel a) is for systems in d > 1 dimensions: at finite temperature, a line of classical transitions separates an ordered phase from a disordered phase, terminating at the QCP (for T = 0, g = gc). The theory of phase transitions in classical systems driven by thermal fluctuations can be applied within the shaded blue region across… view at source ↗
Figure 2
Figure 2. Figure 2: Three dimensional successive snapshots showing the velocity distribution data for a gas of rubidium atoms, which [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sketch of the phase diagram, in the T-µ plane, for the BH model in the hard-core U → ∞ limit (27). We adopt units of the hopping parameter t. Panel a) shows the 3d case: The BEC phase is restricted to a finite region for |µ| ≤ 6. It is bounded by a BEC transition line Tc(µ), which satisfies Tc(µ) = Tc(−µ) due to a particle-hole symmetry. Its maximum occurs at µ = 0, where [186, 190] Tc(µ = 0) = 2.01599(5);… view at source ↗
Figure 4
Figure 4. Figure 4: Sketch of the zero-temperature mean-field phase diagram, in the [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sketch which highlights the emergence of the critical modes within a trap. [PITH_FULL_IMAGE:figures/full_fig_p032_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The particle density vs. x/` for p = 2 and several values of the chemical potential µ, as obtained from the LDA, cf. Eq. (83), and numerical calculations on a large chain with ` = 200. The differences are hardly visible in the figure. Adapted from Ref. [318]. is reported in Eq. (76). The corresponding Fermi momentum is kF = πf. In the following, f will always denote the value for the infinite homogeneous c… view at source ↗
Figure 7
Figure 7. Figure 7: FSS of the energy difference of the lowest states and magnetization of the quantum Ising chain with OFBC, at [PITH_FULL_IMAGE:figures/full_fig_p039_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Central magnetization Mc ≡ mL/2/m0 (normalized so that it ranges from -1 to 1) [panel (a)] and energy gap ∆ [panel (b)] in the quantum Ising chain with EFBC, as a function of the longitudinal field h, for fixed transverse field g = 0.8. The various data sets correspond to different system sizes, as indicated in the legend. The continuous vertical lines and arrows denote the magnetic fields htr(L) correspon… view at source ↗
Figure 9
Figure 9. Figure 9: The central magnetization Mc, defined in [PITH_FULL_IMAGE:figures/full_fig_p041_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The scaling functions Dn(ζs) of Eq. (119) (dashed lines) and numerical data (symbols) for the ratio ∆n(L, ζ)/∆(L, ζc) as functions of the scaling variable ζs, for n = 1 (bottom) and n = 2 (top), separated by the dotted line. Numerical data clearly approach the g-independent scaling curves Dn(ζs) (differences are hardly visible). Adapted from Ref. [56]. for L → ∞, keeping the scaling variable ζs fixed. The… view at source ↗
Figure 11
Figure 11. Figure 11: Fidelity susceptibility χA(L, h) for the quantum Ising ring (113) at fixed g, associated with changes of the longitudinal parameter h, for some values of L. Panel (a) is for g = 0.9 and ζ = 1 (PBC), for which one obtains the scaling variable Φ = 2m0hL/∆(L). Panel (b) is for g = 0.5 and ζ = −1 (ABC), for which the scaling variable Φ = hL3 can be used. The two insets display curves for χA/(∂Φ/∂h) 2 , which … view at source ↗
Figure 12
Figure 12. Figure 12: Magnetization for fixed Φ = 1 and for two different rescaled times Θ. The curves are plotted against the rescaled [PITH_FULL_IMAGE:figures/full_fig_p059_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Temporal behavior of the Loschmidt echo Q(t) defined in Eq. (185) for δw = −2, and two different values of Φ = 1 (a) and Φ = 3 (b). Data are plotted against the rescaled time Θ = L−z t, so that the convergence to a scaling function, in the large-L limit, is clearly visible. Adapted from Ref. [527]. 8.4. Scaling behavior of the Loschmidt echo The Loschmidt amplitude quantifies the deviation of the post-que… view at source ↗
Figure 14
Figure 14. Figure 14: Scaling of the modulus of the characteristic function [PITH_FULL_IMAGE:figures/full_fig_p063_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Temporal behavior of the entanglement entropy ∆ [PITH_FULL_IMAGE:figures/full_fig_p064_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The large-time limit of the transverse magnetization for the quantum XY chain with different anisotropies [PITH_FULL_IMAGE:figures/full_fig_p065_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Finite-size features of the temporal behavior of the transverse magnetization after a quench from [PITH_FULL_IMAGE:figures/full_fig_p066_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: A sketch containing the idea beyond the KZ mechanism. The green and red curves respectively indicate the [PITH_FULL_IMAGE:figures/full_fig_p069_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Rescaled correlations λ C(x, t) (a) and λ 2 G(x, t) (b), at fixed x/λ = 1 (results for other values of x/λ show analogous behaviors), for the unitary dynamics of the Kitaev quantum wire in the thermodynamic limit, as a function of the rescaled time Ωt. The correlation functions C and G are defined in Eqs. (232b) and (232c), respectively. Different line styles stand for various values of the length scale λ… view at source ↗
Figure 20
Figure 20. Figure 20: Rescaled correlations L C(x, t) (a) and L2 G(x, t) (b), defined in Eqs. (232b) and (232c) respectively, as a function of the rescaled time Ωt, fixing the initial Hamiltonian parameter wi = −0.5. We also fix x/L = 1/4 and Υ = 0.1. Different lines are for various sizes L, as indicated in the legend. The insets show magnifications of the main frames in the regions 6 ≤ Ωt ≤ 8 enclosed in the blue boxes, to hi… view at source ↗
Figure 21
Figure 21. Figure 21: Average magnetization M for the quantum Ising chain with OFBC, after a sudden quench of the longitudinal field close to the FOQT, as a function of the rescaled time variable Θ ∼ L−2 t. We fix g = 0.5 and the values of the rescaled variables Φi and Φ (see legends in the two panels). Different data sets are for various chain lengths L, as indicated in the legend. In both cases, as L increases, the data nice… view at source ↗
Figure 22
Figure 22. Figure 22: Sketch representing a qubit q (red arrow) coupled to an environment system S modeled by a quantum many-body spin chain (blue arrows). In the figure, homogeneous couplings are considered, however more general inhomogeneous (partial or local) couplings can be assumed. the decoherence growth rate at CQTs turns out to be characterized by power laws L ζ of the size L, with exponents ζ that are generally larger… view at source ↗
Figure 23
Figure 23. Figure 23: Decoherence function D versus the rescaled time Θ, for a qubit coupled to Ising spin-chain systems with PBC and of different lengths L at the CQT, g = gc = 1 [left panel (a)], or at the FOQT, g = 0.9 [right panel (b)]. All numerical data are for a qubit-system coupling realized through u = 0 and v 6= 0 in Eq. (247), such that [Hˆq, HˆqS] 6= 0. We fix Φw = 0.8, Φv = 1, Λ = 0.5, while the qubit is initializ… view at source ↗
Figure 24
Figure 24. Figure 24: Scaling of the function Q vs. the rescaled time Θ, for three distinct situations of the Ising system S: (a) on the FOQT line, for g = 0.9; (b) at the CQT, for g = gc = 1; (c) in the disordered phase, for g = 2. The evaluated growth-rate function quantifies the sensitivity of the qubit coherence to the coupling v. As in [PITH_FULL_IMAGE:figures/full_fig_p084_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Sketch of a quantum spin-chain model locally and globally coupled to external baths. Neighboring spins are coupled [PITH_FULL_IMAGE:figures/full_fig_p090_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Dynamic scaling of the correlation function [PITH_FULL_IMAGE:figures/full_fig_p093_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Time behavior of the longitudinal magnetization for a quantum Ising ring close to the FOQT, with [PITH_FULL_IMAGE:figures/full_fig_p095_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Rescaled correlations λ P(x, t) at fixed initial wi, for the dissipative Kitaev quantum wire in the thermodynamic limit, as a function of the scaling variable Ωt. Here we fix x/λ = 1 and Γs = 0.5. Each panel refers to a specific type of dissipation mechanism [see Eq. (317)]: decay (a), pumping (b), and dephasing (c). The color code refers to wi = −0.1 (black) and wi = −0.5 (red). Different line styles are… view at source ↗
Figure 29
Figure 29. Figure 29: The rescaled correlation L P(x, t), with x/L = 1/4, as a function of Ωt, fixing the initial Hamiltonian parameter wi = −0.1 (left panels, black curves), −0.2 (central panels, red curves), and −0.5 (right panels, blue curves). Different line styles stand for various L (see legend). The lower panels show magnifications of the upper ones, for 6 ≤ Ωt ≤ 9. We fix Υ = 0.1 and Γ = 1, with dissipation given by in… view at source ↗
Figure 30
Figure 30. Figure 30: Sketch of a quantum-measurement protocol: A quantum spin system, initially frozen in its ground state at quantum [PITH_FULL_IMAGE:figures/full_fig_p100_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Time behavior of Rχ in the quantum Ising chain at criticality, for various sizes. Random measurements are either along the longitudinal [panel (a)] or the transverse [panel (b)] direction. Here tm = 0.1, while p = 1/L2 has been fixed according to the guess (335). The two insets display data for specific values of Θ (dashed lines in the main frames), showing that the convergence to the asymptotic behavior … view at source ↗
read the original abstract

The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we first give a pedagogical introduction to the equilibrium behavior of systems in that context, whose scaling framework is essentially developed by exploiting the quantum-to-classical mapping and the renormalization-group theory of critical phenomena at continuous phase transitions. Then we specialize to protocols entailing the out-of-equilibrium quantum dynamics, such as instantaneous quenches and slow passages across quantum transitions. These are mostly discussed within dynamic scaling frameworks, obtained by appropriately extending the equilibrium scaling laws. We review phenomena at first-order quantum transitions as well, whose peculiar scaling behaviors are characterized by an extreme sensitivity to the boundary conditions, giving rise to exponentials or power laws for the same bulk system. In the last part, we cover aspects related to the effects of dissipative interactions with an environment, through suitable generalizations of the dynamic scaling at quantum transitions. The presentation is limited to issues related to, and controlled by, the quantum transition developed by closed many-body systems, treating the dissipation as a perturbation of the critical regimes, as for the temperature at the zero-temperature quantum transition. We focus on the physical conditions giving rise to a nontrivial interplay between critical modes and various dissipative mechanisms, generally realized when the involved mechanism excites only the low-energy modes of the quantum transitions.

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

0 major / 2 minor

Summary. This review paper offers a pedagogical introduction to the equilibrium scaling behavior at quantum phase transitions using the quantum-to-classical mapping and renormalization-group theory. It then extends these ideas to out-of-equilibrium dynamics through dynamic scaling frameworks for quenches and slow passages across the transition. The manuscript also addresses scaling at first-order quantum transitions, emphasizing sensitivity to boundary conditions, and concludes with a discussion of dissipative effects treated as perturbations that excite only low-energy modes, analogous to finite-temperature effects.

Significance. If the summaries of the cited literature are accurate, this review provides a valuable organized framework for understanding the interplay of quantum and thermal fluctuations in both coherent and dissipative regimes at quantum phase transitions. It highlights controlled extensions of equilibrium scaling laws, which can guide further research in nonequilibrium many-body physics.

minor comments (2)
  1. [Abstract] Abstract: the phrase 'suitable generalizations of the dynamic scaling' is used without naming the primary references or models that define those generalizations; adding one or two key citations here would improve immediate accessibility.
  2. [Last part (dissipative interactions)] The final section states the scope is limited to dissipation exciting only low-energy modes, but a single sentence contrasting this with the high-energy excitation regime (even if outside scope) would sharpen the boundary of applicability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our review, as well as the recommendation for minor revision. No major comments were listed in the report.

Circularity Check

0 steps flagged

Review paper summarizing external results; no original derivations present

full rationale

This is a review article that provides a pedagogical introduction to equilibrium scaling at QPTs via quantum-to-classical mapping and RG theory (citing external literature), then organizes extensions to dynamic quenches, slow passages, first-order transitions, and weak dissipation as perturbations. The text explicitly scopes claims to controlled extensions of equilibrium frameworks and states that it covers 'issues related to, and controlled by, the quantum transition developed by closed many-body systems' without introducing new derivations or self-referential predictions. All load-bearing content reduces to cited external results rather than internal fits or self-citations. No circular steps identified.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper; the ledger entries reflect the underlying literature on quantum phase transitions rather than new postulates introduced here.

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Forward citations

Cited by 1 Pith paper

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