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arxiv: 2606.28750 · v1 · pith:PPJEVD2Ynew · submitted 2026-06-27 · 🪐 quant-ph · cond-mat.str-el

Dissipative phase decision without ground-state preparation

Hao-En Li , Yilun Yang , Lin Lin This is my paper

Pith reviewed 2026-06-30 09:53 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords dissipative coolingquantum phase decisionground-state phasesKitaev honeycomb modelJ1-J2 Heisenberg chaintopological phase transitionsLuttinger parameteropen quantum systems
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The pith

Dissipative evolution under tailored jump operators reveals the ground-state phase from low-energy observables at early times without accurate ground-state preparation.

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

The paper proposes a dynamical method for deciding quantum phases by preparing a representative state and tracking early-time responses of phase-sensitive observables under short-time dissipative cooling tailored to the Hamiltonian. For problems where those observables can be read from the low-energy manifold and the required jump operators are realizable by short Hamiltonian simulation, the dynamics rapidly damps high-energy components and exposes the phase signature well before the system reaches steady state. Demonstrations cover the J1-J2 Heisenberg chain, the Kitaev honeycomb model, and the XXZ chain, including Berezinskii-Kosterlitz-Thouless and topological transitions, with recovery of quantities such as the Luttinger parameter using coarse filters and short evolution. Theoretical justification shows that the same cooling rigorously prepares low-energy manifolds for free-fermion and free-boson systems and is examined for interacting fermions. The results position phase decision as a target for early fault-tolerant quantum hardware.

Core claim

Rather than determining the phase by preparing highly accurate approximations to ground states, we prepare a representative state of a candidate phase and monitor the early-time response of phase-sensitive observables under cooling dynamics tailored to the target Hamiltonian. For a class of phase-decision problems in which the relevant observables can be inferred from the low-energy manifold, and with jump operators implementable using only short-time Hamiltonian simulation, the dissipative evolution rapidly suppresses high-energy components and drives the system into a low-energy manifold whose observables already reveal the underlying ground-state phase, well before mixing to the steady st

What carries the argument

Tailored dissipative cooling dynamics whose jump operators are realized by short-time Hamiltonian simulation; the dynamics suppress high-energy components to access a low-energy manifold whose observables encode the ground-state phase.

If this is right

  • Coarse filter resolutions and short evolution times suffice to recover phase-sensitive quantities such as the Luttinger parameter and topological diagnostics.
  • The strategy applies to the frustrated J1-J2 Heisenberg chain, the Kitaev honeycomb model, and the XXZ chain, including Berezinskii-Kosterlitz-Thouless and topological phase transitions.
  • Cooling dynamics with the described jump operators can rigorously prepare low-energy manifolds for free-fermionic and free-bosonic systems.
  • Phase decision becomes a plausible target for future utility-scale studies on early fault-tolerant quantum devices.

Where Pith is reading between the lines

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

  • The method may reduce circuit depth requirements for phase identification on near-term quantum hardware by replacing deep ground-state preparation circuits with shorter dissipative evolution.
  • The same low-energy-manifold principle could be tested in other open-system protocols where only partial thermalization is feasible.
  • Optimal design of jump operators for strongly interacting cases remains open and could be explored by varying the short-time Hamiltonian segments used to implement them.

Load-bearing premise

The assumption that phase-sensitive observables can be inferred from the low-energy manifold reached by the tailored dissipative dynamics.

What would settle it

A numerical simulation of one of the demonstrated models in which the early-time phase-sensitive observables after the proposed cooling fail to match the known ground-state phase indicators.

Figures

Figures reproduced from arXiv: 2606.28750 by Hao-En Li, Lin Lin, Yilun Yang.

Figure 1
Figure 1. Figure 1: FIG. 1: Conceptual illustration of the static and dynamical viewpoints for solving the phase-decision problem. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Comparison between ideal and realistic filters in [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_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Dissipative dynamics for probing the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Part of the phase diagram of the one-dimensional XXZ model. The blue region denotes the critical, gapless [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The dissipative cooling dynamics of the XX [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The dissipative cooling dynamics of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Populations of 20 lowest energy levels for [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Representative evolution of [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Schematic illustration of the mechanism [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: a, we demonstrate the dynamics of the canonical population operators ⟨nei⟩, defined with respect to the di￾agonal modes of the noninteracting Hamiltonian H0. We set the interaction strength Jz = 0.5, while maintaining a filter resolution of ∆ = 0.5, which remains larger than the free fermion spectral gap. The data show that the non￾interacting canonical occupations are no longer sharply cut off at |εi | =… view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: The “spillover” type filter function in frequency domain. Here [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: The fitted logarithmic coefficient, interpreted as the Luttinger parameter in the TLL regime, for the [PITH_FULL_IMAGE:figures/full_fig_p034_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Fitting the Luttinger parameter [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: The quench dynamics of the [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: The dissipative cooling dynamics of the Kitaev honeycomb model with [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Numerical validations of the realistic filter. Top row: filter profiles. Bottom row: the time evolution of [PITH_FULL_IMAGE:figures/full_fig_p037_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Numerical validation of the realistic filter for a free bosonic mode. The dashed line represents the [PITH_FULL_IMAGE:figures/full_fig_p037_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Numerical validation of the realistic filter for the interacting XXZ model. The results are shown for a [PITH_FULL_IMAGE:figures/full_fig_p038_20.png] view at source ↗
read the original abstract

We propose a dynamical approach to identifying ground-state quantum phases through short-time dissipative cooling. Rather than determining the phase by preparing highly accurate approximations to ground states, we prepare a representative state of a candidate phase and monitor the early-time response of phase-sensitive observables under cooling dynamics tailored to the target Hamiltonian. For a class of phase-decision problems in which the relevant observables can be inferred from the low-energy manifold, and with jump operators implementable using only short-time Hamiltonian simulation, the dissipative evolution rapidly suppresses high-energy components and drives the system into a low-energy manifold whose observables already reveal the underlying ground-state phase, well before mixing to the steady state. We demonstrate this strategy for the frustrated $J_1$--$J_2$ Heisenberg chain, the Kitaev honeycomb model, and the XXZ chain, including Berezinskii--Kosterlitz--Thouless and topological phase transitions. In particular, coarse filter resolutions and short evolution times suffice to recover phase-sensitive quantities such as the Luttinger parameter and topological diagnostics. We further provide theoretical justification that cooling dynamics with such jump operators can rigorously prepare low-energy manifolds for free-fermionic and free-bosonic systems, and investigate this mechanism for interacting fermionic systems. Our results suggest that phase decision is a plausible target for future utility-scale studies on early fault-tolerant 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 / 0 minor

Summary. The manuscript proposes a dynamical approach to ground-state phase decision via short-time dissipative cooling. Rather than preparing accurate ground states, tailored jump operators (implementable via short-time Hamiltonian simulation) drive the system into a low-energy manifold whose phase-sensitive observables reveal the underlying phase well before steady-state mixing. The strategy is demonstrated numerically on the frustrated J1-J2 Heisenberg chain, Kitaev honeycomb model, and XXZ chain (including BKT and topological transitions), with rigorous justification that the dynamics prepare low-energy manifolds for free-fermionic and free-bosonic systems and numerical investigation of the mechanism for interacting fermionic systems.

Significance. If the early-time manifold suppression holds, the approach could enable phase identification on early fault-tolerant devices with substantially reduced evolution times and without full ground-state preparation. The paper's explicit distinction between rigorous free-system guarantees and numerical interacting demonstrations is a strength, as is the coverage of multiple models and diagnostics such as the Luttinger parameter. The result is of interest for near-term quantum simulation but its broader impact depends on establishing greater generality beyond the specific numerics shown.

major comments (2)
  1. [Abstract] Abstract: the central claim is framed for a class of phase-decision problems that includes interacting models (frustrated J1-J2 Heisenberg chain, XXZ chain), yet the manuscript supplies rigorous preparation guarantees only for free-fermionic and free-bosonic systems while relying on model-specific numerical investigation for interacting cases. This distinction is load-bearing for the stated applicability.
  2. [Theoretical justification] Theoretical justification paragraph: the statement that the mechanism is investigated for interacting fermionic systems does not include a general proof that the low-energy manifold reached by the dissipative dynamics encodes the ground-state phase for arbitrary interacting Hamiltonians; the demonstrations remain specific to the three models studied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of clearly delineating the scope of our rigorous results from our numerical demonstrations. We address each major comment below and will make the requested clarifications in a revised version.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim is framed for a class of phase-decision problems that includes interacting models (frustrated J1-J2 Heisenberg chain, XXZ chain), yet the manuscript supplies rigorous preparation guarantees only for free-fermionic and free-bosonic systems while relying on model-specific numerical investigation for interacting cases. This distinction is load-bearing for the stated applicability.

    Authors: We agree that the abstract should more explicitly distinguish the rigorous guarantees (limited to free-fermionic and free-bosonic systems) from the numerical evidence for interacting models. We will revise the abstract to state that the strategy is demonstrated numerically for the J1-J2 Heisenberg chain, Kitaev honeycomb model, and XXZ chain, while rigorous low-energy manifold preparation is proven only for free systems. revision: yes

  2. Referee: [Theoretical justification] Theoretical justification paragraph: the statement that the mechanism is investigated for interacting fermionic systems does not include a general proof that the low-energy manifold reached by the dissipative dynamics encodes the ground-state phase for arbitrary interacting Hamiltonians; the demonstrations remain specific to the three models studied.

    Authors: We acknowledge that the manuscript provides no general proof for arbitrary interacting Hamiltonians and that the demonstrations are specific to the three models. We will revise the theoretical justification paragraph to emphasize that the mechanism is investigated numerically for these specific cases and that a general proof for all interacting systems lies outside the present scope. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper introduces a dissipative cooling strategy for phase identification, with explicit separation between rigorous guarantees (free-fermion/boson systems) and numerical investigation (interacting models like J1-J2 and XXZ). No equations, fitted parameters, or self-citations are shown to reduce any central claim to a tautology or input by construction. The low-energy manifold inference and jump-operator implementation are presented as independent assumptions whose validity is tested externally via simulation and free-system proofs, not derived from the target observables themselves. This matches the default expectation of non-circularity for a methods paper whose core content is a new dynamical protocol rather than a closed algebraic reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; all such elements remain unknown.

pith-pipeline@v0.9.1-grok · 5770 in / 1127 out tokens · 30986 ms · 2026-06-30T09:53:29.400671+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

13 extracted references

  1. [1]

    The term “bulk” means that we apply the coupling on all sites of the system

    Free fermionic systems Let us consider a general quadratic fermionic Hamiltonian H= LX i,j=1 Fijc† i cj,(B7) and bulk coupling operators{c † i , ci}L i=1 to construct the Lindbladian jump operators for dissipative cooling dynamics. The term “bulk” means that we apply the coupling on all sites of the system. We first simplify the free-fermionic Hamiltonian...

  2. [2]

    Diagonalize the Hermitian matrixF=Udiag(ε k)L k=1U †, and chooseec† k =PL j=1 Ujk c† j such that H= LX k=1 εkec† keck.(B8) We calleck the canonical modes and assumeε k ̸= 0 for allk

  3. [3]

    Here we usen k to denote the quasiparticle number operator on thek-th canonical mode, i.e

    Apply the particle–hole transformation bk := ( eck,ifε k >0, ec† k,ifε k <0, (B9) so that each mode has positive excitation energyλ k: H=E 0 + LX k=1 |εk|b† kbk =:E 0 + LX k=1 λkb† kbk =E 0 + LX k=1 λknk,(B10) A ground state is the quasiparticle vacuum state|ψ 0⟩=|0⟩ b satisfyingb k |ψ0⟩= 0 for allk, and the ground state energy isE 0 = P k:εk<0 εk. Here w...

  4. [4]

    The Hamiltonian and the coupling operator are H= Ωa †a=: ΩN(Ω>0), A=a+a †.(B35) Here N:=a †a(B36) is the number operator

    Free bosonic systems We begin with the single bosonic mode. The Hamiltonian and the coupling operator are H= Ωa †a=: ΩN(Ω>0), A=a+a †.(B35) Here N:=a †a(B36) is the number operator. Using free-bosonic version of the Thouless theorem Eq. (B17), we have eiHs ae−iHs =e −iΩsa, e iHs a†e−iHs =e iΩsa†.(B37) Therefore, the jump operator is constructed as K= Z ∞ ...

  5. [5]

    squeezed number operator

    Additional results on free bosonic systems Since the steady state is a Gaussian state, we could also understand the free bosonic systems by directly solving the steady state or the covariance matrix. In this section, we present some additional results about the steady state of the free bosonic system such as the trace-distance convergence and the generali...

  6. [6]

    Kitaev honeycomb model Besides the Chern number, another phase-sensitive diagnostic for this phase transition is the mutual information between the two sites in the unit cell [153], which can be computed as I(sA,sB) = 1−H b 1 2 + 2⟨Sz sASz sB⟩ ,(D2) since for the states considered here the reduced density matrix of the two sites has an explicit form ρsA,s...

  7. [7]

    The results are shown in Fig

    Trends in the realistic cooling dynamics for free and interacting systems Free fermions.We provide more results on the dissipative cooling for the tight-binding model that is equivalent to the XX model by Jordan–Wigner transformation H= L−1X i=1 (c† i+1ci +c † i ci+1).(D4) Here we apply the same setting of the initial state and jump operators as in Sectio...

    2010

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    The gauge field is defined on the bonds as uij := 2iηα i ηα j (E2) ifi, jare connected by anα-type bond. It is easy to check that for any bonds⟨i, j⟩ α(i,j) and⟨k, l⟩ α(k,l), the gauge field satisfies the constraint [uij,u kl] = 0,[u ij, H] = 0.(E3) This means that each operatoru ij, together with the Hamiltonian can be simultaneously diagonalized in some...

  9. [9]

    We will discuss the details of the simulation of the dissipative dynamics in Section G 2

    Chern number and purity gap We could probe the topological properties of the states along the dissipative dynamics by evaluating the Chern number of the covariance matrix Γ in the real space, defined as Γsµ,tν = i 2 Tr (ρ[ηsµ, ηtν]) = i⟨ηsµηtν⟩ − i 2 δsµ,tν, µ, ν=A, B,(F1) which only involves the two-point correlation functions in the real space and can b...

  10. [10]

    A simple mechanism for dissipative preparation of Chern insulators We explain how dissipative protocols can evade the unitary topological obstruction to preparing a Chern insulator. Consider a general two-band Chern insulator with Bloch Hamiltonian [155] H(q) =d(q)·σ= dz(q)d x(q)−id y(q) dx(q) + idy(q)−d z(q) ,σ= (σ x, σy, σz),(F13) The Qi–Wu–Zhang model ...

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    Probing the topological properties with realistic filters In Section III C, we demonstrate that the ground-state topological phase of the Kitaev honeycomb model can be probed by computing the Chern number directly from finite-filter-resolution dissipative dynamics. Following the approach in [97], computing the Chern number only requires distinguishing the...

  12. [12]

    pure N´ eel state

    The XX model with bulk cooling a. Solving the 1-RDM dynamics We recall that the XX model can be fermionized into a free fermionic model by the Jordan–Wigner transformation, and the resulting Hamiltonian is given by Eq. (26). We consider the bulk cooling, where the coupling operators are chosen as the local fermionic creation and annihilation operators{c i...

  13. [13]

    anomalous

    The Kitaev honeycomb model with local Majorana cooling a. Solving the covariance matrix dynamics We next discuss the Kitaev honeycomb model, where the jump operators are chosen as the local Majorana operators {ηsA, ηsB}s. We recall that, after fixing theZ 2 gauge and diagonalizing the Hamiltonian as discussed in Appendix E, the Kitaev honeycomb model can ...