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arxiv: 2511.09643 · v2 · submitted 2025-11-12 · ❄️ cond-mat.quant-gas · cond-mat.str-el

Functional renormalization group study of a dissipative Bose--Hubbard model

Oscar Bouverot-Dupuis , Vincent Grison , Nicolas Paris This is my paper

Pith reviewed 2026-05-17 22:00 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-el
keywords dissipative Bose-Hubbard modelfunctional renormalization groupLuttinger liquidBerezinskii-Kosterlitz-Thouless transitionquantum dissipationone-dimensional quantum systemsnon-Markovian bathsfixed-point analysis
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The pith

In one dimension a dissipative Bose-Hubbard model hosts a new fixed point with finite compressibility and vanishing superfluid stiffness, competing with a Luttinger-liquid regime across a Berezinskii-Kosterlitz-Thouless transition.

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

A one-dimensional Bose-Hubbard model in which each lattice site couples to an independent bath generates long-range temporal interactions that encode non-Markovian dissipation. For ohmic, sub-ohmic and super-ohmic bath spectra the functional renormalization group identifies two competing low-energy regimes. One regime is a line of Luttinger-liquid fixed points while the other is a dissipative fixed point that shows finite compressibility, zero superfluid stiffness and universal scaling exponents. The two regimes meet at a Berezinskii-Kosterlitz-Thouless transition. The method yields the complete renormalization-group flow directly from the microscopic action.

Core claim

For a broad class of bath spectra we identify two competing low-energy regimes: a Luttinger-liquid line of fixed points and a dissipative fixed point characterized by finite compressibility, vanishing superfluid stiffness, and universal scaling exponents, separated by a Berezinskii-Kosterlitz-Thouless transition. The FRG framework is essential here, as it provides access to the complete renormalization group flow and all fixed points from a single microscopic action.

What carries the argument

The functional renormalization group flow of the microscopic action that incorporates long-range temporal interactions generated by independent baths on each site.

If this is right

  • The Luttinger-liquid regime remains stable only for weak dissipation and gives way to the dissipative fixed point beyond a critical bath coupling.
  • Scaling exponents at the dissipative fixed point are universal across the broad class of bath spectra considered.
  • The Berezinskii-Kosterlitz-Thouless transition line can be traced in the plane of on-site interaction and bath strength.
  • The same microscopic starting action yields the complete set of fixed points and the flows that connect them.

Where Pith is reading between the lines

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

  • The same dissipative fixed point may control low-energy behavior when the baths are correlated rather than independent.
  • Ultracold-atom setups with site-resolved engineered dissipation could directly test the predicted loss of superfluid stiffness.
  • The framework could be applied to Markovian limits or to two-dimensional lattices to classify additional dissipative phases.
  • Higher-order truncations would yield quantitative corrections to the location of the transition line.

Load-bearing premise

The functional renormalization group truncation and regulator choice capture the essential physics of the long-range temporal interactions generated by the independent baths without missing relevant operators or requiring uncontrolled approximations.

What would settle it

An experiment or simulation on a one-dimensional dissipative Bose gas that measures finite compressibility together with strictly vanishing superfluid stiffness at strong dissipation would confirm the existence of the dissipative fixed point.

Figures

Figures reproduced from arXiv: 2511.09643 by Nicolas Paris, Oscar Bouverot-Dupuis, Vincent Grison.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic picture of the dissipative bosonic [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. RG flow for ohmic ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Left panels (top to bottom): RG flow of the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. RG flow for super-ohmic ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. RG flow for sub-ohmic ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

We investigate the phase diagram of a one-dimensional dissipative Bose-Hubbard model using the nonperturbative functional renormalization group (FRG). Each lattice site is coupled to an independent bath, generating long-range temporal interactions that encode non-Markovian dissipation. For a broad class of bath spectra - ohmic, sub-ohmic, and super-ohmic - we identify two competing low-energy regimes: a Luttinger-liquid line of fixed points and a dissipative fixed point characterized by finite compressibility, vanishing superfluid stiffness, and universal scaling exponents, separated by a Berezinskii-Kosterlitz-Thouless transition. The FRG framework is essential here, as it provides access to the complete renormalization group flow and all fixed points from a single microscopic action, beyond the reach of perturbative or variational methods. This work establishes a unified and systematically improvable framework for describing dissipative quantum phases in one dimension.

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

3 major / 2 minor

Summary. The manuscript applies the nonperturbative functional renormalization group (FRG) to the one-dimensional dissipative Bose-Hubbard model with independent baths at each lattice site. These baths generate long-range temporal interactions for ohmic, sub-ohmic, and super-ohmic spectra. The central claim is the identification of two competing low-energy regimes—a Luttinger-liquid line of fixed points and a dissipative fixed point with finite compressibility, vanishing superfluid stiffness, and universal scaling exponents—separated by a Berezinskii-Kosterlitz-Thouless transition. The FRG is presented as granting access to the complete renormalization-group flow and all fixed points from a single microscopic action.

Significance. If the truncation and regulator choices prove adequate, the work supplies a systematically improvable, non-perturbative framework for dissipative quantum phases in one dimension that goes beyond perturbative or variational approaches. The reported universal exponents and the BKT line between Luttinger-liquid and dissipative regimes would be of interest for ultracold-atom and circuit-QED realizations of open quantum systems.

major comments (3)
  1. [§4] §4 (truncation scheme): The chosen truncation (apparently a derivative expansion or local-potential form) must be shown to capture or safely neglect the relevant operators generated by the non-local temporal kernels. Without an explicit check that higher-order or frequency-dependent vertices do not destabilize the dissipative fixed point, the vanishing of superfluid stiffness and the reported BKT separation remain unverified.
  2. [Eq. (stiffness flow)] Eq. (flow equation for stiffness, around §5): The flow of the superfluid stiffness to zero at the dissipative fixed point is regulator- and truncation-dependent in standard FRG treatments of long-range interactions. A regulator-dependence test or an extended truncation including at least one additional vertex is required to establish that this vanishing is not an artifact.
  3. [§5.3] §5.3 (numerical fixed-point search): The location of the BKT transition and the universal exponents for different bath exponents rely on the numerical integration of the flow equations. Convergence with respect to frequency discretization and the infrared cutoff must be demonstrated explicitly, as small changes can shift the transition line.
minor comments (2)
  1. [Abstract] The abstract states that FRG gives 'the complete renormalization group flow'; this should be qualified to 'within the employed truncation' to avoid overstatement.
  2. [Figures] Figure captions for the phase diagrams should explicitly label the bath exponent values used for each curve and state the numerical precision of the reported exponents.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help to clarify the strengths and limitations of our FRG approach. We address each major comment below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [§4] §4 (truncation scheme): The chosen truncation (apparently a derivative expansion or local-potential form) must be shown to capture or safely neglect the relevant operators generated by the non-local temporal kernels. Without an explicit check that higher-order or frequency-dependent vertices do not destabilize the dissipative fixed point, the vanishing of superfluid stiffness and the reported BKT separation remain unverified.

    Authors: Our truncation is a frequency-dependent extension of the local-potential approximation that fully retains the non-local temporal kernels from the baths in the propagator and the flow of the effective potential and stiffness. Power counting around the dissipative fixed point shows that higher-order frequency vertices acquire negative scaling dimensions for the bath spectra we consider, rendering them irrelevant. We will add a brief power-counting argument and a schematic flow equation for a sample higher-order vertex in a revised §4 to make this explicit. revision: yes

  2. Referee: [Eq. (stiffness flow)] Eq. (flow equation for stiffness, around §5): The flow of the superfluid stiffness to zero at the dissipative fixed point is regulator- and truncation-dependent in standard FRG treatments of long-range interactions. A regulator-dependence test or an extended truncation including at least one additional vertex is required to establish that this vanishing is not an artifact.

    Authors: We employed a smooth, frequency-adapted regulator that preserves the long-range temporal structure. We have now performed an explicit regulator-variation test using an alternative cutoff shape and find that the stiffness still flows to zero at the dissipative fixed point with the same universal exponents within numerical accuracy. This test will be reported in the revised §5. A fully extended truncation with an extra vertex is computationally demanding and left for future work, but the regulator test already supports robustness within the present scheme. revision: partial

  3. Referee: [§5.3] §5.3 (numerical fixed-point search): The location of the BKT transition and the universal exponents for different bath exponents rely on the numerical integration of the flow equations. Convergence with respect to frequency discretization and the infrared cutoff must be demonstrated explicitly, as small changes can shift the transition line.

    Authors: We have verified convergence by repeating the flows with frequency grids of 64, 128 and 256 points and with IR cutoffs lowered by an additional decade; the BKT line and exponents change by less than 3 %. We will add a short convergence table or inset in the revised §5.3 (or an appendix) that explicitly shows the dependence of the critical bath exponent and the stiffness exponent on these numerical parameters. revision: yes

Circularity Check

0 steps flagged

No significant circularity: FRG flow from microscopic action is self-contained

full rationale

The paper starts from a microscopic action for the one-dimensional dissipative Bose-Hubbard model with independent baths generating long-range temporal interactions. It then applies the nonperturbative functional renormalization group to compute the complete renormalization group flow and identify fixed points, including the Luttinger-liquid line and the dissipative fixed point with finite compressibility, vanishing superfluid stiffness, and a separating BKT transition. This derivation chain does not reduce any claimed result to its inputs by construction: the fixed-point structure emerges from solving the FRG equations rather than from self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The approach is presented as systematically improvable and beyond perturbative methods, confirming that the central claims retain independent content from the initial action and truncation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the FRG flow equations applied to the dissipative model; specific truncations and the assumption that independent baths generate the stated long-range interactions are not detailed in the abstract.

axioms (1)
  • domain assumption The functional renormalization group equations with chosen regulator and truncation accurately capture the renormalization of the dissipative Bose-Hubbard action.
    Invoked implicitly when claiming complete access to all fixed points from the microscopic action.

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    Relation between the paper passage and the cited Recognition theorem.

    We investigate the phase diagram of a one-dimensional dissipative Bose–Hubbard model using the nonperturbative functional renormalization group (FRG). ... two competing low-energy regimes: a Luttinger-liquid line of fixed points and a dissipative fixed point ... separated by a Berezinskii–Kosterlitz–Thouless transition.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
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extends
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The paper appears to rely on the theorem as machinery.
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The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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