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Interacting bosons with Ohmic dissipation undergo a superconductor-metal transition in the Wilson-Fisher class with dynamical exponent z approximately 2

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load-bearing objection Derives dissipative TDGL from 1D boson puddles with a controlled mapping but the universality assignment rests on the completeness of the operator content after the puddle construction. the 1 major comments →

arxiv 2605.30746 v2 pith:NM7G3IGK submitted 2026-05-29 cond-mat.mes-hall cond-mat.quant-gascond-mat.str-elcond-mat.supr-conquant-ph

Superconductor-"Metal" Transition of One-dimensional Interacting Bosons with Ohmic Quantum Dissipation

Miguel A. Cazalilla This is my paper
classification cond-mat.mes-hall cond-mat.quant-gascond-mat.str-elcond-mat.supr-conquant-ph
keywords one-dimensional bosonsOhmic quantum dissipationsuperconductor-metal transitionWilson-Fisher universality classdissipative Mott insulatorphase diagrambosonization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper examines a one-dimensional lattice of interacting bosons subject to onsite phase dissipation modeling coupling to a diffusive normal metal. It identifies two phases at commensurate filling: a dissipative Mott insulator with exponentially decaying phase correlations and a dissipative Bose-Einstein condensate with long-range order. By modeling the Mott phase as an array of dissipative boson puddles and deriving the time-dependent Ginzburg-Landau theory, the transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent z approximately 2. At larger doping, a pseudospin chain mapping combined with bosonization establishes the superconducting phase as stable even for arbitrarily small dissipation.

Core claim

The D-Mott to D-BEC transition criticality belongs to the Wilson-Fisher universality class with dynamical exponent z≈2, obtained by deriving the dissipative TDGL theory from the microscopic picture of weakly coupled dissipative boson puddles. At larger doping the D-BEC phase is the ground state for non-vanishing but arbitrarily small dissipation.

What carries the argument

The dissipative time-dependent Ginzburg-Landau theory derived from the array of dissipative boson puddles whose size is set by the phase-slip length.

Load-bearing premise

That the commensurate system maps to an array of dissipative boson puddles with size given by the phase-slip length, and that bosonization plus pseudospin mapping produces the Wilson-Fisher fixed point without extra relevant operators.

What would settle it

Measuring dynamical critical exponent z significantly different from 2 or correlation functions not matching Wilson-Fisher predictions at the D-Mott to D-BEC transition.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The D-Mott phase is stable at small doping due to its finite compressibility computed to leading order in perturbation theory.
  • The D-BEC phase prevails at larger doping for arbitrarily small dissipation via pseudospin mapping.
  • The approach shares similarities with deconfinement transitions in arrays of 1D bosonic Mott insulators.

Where Pith is reading between the lines

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

  • The puddle model provides a microscopic justification for phenomenological descriptions of superconductor-metal transitions in quasi-1D wires.
  • This framework could be extended to study effects of disorder or different dissipation spectra in bosonic systems.
  • Experimental realization might involve Josephson junction chains coupled to normal metals to test the predicted critical behavior.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 0 minor

Summary. The manuscript examines the phase diagram of 1D interacting bosons on a lattice with onsite Ohmic phase dissipation from coupling to a diffusive normal-metal electrode. Starting from commensurate filling, it employs bosonization, pseudospin mapping, and perturbation theory to identify a dissipative Mott insulator (D-Mott) phase, modeled as weakly coupled dissipative boson puddles, and a dissipative BEC (D-BEC) superconductor phase. The puddle construction is used to derive the dissipative TDGL theory, placing the D-Mott/D-BEC transition in the Wilson-Fisher universality class with z≈2. At small doping the D-Mott phase remains stable due to finite compressibility; at larger doping the D-BEC phase is stable for arbitrarily small dissipation.

Significance. If the puddle mapping is free of additional relevant operators, the work supplies a microscopic derivation of the dissipative TDGL theory and assigns a specific universality class (Wilson-Fisher with z≈2) to the superconductor-metal transition in quasi-1D bosonic systems, which would be a useful benchmark for dissipative quantum phase transitions.

major comments (1)
  1. [Abstract (puddle-picture paragraph) and the derivation of the TDGL theory] The central assignment of the D-Mott/D-BEC transition to the Wilson-Fisher class with z≈2 rests on the mapping of the commensurate lattice to an array of dissipative boson puddles (size set by phase-slip length) whose effective theory is the dissipative TDGL of Sachdev et al. (abstract). The manuscript must explicitly demonstrate that the Ohmic bath and lattice do not generate additional relevant operators beyond those in the target TDGL; without this operator-content check the universality-class claim is not secured.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the universality-class assignment. We respond point-by-point below.

read point-by-point responses

  1. Referee: [Abstract (puddle-picture paragraph) and the derivation of the TDGL theory] The central assignment of the D-Mott/D-BEC transition to the Wilson-Fisher class with z≈2 rests on the mapping of the commensurate lattice to an array of dissipative boson puddles (size set by phase-slip length) whose effective theory is the dissipative TDGL of Sachdev et al. (abstract). The manuscript must explicitly demonstrate that the Ohmic bath and lattice do not generate additional relevant operators beyond those in the target TDGL; without this operator-content check the universality-class claim is not secured.

    Authors: We agree that an explicit operator-content check is required to fully secure the universality-class claim. The puddle construction follows from the bosonization analysis combined with the phase-slip length scale that emerges at commensurate filling; the inter-puddle Josephson coupling together with the local Ohmic dissipation then maps onto the dissipative TDGL. In the revised manuscript we will add a dedicated paragraph (or short appendix) that enumerates the leading operators allowed by the underlying symmetries and the Ohmic bath. Using the scaling dimensions obtained from the dissipative Luttinger-liquid description, we will show that all additional operators generated by the bath or the lattice are irrelevant at the Wilson-Fisher fixed point with z≈2. This explicit check will be included in the next version. revision: yes

Circularity Check

0 steps flagged

Derivation proceeds from microscopic lattice model via standard mappings; no reduction to inputs by construction

full rationale

The paper starts from a microscopic 1D lattice model of interacting bosons with onsite phase dissipation. It constructs the D-Mott phase as an array of dissipative puddles, applies bosonization and a pseudospin mapping, and derives the dissipative TDGL theory from that picture. The Wilson-Fisher assignment with z≈2 follows from the resulting effective theory. No equation or step equates a claimed prediction to a fitted parameter or self-citation by definition; the cited Sachdev et al. work is external and the derivation runs in the forward direction. The central claims therefore remain independent of the target phenomenology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claims rest on standard condensed-matter techniques (bosonization, pseudospin-chain mapping) whose validity for this dissipative model is assumed rather than re-derived; the puddle-size identification is introduced phenomenologically to match the phase-slip length. No new free parameters are fitted to data; the dissipation strength and Josephson coupling appear as expansion parameters.

axioms (2)
  • domain assumption Bosonization and pseudospin mapping remain valid in the presence of Ohmic phase dissipation at the lattice sites.
    Invoked when the authors map the lattice model to a pseudospin chain and apply bosonization to obtain the phase diagram.
  • domain assumption The dissipative time-dependent Ginzburg-Landau theory can be obtained by coarse-graining the microscopic puddle array without additional relevant operators.
    Central step that links the microscopic description to the phenomenological theory of Sachdev et al.
invented entities (1)
  • Dissipative boson puddle no independent evidence
    purpose: To describe the local regions of phase coherence in the D-Mott phase whose size is set by phase slips.
    Introduced to connect the microscopic lattice model to the observed exponential decay of phase correlations; no independent experimental signature is provided beyond the phase diagram itself.

pith-pipeline@v0.9.1-grok · 5896 in / 1739 out tokens · 33649 ms · 2026-06-28T21:37:29.003180+00:00 · methodology

0 comments
read the original abstract

The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. {\bf 92} 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent $z\approx 2$. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.

Figures

Figures reproduced from arXiv: 2605.30746 by Miguel A. Cazalilla.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram for the bosonized model (8) for a com [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Sketch of the D-Mott/Metal phase after coarse [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Sketch of the D-Mott/Metal phase diagram as a func [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dissipation splits the Mott transition in one dimension

    cond-mat.str-el 2026-06 unverdicted novelty 8.0

    Dissipation splits the 1D Mott transition into two distinct critical points via an intermediate compressible gapless dissipative phase with zero superfluid stiffness.

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