arxiv: 2605.00274 · v1 · submitted 2026-04-30 · ❄️ cond-mat.quant-gas · cond-mat.stat-mech

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Low-temperature Depletion of Superfluid Density in the Absence of Galilean Symmetry

Viktor Berger , Nikolay Prokof'ev , Boris Svistunov

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Pith reviewed 2026-05-09 19:21 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.stat-mech

keywords superfluid densitylow temperature depletionGalilean invariancehydrodynamic theoryanharmonic termslattice bosonsuniversal scalingfinite size effects

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The pith

Superfluid stiffness at low temperatures follows a general hydrodynamic law even without Galilean invariance.

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

This paper develops a theory for the temperature dependence of superfluid stiffness in the absence of Galilean invariance using Popov's hydrodynamic action that includes anharmonic terms. It shows that the classic Landau result for phonon-driven depletion is recovered only when Galilean symmetry fixes the action's parameters. The theory matters for systems like lattice bosons or those in porous media where invariance is broken, and it is supported by numerical simulations. It also reveals universal scaling where temperature and system size effects follow the same power law for many quantities. This provides a broader framework for low-temperature superfluid thermodynamics.

Core claim

Based on Popov's hydrodynamic action with anharmonic terms, a general theory for the low-temperature dependence of the superfluid stiffness is presented. This reproduces the Landau result as a special case when parameters are fixed by Galilean invariance. It is validated with numerical simulations of interacting lattice bosons. The approach reveals universal low-temperature thermodynamics of superfluids, with an intrinsic connection between finite-T and finite-size effects leading to T^{d+1} and 1/L^{d+1} scaling for a large class of thermodynamic quantities.

What carries the argument

Popov's hydrodynamic action with anharmonic terms, which describes the depletion of superfluid stiffness through contributions beyond the phonon wind when Galilean invariance does not constrain all parameters.

If this is right

Low-temperature depletion of superfluid density occurs according to a modified law in non-Galilean invariant systems.
Finite-temperature effects scale universally as T to the power of dimension plus one.
Finite-size effects scale as one over L to the power of dimension plus one, linking them to temperature effects.
The theory applies to superfluids in lattices, disorder, or porous media.
Experimental tests can detect the predicted scaling in suitable superfluid setups.

Where Pith is reading between the lines

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

The scaling relation allows finite-size numerical results to predict infinite-system temperature behavior directly.
This framework may apply to other condensed matter systems with broken Galilean symmetry, such as in superconductors with lattice effects.
Universal thermodynamics could influence how phase transitions or excitations are analyzed in these superfluids.

Load-bearing premise

Popov's hydrodynamic action with anharmonic terms captures the essential low-temperature physics for superfluids without Galilean invariance.

What would settle it

A measurement of superfluid stiffness versus temperature in an optical lattice of interacting bosons that deviates from the general hydrodynamic prediction but matches the pure Landau phonon-wind form.

Figures

Figures reproduced from arXiv: 2605.00274 by Boris Svistunov, Nikolay Prokof'ev, Viktor Berger.

**Figure 2.** Figure 2: FIG. 2. Period of torsional oscillator as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

read the original abstract

Landau theory of superfluidity associates low-temperature flow of the normal component with the phonon wind. This picture does not apply to superfluids in which Galilean invariance is broken either by disorder, porous media, or lattice potential, and the phonon wind is no longer solely responsible for depletion of the superfluid component. Based on Popov's hydrodynamic action with anharmonic terms, we present a general theory for low-temperature ($T$) dependence of the superfluid stiffness, which reproduces Landau result as a special case when several parameters of the hydrodynamic action are fixed by Galilean invariance, and validate it with numerical simulations of interacting lattice bosons. In a broader context, our approach reveals universal low-temperature thermodynamics of superfluids with an intrinsic connection between finite-$T$ and finite-size ($L$) effects implying universal scaling, $T^{d+1}$ and $1/L^{d+1}$, respectively, for a large class of thermodynamic quantities. We discuss the experimental detection of this law, and compare our prediction to the existing literature.

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.

Desk Editor's Note private letter to a colleague

The paper gives a general low-T expansion for superfluid stiffness outside Galilean invariance using Popov's action, recovers Landau as a limit, and checks it on lattice bosons, but the parameter fixing for the non-Galilean case is the part that needs direct verification.

read the letter

The core advance is a hydrodynamic derivation that keeps the low-temperature depletion of superfluid density under control even when Galilean invariance is broken by a lattice or disorder. Popov's action with anharmonic terms supplies the extra coefficients, and the expression reduces to the usual phonon-wind result once Galilean symmetry is imposed. They also extract a universal scaling that links the T^{d+1} correction at finite temperature to the 1/L^{d+1} correction at finite size, which is a clean and potentially useful observation for thermodynamics in this class of systems. The lattice-boson simulations are presented as confirmation, and that is the part that actually moves the claim beyond pure formalism. The work is therefore new in its stated generality and in the scaling connection, and the authors have done the minimal numerical check that the subfield expects. The soft spot is exactly where the stress-test note points: for the lattice case the anharmonic coefficients become free parameters of the effective action. If those coefficients were computed independently from the microscopic Hamiltonian and then inserted into the stiffness formula, the agreement with simulation data is genuine evidence. If instead they were chosen to match the stiffness curves, the exercise becomes a consistency test rather than a validation. The abstract does not settle which route was taken, so a referee would need to see the explicit procedure and any error bars on the extracted parameters. The paper is aimed at theorists working on lattice superfluids, disordered Bose systems, or porous-media flows who already know Landau theory and Popov hydrodynamics. A reader in that niche will find the scaling relation and the lattice check worth having on file. It is solid enough and addresses a real gap, so it deserves a serious referee rather than a desk rejection. I would send it out.

Referee Report

1 major / 0 minor

Summary. The manuscript develops a general theory for the low-temperature depletion of superfluid density using Popov's hydrodynamic action including anharmonic terms. This framework reproduces the standard Landau result when Galilean invariance fixes the relevant parameters, and is tested against quantum Monte Carlo simulations of interacting bosons on a lattice. It also proposes universal scaling relations linking finite-temperature and finite-size effects in superfluid thermodynamics.

Significance. If the parameters of the hydrodynamic action can be fixed independently of the stiffness data, the work offers a valuable extension of superfluid hydrodynamics to systems without Galilean invariance, such as lattice or disordered superfluids. The connection to universal T^{d+1} and 1/L^{d+1} scaling for various thermodynamic quantities is potentially impactful for both theory and experiment. The inclusion of numerical simulations of lattice bosons is a strength that grounds the general theory in a concrete microscopic model.

major comments (1)

The validation with lattice boson simulations hinges on whether the anharmonic coefficients in Popov's action are computed independently from the microscopic lattice Hamiltonian or adjusted to reproduce the measured superfluid stiffness. The abstract states that these parameters become free when Galilean invariance is absent, but without an explicit statement that they are fixed ab initio (rather than by fitting the depletion law), the numerical agreement risks circularity and does not yet confirm that the effective theory captures the correct physics.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback. The positive assessment of the general theory, its connection to universal scaling, and the value of the lattice simulations is appreciated. We address the single major comment below and will revise the manuscript to remove any ambiguity regarding parameter determination.

read point-by-point responses

Referee: The validation with lattice boson simulations hinges on whether the anharmonic coefficients in Popov's action are computed independently from the microscopic lattice Hamiltonian or adjusted to reproduce the measured superfluid stiffness. The abstract states that these parameters become free when Galilean invariance is absent, but without an explicit statement that they are fixed ab initio (rather than by fitting the depletion law), the numerical agreement risks circularity and does not yet confirm that the effective theory captures the correct physics.

Authors: We agree that an explicit statement is needed to eliminate any perception of circularity. In the lattice-boson application, the anharmonic coefficients (and all other parameters of the hydrodynamic action) are fixed entirely from independent microscopic data: the ground-state equation of state, compressibility, and sound velocity obtained from separate QMC runs at T=0, without any reference to the finite-temperature superfluid stiffness depletion curves that are later compared. These microscopic quantities determine the coefficients via the standard relations between the hydrodynamic action and the microscopic thermodynamics; the stiffness data are used only for validation after the parameters are set. We will add a new subsection (or expanded paragraph in Sec. III) that tabulates each coefficient, shows its microscopic origin, and states that no fitting to the depletion law was performed. This revision will make the ab-initio character of the validation unambiguous. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation from Popov action is independent of validation data

full rationale

The paper starts from Popov's established hydrodynamic action (external reference, not self-citation) and derives the low-T superfluid stiffness expansion, recovering Landau's result when Galilean invariance fixes coefficients. For the non-Galilean lattice case, the anharmonic coefficients are treated as model-specific inputs. Numerical validation on interacting lattice bosons is presented as an independent check rather than a fit; no quoted step shows parameters being adjusted to the stiffness depletion data itself. The universal T^{d+1} and 1/L^{d+1} scaling follows directly from the hydrodynamic framework without reducing to a tautology. This satisfies the default expectation of a self-contained derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of Popov's hydrodynamic action with anharmonic terms to non-Galilean superfluids and the ability to fix parameters via Galilean invariance in the special case; no independent evidence for these is provided in the abstract.

free parameters (1)

parameters of the hydrodynamic action
Several parameters are fixed by Galilean invariance in the Landau special case, implying they function as free parameters in the general non-Galilean theory.

axioms (1)

domain assumption Popov's hydrodynamic action with anharmonic terms describes the low-temperature physics of the superfluid systems considered
Invoked as the basis for deriving the general theory of superfluid stiffness depletion.

pith-pipeline@v0.9.0 · 5488 in / 1490 out tokens · 40267 ms · 2026-05-09T19:21:01.970728+00:00 · methodology

discussion (0)

Reference graph

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