All-temperature superfluidity in two dimensions

arXiv:2610.20717 · cond-mat.str-el, cond-mat.stat-mech, hep-th · Submitted 2026-10-14 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: Today's paper: "All-temperature superfluidity in two dimensions".

Mira: The gist The thermal state of the underlying conformal field theory defined by the biconical fixed point exhibits quasilong-range order at all temperatures.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, to look at the paper "All-temperature superfluidity in two dimensions," the authors are essentially confirming that a BKT phase, and with it superfluidity, can indeed persist to arbitrarily high temperatures in a local unitary quantum field theory <ref:2610.20717#pg1>.

Mira: They achieve this by studying a (two + one)-dimensional quantum field theory where a complex scalar is coupled to the critical O(N) model <ref:2610.20717#pg3>. The key mechanism they point to is the biconical fixed point where the inter-sector coupling is negative <ref:2610.20717#pg3>.

Lev: And what this implies for us, Lev-wise, is that this isn't just a low-temperature thing anymore; it’s possible to have long-range order at high temperatures in these specific theoretical models <ref:2610.20717#pg3>.

Kai: The paper uses the large-N expansion to show that for sufficiently large N, the vortex perturbation is strongly irrelevant because the phase stiffness grows linearly with temperature <ref:2610.20717#pg3>. This makes them think that in the limit of large N, you can safely ignore those vortex effects <ref:2610.20717#pg2>.

Mira: And they quantify this by showing the vortex fugacity is exponentially small in N, which is what keeps the system deep within the BKT phase at large but finite N <ref:2610.20717#pg3>.

Lev: From an engineering viewpoint, this means for large N, you can treat this system as if it's deep in the superfluid regime without worrying about those vortex instabilities dominating your calculations <ref:2610.20717#pg3>.

Kai: So, to summarize the authors' conclusion on "All-temperature superfluidity in two dimensions," they’re showing that for large N, you can have persistent superfluidity at any temperature because the vortex effects become negligible <ref:2610.20717#pg2>.

Mira: This result challenges the conventional understanding of when continuous symmetries can be spontaneously broken in two spatial dimensions <ref:2610.20717#pg1>, showing that a BKT phase and superfluidity can survive at all temperatures under these specific conditions <ref:2610.20717#pg3>.

Conclusion: Kai: So, we've been looking at how this paper "All-temperature superfluidity in two dimensions" is trying to tackle that weird idea of symmetry breaking at high temperatures in 2D systems <ref:2610.20717#pg1>.

Mira: Exactly. The core claim here is that you can actually have quasi-long-range order and superfluidity persisting all the way up to arbitrarily high temperatures <ref:2610.20717#pg3>.

Lev: But we gotta ask, this is about local unitary quantum field theories, right? Because in standard physics, Coleman–Hohenberg–Mermin–Wagner says that global U(one) symmetry can't break at any nonzero temperature in two spatial dimensions <ref:2610.20717#pg3>.

Kai: Right. So what's the trick they use? They aren't just ignoring the theorem; they found a specific fixed point, a biconical one, in an O(N) times U(one) model where that inter-sector coupling becomes negative <ref:2610.20717#pg3>.

Mira: That negative coupling is what sets up the whole thing. It means that at this special point, the fluctuations in the O(N) part actually make the phase stiffness finite and large <ref:2610.20717#pg3>.

Lev: From an error correction standpoint, if that phase stiffness grows linearly with temperature, that’s a big deal for running real hardware; it means the overhead doesn't just explode <ref:2610.20717#pg3>.

Kai: And they link this to the vortex physics because at large N, the vortex operators become irrelevant because their fugacity is exponentially small <ref:2610.20717#pg3>.

Mira: It’s a big statement about how these specific models can evade the usual temperature restrictions through that large N limit, which then keeps them deep inside the BKT phase <ref:2610.20717#pg3>.

Lev: So what this implies for us on real hardware is that if we can engineer a system near this fixed point, we might be able to achieve superfluidity conditions even when thermal noise is pretty high <ref:2610.20717#pg3>.

Kai: It really changes how you think about the phase transitions in these quantum systems, moving beyond just low-temperature approximations <ref:2610.20717#pg3>.

Mira: And it opens up a whole new avenue for exploring ordered states in two dimensions that we previously thought were impossible at high T <ref:2610.20717#pg3>.

Lev: So next, we gotta look at how this scaling with N behaves when we try to translate this onto the actual physical systems you build <ref:2610.20717#pg3>.

Bilal Hawashin, *Soumyadeep Chaudhuri, ×Igor F. Herbut, ×Michael M. Scherer

Theoretische Physik III, Ruhr-Universität Bochum · Physique Thẞorique et Mathẞmatique, Université Libre de Bruxelles · Department of Physics, Simon Fraser University

cond-mat.str-el, cond-mat.stat-mech, hep-th

Submitted: 2026-10-14

Updated: 2026-10-14

Comments: 7 pages, 2 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 90/100

The gist: The gist The thermal state of the underlying conformal field theory defined by the biconical fixed point exhibits quasilong-range order at all temperatures.

Key concepts

Berezinskii–Kosterlitz–Thouless (BKT) phase: This phase describes quasi-long-range order in two dimensions, allowing for superfluidity. Usually destroyed by high temperatures through vortex proliferation, this paper demonstrates it can survive to very high temperatures in specific quantum field theories.
Large-$N$ expansion: This is a mathematical technique used to simplify complex quantum field theories by treating the number of components (N) as a large parameter. It helps identify important physical behaviors and fixed points, like the biconical fixed point, which governs the system's behavior.
Vortex fugacity: The vortex fugacity is a measure related to how likely vortices are to appear in the system. The paper proves that for large N, this value becomes exponentially small. This makes vortex operators irrelevant and ensures the BKT phase remains stable even at high temperatures.

Summary

The gist The thermal state of the underlying conformal field theory defined by the biconical fixed point exhibits quasilong-range order at all temperatures.

Background and Problem

Spontaneous symmetry breaking is usually regarded as a low-temperature phenomenon, but this paper shows that a BKT phase, and with it superfluidity, can persist to arbitrarily high temperatures in local, unitary quantum field theories. The standard argument against long-range order in two spatial dimensions is the Coleman–Hohenberg–Mermin–Wagner (CHMW) theorem. In local quantum field theories of complex scalars in two spatial dimensions, the global U(1) symmetry cannot be spontaneously broken at any nonzero T.

Fixed-Point Mechanism

The persistence of the BKT phase is explained by a fixed-point mechanism at work in the discrete case where O(N)×U(1) models possess a biconical fixed point at which, for sufficiently large N, the mixed coupling is negative. At this fine-tuned point, fluctuations in the O(N) sector render the phase stiffness finite and large, and exponentially suppress the vortex fugacity. This renders vortex operators irrelevant for sufficiently large N.

Model and Large-N Expansion

The analysis considers a (2 + 1)-dimensional quantum field theory with global O(N) × U(1) symmetry defined by the Euclidean action S. The large-N expansion is performed using a Hubbard–Stratonovich field σ [32–34] to integrate out the N − 1 components of the O(N) vector field. When tuned to criticality, the (2 + 1)-dimensional O(N) model flows to the interacting Wilson–Fisher fixed point, at which the large-N expansion yields leading-order scaling dimensions.

Vortex Physics and BKT Transition

The effective action for the phase mode at distances large compared to 1/T is described by Seff = K squared Z d 2x(∂µθ) squared, where K = βρs is the dimensionless parameter. The theory exhibits quasi-long-range order for K > 2/π, which corresponds to the BKT phase. For K < 2/π, the vortex operator is relevant and drives the system into a gapped phase with an exponential decay of correlations. The vortex fugacity y is exponentially small in N for sufficiently large N because it is bounded by y ≤ A e−cN.

Conclusion

The paper concludes that a BKT phase, and with it two-dimensional superfluidity, can persist at all temperatures in a local, unitary quantum field theory. At large but finite N, K ∝ N and y is bounded by an exponentially small value, placing the theory deep within the BKT phase.

Acknowledgments

MMS was funded by Deutsche Forschungsgemeinschaft (DFG) within ProjectID 277146847, SFB 1238 (project C02), and the DFG Heisenberg programme (Project-ID 452976698). IFH was supported by the NSERC of Canada. The work of SC is partially supported by the International Solvay Institutes and the Belgian Fonds National de la Recherche Scientifique FNRS (convention IISN 4.4503.15). SC is also supported by a postdoctoral research fellowship of FNRS. The numerical solution for the unit-vortex saddle was obtained with the help of OpenAI GPT-6 Astra.

References

[1] N. Chai, S. Chaudhuri, C. Choi, Z. Komargodski, E. Rabinovici, and M. Smolkin, Phys Rev Lett 125 131603 (2020)

[2] N. Chai, S. Chaudhuri, C. Choi, Z. Komargodski, E. Rabinovici, and M. Smolkin Phys Rev D 102 065014 (2020) arXiv:2005.03676 [hep-th]

[3] A. Buchel, Nucl Phys B 967 115425 (2021) arXiv:2005.07833 [hep-th]

[4] S. Chaudhuri, C. Choi, and E. Rabinovici JHEP 04 203 (2021) arXiv:2011.13981 [hep-th]

[5] N. Chai, E. Rabinovici, R. Sinha, and M. Smolkin JHEP 05 192 (2021) arXiv:2011.06003 [hep-th]

[6] B. Bajc, A. Lugo, and F. Sannino Phys Rev D 103 096014 (2021)

[7] N. Chai, A. Dymarsky, and M. Smolkin Phys Rev Lett 128 011601 (2022) arXiv:2106.09723 [hep-th]

[8] S. Chaudhuri and E. Rabinovici JHEP 08 148 (2021) arXiv:2106.11323 [hep-th]

[9] N. Chai, A. Dymarsky, M. Goykhman, R. Sinha, and M. Smolkin SciPost Phys 12 181 (2022) arXiv:2111.02474 [hep-th]

[10] P. Liendo, J. Rong, and H. Zhang SciPost Phys 14 168 (2023) arXiv:2205.13964 [hep-th]

[11] R. Ciccone, L. Di Pietro, and M. Serone JHEP 02 211 (2024) arXiv:2312.13756 [hep-th]

[12] B. Hawashin, J. Rong, and M. M. Scherer Phys Rev Lett 134 041602 (2025)

[13] Z. Komargodski and F. K. Popov Phys Rev Lett 135 091602 (2025) arXiv:2412.09459

[14] B. Bajc, G. Muco, F. Sannino, and S. Wagner (2026) arXiv:2604.01184 [hep-th]

[15] B. Hawashin, M. M. Scherer, M. Smolkin, and L Yung Phys Rev D 114 065005 (2026) arXiv:2507.19890 [hepth]

[16] M. Smolkin and L Yung (2026) arXiv:2608.

Improvements for AI systems

The improved AI system can accurately model and predict emergent quasi-long-range order in two-dimensional quantum field theories at arbitrarily high temperatures by utilizing a fixed-point mechanism that persists across all temperatures, as shown by the thermal state of the underlying conformal field theory defined by the biconical fixed point exhibits quasilongrange order at all temperatures.
The system can perform high-precision calculations for superfluid properties in two dimensions, specifically determining the temperature dependence of phase stiffness, which is shown to grow linearly with temperature, with a proportionality factor that scales linearly with N and is fixed entirely by the fixed point.
The AI can evaluate whether vortex operators are relevant or irrelevant in a thermal state by comparing the dimensionless stiffness K to its critical value, as described by the condition: "For K > 2/π, the vortex operator is an irrelevant perturbation."
The system can estimate the exponential suppression of vortex fugacity at large N by calculating Score(r0) ≥ πβρ0N log(2) = π2K log(2) ≈ 0.065N, thereby confirming that the vortex fugacity y ∼ exp(-Score) is exponentially small in N.
The system can distinguish between different fixed points of the coupled O(N)×U(1) model, specifically identifying the biconical fixed point where t∗ = −1 leads to a lower free energy than the isotropic fixed point (IFP).

Abstract

In local theories with short-range interactions, continuous symmetries cannot be spontaneously broken in two spatial dimensions at nonzero temperature. U(1) -symmetric models instead admit a Berezinskii--Kosterlitz--Thouless (BKT) phase with quasi-long-range order and nonzero phase stiffness, which is normally destroyed at high temperatures by vortex proliferation. Here, we show that a BKT phase, and with it superfluidity, can persist to arbitrarily high temperatures. Using the large- N expansion, we study a (2+1) -dimensional quantum field theory in which a complex scalar is coupled to the critical O(N) model. At the biconical fixed point, where the inter-sector coupling is negative, the thermal effective potential has a circle of minima with nonzero U(1) amplitude. Integrating out the gapped fluctuations yields an effective theory for the compact phase mode at distances large compared to 1/T. Since temperature is the only scale at the fixed point, the phase stiffness grows linearly with temperature, with a proportionality factor that scales linearly with N and is fixed entirely by the fixed point. This renders vortex operators irrelevant for sufficiently large N. We further show that the vortex fugacity is exponentially small in N.