All-temperature superfluidity in two dimensions

summary

Video file (mp4)

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.

In short

The paper shows that a Berezinskii–Kosterlitz–Thouless (BKT) phase, which implies superfluidity, can persist at arbitrarily high temperatures in local quantum field theories. This is achieved by tuning to a biconical fixed point in the large-$N$ expansion, where thermal fluctuations suppress vortex proliferation even at high 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.

Terminology used across episodes

This episode discusses

The paper

All-temperature superfluidity in two dimensions · Read on arXiv

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

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.

Transcript

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>.

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