Reentrant d=2+1 Superfluidity at High Temperature

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: We're looking at the paper: "Reentrant d=2+1 Superfluidity at High Temperature".

Mira: Here's the gist of the paper. The gist: A local, UV-complete model in d=2+1 dimensions exhibits a Berezinskii-Kosterlitz-Thouless (BKT) ordered phase at arbitrarily high temperatures through a mechanism involving coupling to a Conformal Field Theory (CFT) Model Construction and Symmetry Breaking The paper constructs a local, UV-complete model in d=2+1 dimensions with quasi-long-range U(1) order at arbitrarily high temperatures The system starts with a complex scalar field χ in d=2+1 spacetime dimensions possessing negative mass squared and a weak quartic self-interaction At zero temperature, this field spontaneously breaks the U(1) symmetry, producing a massless Goldstone mode The long-wavelength static modes at any nonzero temperature T are described by a two-dimensional Euclidean theory Mechanism for High-Temperature Superfluidity The reentrant BKT phase at high temperatures is achieved by coupling the scalar field χ to a Conformal Field Theory (CFT) through a parametrically weak portal interaction O∆χ2 The sign of this portal coupling is chosen such that the thermal one-point function ⟨O∆⟩T ∝ T∆ induces a negative scalar mass shift at leading order At high temperatures, the negative conformal contribution to the scalar mass squared dominates the positive scalar thermal correction for ∆ > 1 This results in a dimensionless phase stiffness growing as K(T) ∼ (T /m) ∆−1 so that algebraic correlations decay more slowly as temperature increases The mechanism is controlled in the window 1 < ∆ < 3/2, which ensures both stability of the vacuum effective potential and parametrically decreasing backreaction on the conformal sector at high temperature Phase Determination via Static Theory The leading static theory (5) is analyzed to determine whether it is gapped or exhibits quasi-long-range order The phase is diagnosed by the quantity R(T) = 2r2(T; µ)/u2(T)+π−1 log

2µ2 / u2(T): The deep massive regime is characterized by R ≫ 1, leading to an exponential decay of the two-point function and placing the theory deep in the disordered regime Conversely, the deep algebraic regime is characterized by R ≪ −1, where a phase EFT describes a compact phase with vortex defects The critical point is determined nonperturbatively by Monte Carlo simulation of a regulated ψ4 model and BKT finite-size scaling, yielding the nonperturbative position Rc = −0.821(10) Reentrant Phase Sequence The coupled trajectory shares the ordinary low-temperature endpoint but has high-temperature asymptotics described by δU(1)+CFT=− 2bOhλ T m∆−1 + O log T g → −∞ as T → ∞ This asymptotic behavior places the coupled trajectory in the BKT region at arbitrary high temperatures For a sufficiently small but nonzero favorable portal coupling, the intermediate massive region of the ordinary trajectory persists, leading to a reentrant phase sequence BKT-massive-BKT For a sufficiently strong portal contribution relative to the scalar self-interaction with the favorable sign, an intermediate massive interval can disappear, leaving a BKT phase at every nonzero temperature Concrete Example and Future Directions The d=2+1 Ising CFT provides a concrete candidate for this mechanism through its energy operator ϵ, which has a scaling dimension ∆ϵ ≃ 1.4126 within the required window 1 < ∆ϵ < 3/2 This suggests that the simplest realization involves just χ and a critical Ising field Further investigations are suggested in real-time dynamics of the high-temperature BKT phase, non-Abelian generalizations, and gauged versions of these theories Acknowledgements The authors acknowledge Olivier Delouche for useful discussions and comments on the draft They are supported by the European Research Council, grant agreement n.

Kai: 101039756 The work was first presented at the University of Geneva on 8 October 2026.

Mira: The authors thank Brando Bellazzini, James Ingoldby, Markus Luty, Francesco Riva, Junchen Rong, Giovanni Villadoro and Yuan Xin for useful discussions.

Kai: S.D.C.

Title and authors: Kai: So this paper is called "Reentrant d=two plusone Superfluidity at High Temperature," and the authors are Subham Dutta Chowdhury and Joan Elias Miró <ref:2610.30236#pg1,Reentrant d=2+1 Superfluidity at High Temperature>. I think that title immediately suggests something counterintuitive because usually, you expect order to disappear when you heat things up, right?

Mira: Yeah, exactly. It points to this idea that the system can actually have some form of U(one) order—that superfluid phase—even at really high temperatures, which is pretty surprising given how thermal fluctuations usually work against it <ref:2610.30236#pg1>.

Lev: From a hardware standpoint, if we were trying to build something like this on a real chip, the fact that they’re talking about high temperature phases means we have to worry about decoherence and thermal noise overwhelming whatever order they're trying to establish, right?

Kai: Right. And looking at the authors, I see Subham Chowdhury is really focused on the UV-complete model construction, which sounds like he’s building a very solid mathematical foundation for this behavior.

Mira: And Joan Miró seems to be steering the work toward how this actually connects to the underlying field theory and what that means physically for condensed matter systems.

The paper's summary: Kai: So, in short, they’re looking at a local, UV-complete model in two plus one dimensions that has this global U(one) symmetry <ref:2610.30236#pg1>. They’ve found that even with the coupling to a Conformal Field Theory, there's a Berezinskii-Kosterlitz-Thouless phase ordered state that persists at arbitrarily high temperatures.

Mira: That persistence is the key point. They start with a complex scalar field chi in two plus one dimensions with negative mass squared and some weak quartic self-interaction, and then they couple it to a Conformal Field Theory through this portal interaction O chi squared <ref:2610.30236#pg1>.

Lev: So, what’s the mechanism here? It seems like the portal coupling h is chosen in a very specific way. They find that at high temperatures, the thermal one-point function of this operator O goes as T, which induces a negative scalar mass shift at leading order.

Kai: That negative shift is what makes the situation interesting because it counteracts the positive thermal correction to the mass squared that usually happens, which favors symmetry restoration at high temperature.

Mira: And this leads to a dimensionless phase stiffness K(T) growing as (T/m)-one which means algebraic correlations decay slower as you increase the temperature. This is what creates that quasi-long-range order even when T is very large.

The paper's improvements: Kai: The paper suggests a couple of key things for improvement, mostly in terms of controlling the regime where this high-temperature superfluidity happens. They focus on the window where one < < three/two <ref:2610.30236#pg2>.

Mira: That window is crucial because it ensures two things: first, the stability of the vacuum effective potential at large field values, and second, that the backreaction from the CFT is parametrically decreasing as temperature goes to infinity.

Lev: From my side, what this means for real hardware is that we need a mechanism that respects these constraints. If goes outside this window, we lose control over the effective potential or the thermal cumulants become unbounded, which would be bad for any simulation trying to predict behavior near T to infinity.

Kai: And they point to a concrete example here—the Ising CFT in two plus one dimensions. Specifically, the energy operator epsilon has a scaling dimension epsilon of about one point four one two six, which fits right into that required window one < epsilon < three/two <ref:2610.30236#pg3>.

Mira: So they suggest that the simplest physical realization of this mechanism might just involve the scalar field chi and this critical Ising field operator epsilon. That simplifies the starting point significantly.

Conclusion: Kai: So, wrapping up, the main thing we’ve seen from "Reentrant d=two plusone Superfluidity at High Temperature" is that we can have a BKT ordered phase at arbitrarily high temperatures if you couple the system correctly to a CFT <ref:2610.30236#pg1,Reentrant d=2+1 Superfluidity at High Temperature>.

Mira: The sequence they describe is interesting: BKT-massive-BKT, meaning you get an intermediate massive region for low temperatures but then it jumps back into the BKT regime at even higher temperatures depending on how strong that coupling is.

Lev: For running this on actual hardware, I think the requirement to stay within that < three/two window is a hard constraint we’d need to satisfy for any error correction scheme trying to maintain coherence in this phase <ref:2610.30236#pg2>.

Kai: So, the paper shows us that even with thermal effects pushing towards disorder, there can be algebraic correlations persisting if you engineer the right interaction between the scalar field and that CFT.

Mira: It suggests that exploring things like the d=two plusone Ising CFT as a candidate for this mechanism could give us a simpler system to study <ref:2610.30236#pg1>.

Lev: I'll keep thinking about how those constraints on translate into practical limitations when we try to implement these ideas in error correcting codes.