[論文レビュー] Temporal Berry Phase and the Emergence of Bose-Glass-Analog Phase in a Clean U(1) Superfluid

Ryuichi Shindou, Pengwei Zhao+1 more|arXiv (Cornell University)|Mar 10, 2026

Quantum, superfluid, helium dynamics被引用数 0

ひとこと要約

The paper shows that a temporal Berry phase in a 2+1D U(1) nonlinear sigma model induces space-time anisotropic vortex proliferation, creating a Bose-glass-analog quasi-disordered phase with short-range spatial order and persistent temporal coherence, via RG analysis and a vortex-membrane duality to a 3D type-II superconductor.

ABSTRACT

A U(1) nonlinear sigma model (NLSM) with a one-dimensional temporal Berry phase term describes the critical theory of phase-fluctuation-driven superfluid (SF) transitions. We clarify that the temporal Berry phase leads to space-time anisotropic interference in vortex proliferation, resulting in a quasi-disordered phase characterized by short-range spatial order but persistent temporal phase coherence. This phase shares the essential SF phase correlation properties of the Bose Glass phase known from disordered boson systems, suggesting a unified topological origin for the emergence of the glassy phase in phase-fluctuation-driven superfluid transitions.

研究の動機と目的

• Motivate and clarify how a temporal Berry phase term affects phase-fluctuation-driven superfluid transitions.
• Show that temporal Berry phase induces space-time anisotropic interference in vortex proliferation.
• Demonstrate the emergence of a quasi-disordered phase with short-range spatial order and persistent temporal coherence.
• Establish a unified topological origin for glassy phases in clean, phase-fluctuation-driven systems via duality to magnetic vortex physics.

提案手法

• Model the system with a D-dimensional U(1) nonlinear sigma model including a temporal Berry phase term S = (1/2g)∫|∇θ|^2 + iχ∫∂τθ.
• Represent vortex excitations with a vortex-membrane (antisymmetric tensor) formulation and couple them to a gauge field via a Maxwell-like action.
• Perform renormalization group analyses in general D, focusing on the ε = D − 2 expansion around χ = 0 and the D = 3 case with χ ≠ 0.
• Analyze how the Berry phase renormalizes e^2, γτ, χ, and vortex fugacities, leading to space-time anisotropy and vortex-line polarization.
• Discuss duality mappings to a 3D type-II superconductor in an external field to interpret correlations as magnetic-monopole-field anisotropy.

Figure 1: A schematic picture of quasi-disordered phases in (2+1) dimensional U(1) NLsM with temporal Berry phase.

実験結果

リサーチクエスチョン

• RQ1 How does a temporal Berry phase χ alter the space-time structure of phase correlations in a U(1) NLSM?
• RQ2 Can the temporal Berry phase stabilize a Bose glass–like phase in a clean system by modifying vortex proliferation?
• RQ3 What is the nature of the ordered-to-quasi-disordered transition and its impact on spatial vs temporal correlations?

主な発見

• The temporal Berry phase causes anisotropic screening that suppresses temporal vortex screening relative to spatial, driving polarization along the imaginary-time direction.
• An intermediate region in the D = 3 RG flow emerges where γτ → 0+, yielding a quasi-disordered phase with persistent temporal correlations but short-range spatial order.
• The intermediate region connects weak- and strong-coupling regimes and corresponds to a first-order transition to the quasi-disordered phase.
• The quasi-disordered phase shares essential features with the Bose glass, including short-range spatial order and persistent temporal coherence, and maps to similar anisotropies seen in vortex lattices of type-II superconductors under magnetic fields.
• The vortex-line proliferation in this phase localizes spatial correlations while maintaining temporal correlations, indicating a topological origin for glassy behavior in phase-fluctuation-driven superfluids.

Figure 2: (left) $Z_{2,\tau}$ , $Z_{2,{\bm{r}}}$ , and $Z_{1}$ as a function of $\nu$ (horizontal axis) with $t_{\tau}=t_{\bm{r}}=0$ . (Right) Contour plot of $Z_{2,\tau}$ as a function of $\nu$ (horizontal axis) and $t_{-}\equiv t_{\tau}-t_{\bm{r}}$ (vertical axis) with $t_{+}=0$ . A Dashed yellow