Temporal Berry Phase and the Emergence of Bose-Glass-Analog Phase in a Clean U(1) Superfluid

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.

Figures (19)

• Figure 1: A schematic picture of quasi-disordered phases in (2+1) dimensional U(1) NLsM with temporal Berry phase.
• 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 line ($t_{-}=\nu^2$) depicts a 'gorge' of negative value of $Z_{2,\tau}$ (see the text).
• Figure 3: Phase diagrams obtained from numerical solutions of the $D=3$ RG equations with initial values of $e^2$ (vertical axis), $t_{\tau}=t_{\bm r} \equiv t$ (horizontal axis), $\gamma_{\tau}=1$ and $\nu=1.2$. Initial parameters in the light blue (gray or white) region go to the weak-coupling (strong-coupling) region with divergent (vanishing) $e^2$ and $\nu$, and negatively (positively) divergent $t_{+}\equiv t_{\tau}+t_{\bm r}$. Initial parameters in the light red region are in the intermediate coupling region, where $\gamma_{\tau}$ goes to zero at a finite RG scale $b$ with positive $t_{\tau}$ and finite $e^2$. Three inset figures show how the inverse space-time anisotropy parameter $\gamma^{-1}_{\tau}$ is renormalized in these three regions.
• Figure 4: $z_1(\nu)$ (green), $z_{2,\tau}(\nu)$(blue) and $z_{2,r}(\nu)$(orange) as functions of $\nu$
• Figure 5: numerical RG phase diagram with initial values of $\gamma_{\tau}=1$ and $\nu=0.2$ (left) and $\nu=0.6$ (right). The horizontal and vertical axes are initial values of $y$, and $e^2$, respectively. When the initial parameters are in the blue and white-colored regions, the RG equations drive them into the weak-coupling fixed line and strong-coupling fixed point, respectively.