Phase Frustration Induced Intrinsic Bose Glass in the Kitaev-Bose-Hubbard Model

TL;DR

The work demonstrates that intrinsic phase frustration between complex hopping and anisotropic pairing in a 2D Kitaev-Bose-Hubbard model yields a robust Bubble Phase that spontaneously fragments into finite superfluid islands, producing a compressible insulating state with a finite excitation gap. Using Inhomogeneous Gutzwiller Mean-Field Theory and a Bogoliubov-de Gennes stability analysis augmented by the Energy Penalty Method to remove spurious gauge modes, the authors show the Bubble Phase is dynamically stable and nonpercolating, lying between the Mott insulator and an unstable superfluid. This disorder-free Bose glass emerges from deterministic phase frustration rather than randomness, offering a clean archetype and blueprint for realizing glassy dynamics in quantum simulators. The results connect intrinsic frustration to localization phenomena, providing a unified framework that parallels off-diagonal-disorder Bose glass physics while enabling experimental access in clean platforms.

Abstract

We report an intrinsic "Bubble Phase" in the two-dimensional Kitaev-Bose-Hubbard model, driven purely by phase frustration between complex hopping and anisotropic pairing. By combining Inhomogeneous Gutzwiller Mean-Field Theory with a Bogoliubov-de Gennes stability analysis augmented by a novel Energy Penalty Method, we demonstrate that this phase spontaneously fragments into coherent islands, exhibiting the hallmark Bose glass signature of finite compressibility without global superfluidity. Notably, we propose a unified framework linking disorder-driven localization to deterministic phase frustration, identifying the Bubble Phase as a pristine, disorder-free archetype of the Bose glass. Our results provide a theoretical blueprint for realizing glassy dynamics in clean quantum simulators.

Figures (4)

• Figure 1: Ground-state phase diagram and coherence signatures for $\alpha=1/16$. (a) Phase diagram in the $(J/U, \mu/U)$ plane determined by the real-space connectivity of the superfluid order parameter. Three distinct phases are identified: the Mott Insulator (MI), the Unstable Superfluid (USF), and the intervening Bubble Phase , which emerges at the phase boundary due to spontaneous fragmentation. (b) Corresponding momentum-space coherence map quantified by the Inverse Participation Ratio (IPR), $\mathcal{I}_k$. The Bubble phase retains structural coherence (higher IPR) arising from its Bragg peaks, whereas the deep USF regime exhibits a suppressed IPR due to the proliferation of diffuse background modes, signaling dynamical instability.
• Figure 2: Dynamical stability and excitation spectrum. Evolution of the lowest Bogoliubov-de Gennes (BdG) excitation energy as a function of hopping strength $J/U$ (at fixed $\mu/U=0.5$). The solid blue line represents the real energy gap $|\mathrm{Re}(E)|$, while the dashed red line indicates the imaginary part $|\mathrm{Im}(E)|$ associated with dynamical instability. The Bubble phase (for $J/U \lesssim 0.046$) is characterized by a purely real spectrum ($|\mathrm{Im}(E)|=0$) with a finite gap, confirming it is a stable eigenstate rather than a numerical artifact. The sudden rise in $|\mathrm{Im}(E)|$ marks the transition into the Unstable Superfluid (USF) phase.
• Figure 3: Microscopic signatures of spontaneous fragmentation. Real-space distribution of the local superfluid order parameter amplitude $|\langle b_i \rangle|$ (top row), phase $\arg(\langle b_i \rangle)$ (middle row), and momentum space distribution $n(\mathbf{k})$ (bottom row) for three representative phases on a $64 \times 64$ lattice. (a, d, g) Mott Insulator ($J/U=0.03$): The system exhibits a uniform vanishing amplitude and a featureless momentum distribution (intensity $\approx 0$). (b, e, h) Bubble Phase ($J/U=0.045$): The system spontaneously fragments into localized superfluid "islands" (bubbles). Within each bubble, the phase is ordered, but global coherence is disrupted by the insulating domain walls. This is confirmed by the momentum distribution (h), which shows distinct Bragg peaks but with significantly reduced intensity compared to the superfluid phase, reflecting the lack of long-range ODLRO. (c, f, i) Unstable Superfluid ($J/U=0.06$): The system regains global connectivity but displays chaotic patterns. The momentum distribution (i) shows strong but diffuse peaks, signaling the onset of dynamical instability.
• Figure 4: Macroscopic bulk properties at fixed hopping $J/U=0.025$. (a) Equation of state showing the average particle number $\langle n \rangle$ as a function of the chemical potential $\mu/U$. The Mott Insulator (red shaded region) is characterized by an integer filling plateau where the compressibility vanishes ($\kappa = \partial n / \partial \mu \approx 0$). Conversely, the Bubble Phase (green shaded region) exhibits a continuously varying density with a finite slope, indicating a finite compressibility ($\kappa > 0$). (b) Particle number fluctuations $\langle \delta \hat{n}^2 \rangle$. The Bubble Phase supports significant number fluctuations ($\langle \delta \hat{n}^2 \rangle > 0$), distinguishing it from the particle-number-squeezed Mott state ($\langle \delta \hat{n}^2 \rangle \approx 0$). These bulk properties identify the Bubble Phase as a compressible insulator.