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arXiv:2601.05781

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

Yifan Zhu, Shi-jie Yang

Published Jan 9, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2601.05781

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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.
The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.
The introduction of disorder in Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass (BG) and disordered solid (DS) phases. In this work, we present the rich phase diagram of interacting bosons in disordered two-dimensional optical lattice, modelled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean field (SGMF) theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the DS and BG phases. We have investigated this transition in greater detail using cluster Gutzwiller mean field theory to study the effect of inter-site correlations which is absent in the SGMF method. We have also studied this phase transition from the perspective of percolation theory.
The Bose glass (BG) phase is the Griffiths region of the disordered Bose–Hubbard model (BHM), characterized by finite, quasi-superfluid clusters within a Mott insulating background. We propose to utilize this characterization to identify the complete zero-temperature phase diagram of the disordered BHM in d ⩾ 2 dimensions by analysing the geometric properties of what we call superfluid (SF) clusters, which are defined to be clusters of sites with non-integer expectation values for the local boson occupation number. The Mott insulator phase then is the region in the phase diagram where no SF clusters exist, and the SF phase the region where SF clusters percolate—the BG phase is inbetween: SF clusters exist, but do not percolate. This definition is particularly useful in the context of local mean field (LMF) or Gutzwiller–Ansatz calculations, where we show that an identification of the phases on the basis of global quantities such as the averaged SF order parameter and the compressibility is misleading. We apply the SF cluster analysis to the LMF ground states of the two-dimensional disordered BHM to produce its phase diagram and find (a) an excellent agreement with the phase diagram predicted on the basis of quantum Monte Carlo simulations for the commensurate density n = 1 and (b) large differences to stochastic mean field and other mean field predictions for fixed disorder strength. The relation of the percolation transition of the SF clusters with the onset of non-vanishing SF stiffness indicating the BG to SF transition is discussed.
In this work, we characterize the glassy character of the Bose-glass phase in a disordered Bose-Hubbard model using three complementary diagnostics: the finite-temperature spectral function, spatial inhomogeneity, and the inverse participation ratio. Spectral analysis, obtained from finite-temperature Green's function and random phase approximation, shows that disorder introduces localized low-energy states within the Mott gap, eventually closing the gap at sufficiently strong disorder. Spatial inhomogeneity, calculated using the Gutzwiller ansatz, increases sharply with disorder and then saturates at moderate disorder strengths. The inverse participation ratio has been calculated from the exact diagonalization of a small system, and it reveals enhanced localization with stronger disorder. Increasing temperature suppresses these disorder-induced features: the low-energy spectral weight diminishes, the spatial inhomogeneity varies more smoothly, and the IPR decreases. Taken together, these diagnostics show that disorder drives the development of glassy character, while thermal fluctuations gradually wash out its signatures. The early saturation of spatial inhomogeneity compared with the continued evolution of low-energy excitations and the inverse participation ratio demonstrates that no single diagnostic fully captures the evolution of the Bose-glass state, highlighting the need for a combined characterization.
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
We study the ground state phases of the Bose-Hubbard model with disordered potentials for quasicrystalline systems, with a focus on the Bose-Glass phase. Generally speaking, disorder can lead to the formation of a Bose-Glass, which is characterised by the lack of global phase coherence across the lattice. Here, we will look at two models; the interacting 2D Aubry-Andre model and disordered vertex models from quasicrystalline tiling patterns. Unlike typical disorder in homogeneous, periodic systems, quasicrystalline models possess self-similarity. This leads to a fascinating interplay between correlated, quasiperiodic order and uncorrelated, random disorder. In this work, we combine Gutzwiller mean-field theory with a percolation analysis of superfluid clusters, allowing the critical points and phase regions of these disordered systems to be mapped. When the long-range order is separate to the random disorder, as is the case for the disordered vertex models, then the physics reflects that of periodic lattices with disorder. However, we find that long-range order present in the disorder term of the 2D Aubry-Andre model can result in some peculiarities to the physics of the Bose-Glass. These peculiarities include stabilisation from weak disorder lines and intricate, ordered structures of the phase itself that may provide fruitful areas of future study.