The competition between strong interactions and disorder can fundamentally alter the ground-state landscape of quantum many-body systems, leading to exotic phases that transcend the conventional dichotomy of order and disorder. In this work, we systematically investigate the ground-state properties of hard-core bosons with nearest-neighbor repulsive interactions on a two-dimensional triangular lattice in the presence of a random on-site chemical potential—a paradigmatic model of diagonal disorder. Using large-scale path-integral Monte Carlo simulations combined with the worm algorithm, we numerically study the system at finite temperature and extract key observables: the superfluid density (characterizing phase coherence and superfluidity, \rho_s), the Edwards-Anderson order parameter (quantifying glassy behavior via frozen local density fluctuations, q_ea), and the static structure factor (probing crystalline order, S(\mathbfk)). Our simulations are performed on lattices of linear size up to L=24, with careful averaging over up to 300 independent Monte Carlo runs and 10 distinct disorder realizations to ensure statistical convergence and to mitigate finite-size effects.
Our results reveal that, for moderate disorder strengths \Delta and at low temperature T=0.2t, the system stabilizes into a superglass phase — a simultaneous manifestation of superfluidity and glassiness without any accompanying crystalline order. Specifically, for average chemical potentials \mu_0/V=3.0 and 6.0, and for t/V=0.1, we find a parameter window \Delta\approx0.1V to 0.4V where \rho_s>0 and q_ea>0 coexist, while \overlineS(\mathbfk)^\mathrmmax remains vanishingly small. This coexistence is robust against finite-size scaling: as system size increases, \overlineS(\mathbfk)^\mathrmmax decays to zero, whereas both \overline\rho_s and q_ea converge to finite values, confirming the thermodynamic stability of the superglass phase. In contrast, for \mu_0/V=4.5 (where the clean system is a solid phase), increasing disorder only leads to a conventional Bose glass phase with q_ea>0 but \overline\rho_s=0. Furthermore, we map out the low-temperature t-\mu phase diagram at fixed \Delta=0.25V, identifying regions of superfluid, Bose glass, and superglass phases. Notably, the superglass emerges in a finite window of intermediate interaction strengths V\approx6-10t, bridging the superfluid and Bose glass regimes. Finite-temperature simulations show that the superglass phase is remarkably robust against thermal fluctuations: the Edwards-Anderson order parameter remains nearly constant for temperatures up to T\lesssim t, and a finite superfluid response persists as long as T\lesssim t. This thermal stability makes the superglass phase experimentally accessible in state-of-the-art ultracold-atom setups. This work provides the first demonstration that a stable superglass phase exists in a hard-core boson system with only diagonal (chemical potential) disorder on a geometrically frustrated triangular lattice—without requiring off-diagonal disorder or random interactions. Our findings significantly expand the parameter space for realizing superglass phases and establish a concrete, experimentally friendly platform for their observation, thereby bridging a critical gap between theoretical prediction and laboratory realization.