At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster-crystal. In the present work we explore the out-of-equilibrium dynamics for a two-dimensional realisation, which is relevant to superconducting materials with multi-scale intervortex forces. We find that for small temperatures following a quench, the suppression of the thermally-activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in terms of an "effective polydispersity" induced by multi-scale interactions. This demonstrates that a vortex glass can form in clean systems of thin films of "type-1.5" superconductors. An additional setup to study this physics can be layered superconducting systems, where the shape of the effective vortex-vortex interactions can be engineered. The vortex glass is one of the key states in the theory of magnetic and transport properties of type-2 superconductors in the presence of disorder [1][2][3][4]. Within this frame, the glassy phase is caused by the pinning of vortices by impurities and is absent in a clean sample. In this work we demonstrate that a vortex glass state can be an inherent property of a superconducting system characterised by multiple coherence lengths. In a more general context, our work demonstrates that a structurally disordered glass state of matter can be obtained in the absence of disordered substrates for a simple two-dimensional monodisperse ensemble of particles interacting via isotropic, repulsive, ultrasoft interactions [5,6]. This is surprising as those conditions are usually associated with minimal frustration [7][8][9][10]. The glass phase appears below a non-equilibrium glass transition temperature and extends to the lowest temperatures examined. We provide a description of the microscopic mechanism responsible for the appearance of glassiness in terms of an effective polydispersity that emerges following a quench due to multi-scale interactions [see Fig. 1]. In typical glass forming liquids, frustration results from polydisperse mixtures of particles [11]. In the present systems, the appearance of glassiness stems from the effective polydispersity of clusters sizes.Several works have recently discussed "type-1.5 superconductors" that are characterised by multiple coherence lengths, some of which are larger and some smaller than the magnetic field penetration length. These multiple coherence lengths arise in superconducting states that break multiple symmetries and also in materials with multiple superconducting bands. Several materials were suggested in experiments to belong to this type of superconductors [12][13][14][15], where vortices can display multi-scale attractive and repulsive inter-vortex interactions [12,14,[16][17][18]. Multiple attractive length scales come from core-core intervortex interactions. Multiple repulsive length scales can be obtained instead in (i) artificially fabrica...

We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium lowtemperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquid-like long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics.