We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact diagonalization and finite-size scaling. The time evolution from a random initial state exhibits features consistent with the localization picture. The dynamics can be observed with quantum gases in optical cavities, localization can be revealed through the time-dependent dynamics of the light emitted by the resonator. Contents arXiv:1902.00357v3 [cond-mat.dis-nn] 12 May 2019 SciPost Physics Submission C Time evolution with Chebyshev expansion technique 25References 26 A Derivation of the Hubbard HamiltonianHere we present the summary of the derivation of Hamiltonian ((1)-(5)). The details in different variants of the model are discussed in e.g. Refs. [26,28,31,[33][34][35].

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We study the phase diagram of the one-dimensional boson gas trapped inside an optical lattice with contact and dipolar interaction taking into account next-nearest terms for both tunneling and interaction. Using the density matrix renormalization group, we calculate how the locations of phase transitions change with increasing dipolar interaction strength for average density ρ = 1. Furthermore, we show an emergence of pair-correlated phases for a large dipolar interaction strength and ρ ≥ 2, including a supersolid phase with an incommensurate density wave ordering manifesting the corresponding spontaneous breaking of the translational symmetry. arXiv:1802.08104v2 [cond-mat.quant-gas]

We study a system of dipolar bosons in a one-dimensional optical lattice using exact diagonalization and density matrix renormalization group methods. In particular, we analyze low energy properties of the system at an average filling of 3/2 atoms per lattice site. We identify the region of the parameter space where the system has non-Abelian Fibonacci anyon excitations that correspond to fractional domain walls between different charge-density-waves. When such onedimensional systems are combined into a two-dimensional network, braiding of Fibonacci anyon excitations has potential application for fault tolerant, universal, topological quantum computation. Contrary to previous calculations, our results also demonstrate that super-solid phases are not present in the phase diagram for the discussed 3/2 average filling. Instead, decreasing the value of the nearest-neighbor tunneling strength leads to a direct, Berezinskii-Kosterlitz-Thouless, super-fluid to charge-density-wave quantum phase transition.

Using exact diagonalization methods we study possible phases in a one-dimensional model of two differently populated fermionic species in a periodically driven optical lattice. The shaking amplitude and frequency are chosen to resonantly drive s − p transition while minimizing the standard intraband tunnelings. We verify numerically the presence of an emergent density wave configuration of composites for appropriate filling fraction and minimized intra-band tunnelings. The majority fermions moving in such a lattice mimic the celebrated Rice-Mele model. Far away from that region, the structure changes to a clustered phase, with the intermediate phase abundantly populated by defects of the density wave. These defects lead to localized modes carrying fractional particle charge. The results obtained are compared with earlier approximate predictions.