Deng, X.-L. DPorras Torres, DiegoCirac, J. Ignacio2023-06-202023-06-202008-031050-294710.1103/PhysRevA.77.033403https://hdl.handle.net/20.500.14352/52214©2008 The American Physical Society. This work was supported by the Deutscher Akademischer Austausch Dienst, SCALA and CONQUEST projects and the DFG.The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose-Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. In addition to that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, such as models with attractive or site-dependent phonon-phonon interactions.engjournal articlehttp://doi.org/10.1103/PhysRevA.77.033403https://journals.aps.orgopen access53Renormalization-groupsTransitionSuperfluidInsulatorAtomsFísica (Física)22 Física