Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models Calixto Molina, Manuel Mayorgas Reyes, Alberto Guerrero, Julio Quantum phase transitions Many-body systems Symmetric quDits Coherent states Parity Pairwise entanglement Spin squeezing We thank the support of the Spanish MICINN through the Project PGC2018-097831-B-I00 and Junta de Andalucia through the Projects SOMM17/6105/UGR, UHU-1262561 and FQM-381. JG also thanks MICINN for financial support from FIS2017-84440-C2-2-P. AM thanks the Spanish MIU for the FPU19/06376 predoctoral fellowship. We all thank Octavio Castanos for his valuable collaboration in the early stages of this work. Collective spin operators for symmetric multi-quDit (namely identical D-level atom) systems generate a U(D) symmetry. We explore generalizations to arbitrary D of SU(2)-spin coherent states and their adaptation to parity (multi-component Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric N-quDit states, expressed in the last two cases in terms of collective U(D)-spin operator expectation values. Then, we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin–Meshkov–Glick models of 3-level identical atoms. We also propose an extension of the concept of SU(2)-spin squeezing to SU(D) and relate it to pairwise D-level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting D-level atom models. 2021-10-19T08:34:33Z 2021-10-19T08:34:33Z 2021-09-13 journal article Calixto, M., Mayorgas, A. & Guerrero, J. Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models. Quantum Inf Process 20, 304 (2021). [https://doi.org/10.1007/s11128-021-03218-6] http://hdl.handle.net/10481/70965 10.1007/s11128-021-03218-6 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Springer