Spin many-body phases in standard and topological waveguide QED simulators

25 pags., 16 figs. 6 apps.Quantum spin models find applications in many different areas, such as spintronics, high-Tc superconductivity, and even complex optimization problems. However, studying their many-body behaviour, especially in the presence of frustration, represents an outstanding computational challenge. To overcome it, quantum simulators based on cold, trapped atoms and ions have been built, shedding light already on many non-trivial phenomena. Unfortunately, the models covered by these simulators are limited by the type of interactions that appear naturally in these systems. Waveguide QED setups have recently been pointed out as a powerful alternative due to the possibility of mediating more versatile spin-spin interactions with tunable sign, range, and even chirality. Yet, despite their potential, the many-body phases emerging from these systems have only been scarcely explored. In this manuscript, we fill this gap analyzing the ground states of a general class of spin models that can be obtained in such waveguide QED setups. Importantly, we find novel many-body phases different from the ones obtained in other platforms, e.g., symmetry-protected topological phases with large-period magnetic orderings, and explain the measurements needed to probe them.M.B. acknowledges support from the ERC Advanced Grant QENOCOBA under the European Union (EU) Horizon 2020 program (Grant Agreement No. 742102), G.P. acknowledges support from the Spanish Ministry of Science and Innovation through Grants No. MAT2017-86717-P and No. PID2020-117787GB-100, and A.G.-T. acknowledges support from the Spanish MCIU/AEI/FEDER (EU) project through Grant No. PGC2018-094792-B-100 and from the Proyecto Sinérgico CAM 2020 through Grant No. Y2020/TCS-6545 [Nanophotonics for Quantum Computation (Nanoquco)-Comunidad de Madrid (CM)]. We all acknowledge support from the CSIC Research Platform on Quantum Technologies PTI-001.Peer reviewe