Circuit QED architectures of superconducting artificial atoms and microwave resonators are currently moving toward multiatom, multiresonator setups with drastically enhanced coherence times, making them increasingly attractive candidates for quantum simulations. We propose and analyze a circuit QED design that simulates a quantum transverse-field Ising chain with current technology. Our setup can be used to study quench dynamics, the propagation of localized excitations, and other nonequilibrium features in a field theory exhibiting a quantum phase transition and based on a design that could easily be extended to break the integrability of the system.

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer or a weak link, when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, $\Delta_{ws}\Delta_{wl}=1 $, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard LL, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model.

Circuit QED systems of artificial atoms interacting with microwaves are promising tools for quantum simulations and quantum information processing. We investigate whether a circuit QED system containing a large number of artificial atoms can undergo a superradiant phase transition. By applying a no-go theorem for such phase transitions known for cavity QED systems with real atoms to circuit QED systems, we find that the currently accepted standard description of circuit QED fails in an important aspect as it erroneously predicts the possibility of a superradiant phase transition. We generalize the no-go theorem to the case of (artificial) atoms with many energy levels and thus make it more applicable for realistic cavity or circuit QED systems.