One-dimensional quantum many body systems with long-range interactions

Abstract

The presence of algebraically decaying long-range interactions may alter the\ncritical as well as topological behaviour of a quantum many-body systems.\nHowever, when the interaction decays at a faster rate, the short-range\nbehaviour is expected to be retrieved. Similarly, the long-range nature of\ninteractions has a prominent signature on the out of equilibrium dynamics of\nthese systems, e.g, in the growth of the entanglement entropy following a\nquench, the propagation of mutual information and non-equilibrium phase\ntransitions. In this review, we summarize the results of long-range interacting\nclassical and quantum Ising chains which have been studied since decades.\nThereafter, we focus on the recent developments on the integrable long-range\nKitaev chain emphasising the role of long-range superconducting pairing term on\ndetermining its topological phase diagram and out of equilibrium dynamics.\n