We investigate the effect of short-range correlations on the dynamical phase diagram of quantum many-body systems with long-range interactions. Focusing on Ising spin chains with power-law decaying interactions and accounting for short-range correlations by a cluster mean field theory we show that short-range correlations are responsible for the emergence of a chaotic dynamical region. Analyzing the fine details of the phase diagram, we show that the resulting chaotic dynamics bears close analogies with that of a tossed coin.
We investigate the effect of short-range correlations on the dynamical phase diagram of quantum many-body systems with long-range interactions. Focusing on Ising spin chains with power-law decaying interactions and accounting for short-range correlations by a cluster mean field theory we show that short-range correlations are responsible for the emergence of a chaotic dynamical region. Analyzing the fine details of the phase diagram, we show that the resulting chaotic dynamics bears close analogies with that of a tossed coin.
In this thesis we study the dynamics of the long-range interacting Ising chain using a cluster mean-field approach, a mean-field theory that accounts for short range correlations. The principal result is that, if the system is isolated from an external environment, the model exhibits two different behaviors depending on the range of the interactions. Whenever the system is truly long-range, it exhibits a sharp mean-field dynamical phase transition from a dynamical ferromagnetic to a dynamical paramagnetic phase. Reducing the range of the interactions a critical region, showing hypersensitivity to initial conditions, appears. Interestingly, this chaotic region shares the same physics of a classical tossed coin that is allowed to bounce on the floor. In a second part of the work we derive the cluster mean-field equations of motion describing the dynamics of a fully connected Ising chain connected to an external bath. In particular we focused on the dynamics in presence of a dissipation generated by string of Glauber operators acting on one or more sites of the chain. This model, in presence of global dissipative processes, exhibits persistent oscillations in time revealing the existence of a boundary time-crystal and we studied the stability of the boundary time-crystal showing that global dissipative processes are a key ingredient for their existence.
Abstract Quantum many body systems with long range interactions are known to display many fascinating phenomena experimentally observable in trapped ions, Rydberg atoms and polar molecules. Among these are dynamical phase transitions which occur after an abrupt quench in spin chains with interactions decaying as and whose critical dynamics depend crucially on the power : for systems with the transition is sharp while for it fans out in a chaotic crossover region. In this paper we explore the fate of critical dynamics in Ising chains with long-range interactions when the transverse field is ramped up with a finite speed. While for abrupt quenches we observe a chaotic region that widens as is increased, the width of the crossover region diminishes as the time of the ramp increases, suggesting that chaos will disappear altogether and be replaced by a sharp transition in the adiabatic limit.
Abstract The presence of algebraically decaying long-range interactions may alter the critical as well as topological behaviour of a quantum many-body systems. However, when the interaction decays at a faster rate, the short-range behaviour is expected to be retrieved. Similarly, the long-range nature of interactions has a prominent signature on the out of equilibrium dynamics of these systems, e.g. in the growth of the entanglement entropy following a quench, the propagation of mutual information and non-equilibrium phase transitions. In this review, we summarize the results of long-range interacting classical and quantum Ising chains mentioning some recent results. Thereafter, we focus on the recent developments on the integrable long-range Kitaev chain emphasising the role of long-range superconducting pairing term on determining its topological phase diagram and out of equilibrium dynamics and also incorporate relevant discussions on the corresponding Ising version.
Understanding the dynamics of many-body systems is crucial for understanding, e.g., thermalization or transmission of information. Nevertheless, little is known in the case of quantum systems with long-range interactions. Here, we analyze the long-range Ising model in a transverse field, where interactions decay as a power-law with distance ∝r−α, α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2; weakly long-range for 1<α<2 without a clear light cone but with a finite propagation speed of excitations; and fully non-local for α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb--Robinson bounds. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasi-particles remains valid for long-range interactions. This allows an intuitive interpretation in terms of qualitative changes to the spin-wave dispersion, leading to diverging quasi-particle velocities in the long-range regime. Our results may be tested in state-of-the-art trapped-ion experiments.
Abstract We discuss how nonlocality originates in long-range quantum systems and how it affects their dynamics at and out of equilibrium. We focus in particular on the Kitaev chains with long-range pairings and on the quantum Ising chain with long-range antiferromagnetic coupling (both having a power-law decay with exponent α ). By studying the dynamic correlation functions, we find that for every finite α two different behaviours can be identified, one typical of short-range systems and the other connected with locality violation. The latter behaviour is shown related also with the known power-law decay tails previously observed in the static correlation functions, and originated by modes—having in general energies far from the minima of the spectrum—where particular singularities develop as a consequence of the long-rangedness of the system. We refer to these modes as to ‘singular’ modes, and as to ‘singular dynamics’ to their dynamics. For the Kitaev model they are manifest, at finite α , in derivatives of the quasiparticle energy, the order of the derivatives at which the singularity occurs is increasing with α . The features of the singular modes and their physical consequences are clarified by studying an effective theory for them and by a critical comparison of the results from this theory with the lattice ones. Moreover, a numerical study of the effects of the singular modes on the time evolution after various types of global quenches is performed. We finally present and discuss the presence of singular modes and their consequences in interacting long-range systems by investigating in the long-range Ising quantum chain, both in the deep paramagnetic regime and at criticality, where they also play a central role for the breakdown of conformal invariance.
The nonequilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power law with distance ∝r(-α), α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2, weakly long range for 1<α<2 without a clear light cone but with a finite propagation speed of almost all excitations, and fully nonlocal for α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb-Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasiparticles remains valid, allowing an intuitive interpretation of our findings via divergences of quasiparticle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.