Out-of-equilibrium dynamics of quantum systems with short- and long-range interactions

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.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.

arXiv:1905.12381Journal of Physics A Mathematical and TheoreticalNov 11, 201946 citations

Critical dynamics of long-range models on dynamical Lévy lattices

Riccardo Aiudi, Raffaella Burioni, A. Vezzani

We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimensions in the presence of long-range interactions, ${J}_{ij}\ensuremath{\propto}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$. We implement a local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\ensuremath{\sigma}$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long-range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\ensuremath{\sigma}$, highlighting that the onset of the short-range regime for the dynamical critical properties appears to occur at a value of $\ensuremath{\sigma}$ which differs from the equilibrium one.We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimensions in the presence of long-range interactions, ${J}_{ij}\ensuremath{\propto}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$. We implement a local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\ensuremath{\sigma}$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long-range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\ensuremath{\sigma}$, highlighting that the onset of the short-range regime for the dynamical critical properties appears to occur at a value of $\ensuremath{\sigma}$ which differs from the equilibrium one.

arXiv:2303.18057Physical review. B./Physical review. BJun 28, 20233 citations

Dynamics of quantum systems with long-range interactions

Alexey Vyacheslavovich Gorshkov

Bulletin of the American Physical SocietyJun 1, 20200 citations

Continuous symmetry breaking in a trapped-ion spin chain

Lei Feng, Or Katz, Casey Haack +5 more

Abstract One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to $23$ spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.Abstract One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to $23$ spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

arXiv:2211.01275NatureNov 15, 202350 citations

z

as a function of the decay parameter $\ensuremath{\sigma}$, highlighting that the onset of the short-range regime for the dynamical critical properties appears to occur at a value of $\ensuremath{\sigma}$ which differs from the equilibrium one.

23

spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.