Metastability and discrete spectrum of long-range systems

Abstract

Long-lived quasi-stationary states (QSSs) are a signature characteristic of long-range interacting systems both in the classical and in the quantum realms. Often, they emerge after a sudden quench of the Hamiltonian internal parameters and present a macroscopic lifetime, which increases with the system size. Despite their ubiquity, the fundamental mechanism at their root remains unknown. Here, we show that the spectrum of systems with power-law decaying couplings remains discrete up to the thermodynamic limit. As a consequence, several traditional results on the chaotic nature of the spectrum in many-body quantum systems are not satisfied in the presence of long-range interactions. In particular, the existence of QSSs may be traced back to the finiteness of Poincaré recurrence times. This picture justifies and extends known results on the anomalous magnetization dynamics in the quantum Ising model with power-law decaying couplings. The comparison between the discrete spectrum of long-range systems and more conventional examples of pure point spectra in the disordered case is also discussed.

Entanglement propagation and dynamics in non-additive quantum systems

“…Here, the spreading of entanglement entropy after a sudden quench is investigated in a prototypical quantum long-range system. The entanglement features evidenced in previous studies is justified in terms of the peculiar spectral properties of strong long-range systems, which have been recently connected with the appearance of metastable states, whose lifetime grow with the system size [16]. The outcome of the present analysis provides analytical support to the suppression of entanglement spreading, evidenced in Refs.…”

“…Let us notice however, that for thermal-like initial conditions, N k , f k (0), p k (0) will depend only on the ω k , so that the m 1 modes will behave as a single particle. Therefore, the in the strict thermodynamic limit N → ∞ no thermalization can occur and the system remains trapped in a metastable quasistationary state for diverging long times [16].…”

“…For simplicity, we first restrict to the case in which only the k = 0 mode may be resonant. Given that the single particle spectrum for long-range interactions accumulates at high-energy in the N → ∞ limit [16] at order 1/N one can discard the k dependence of all modes at k > 0. Therefore, we can replace f k (t) and ḟk (t) with their high energy limit f π (t), ḟπ (t).…”

“…Equilibration is prevented in non-additive many-body systems due to the effectively finite number of excitations caused by long-range interactions [16]. Nevertheless, for large but finite system sizes N , the out-of-equilibrium phase diagram of long-range interacting quantum systems presents a rich mosaic of phases.…”

“…Signature characteristics of long-range physics are observed across several fields from astrophysics [1,2], to plasma physics [3] and experimental realizations on atomic, molecular and optical systems [4] (AMO), such as, trapped ions [5,6], Rydberg gases [7] and optical cavities [8,9]. Plenty of exotic equilibrium and dynamical features have been detected, including dynamical phase transitions [10,11], time crystals [10,12,13], defect scaling [14,15] and long-lived metastable states [2,16]. These experimental results stimulated an impressive theoretical activity to characterize the equilibrium and dynamical critical scaling induced by long-range interactions in a wide variety of different systems [4,5,9].…”