Cooperative Shielding in Many-Body Systems with Long-Range Interaction

Abstract

In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with the suppression of propagation. Here, we show that such apparently contradictory behavior is caused by a general property of longrange interacting systems, which we name Cooperative Shielding. It refers to shielded subspaces that emerge as the system size increases and inside of which the evolution is unaffected by long-range interactions for a long time. As a result, the dynamics strongly depends on the initial state: if it belongs to a shielded subspace, the spreading of perturbation satisfies the Lieb-Robinson bound and may even be suppressed, while for initial states with components in various subspaces, the propagation may be quasi-instantaneous. We establish an analogy between the shielding effect and the onset of quantum Zeno subspaces. The derived effective Zeno Hamiltonian successfully describes the short-ranged dynamics inside the subspaces up to a time scale that increases with system size. Cooperative Shielding can be tested in current experiments with trapped ions. Introduction.-A better understanding of the nonequilibrium dynamics of many-body quantum systems is central to a wide range of fields, from atomic, molecular, and condensed matter physics to quantum information and cosmology. New insights into the subject have been obtained thanks to the remarkable level of controllability and isolation of experiments with optical lattices [1][2][3][4][5][6][7] and trapped ions [8,9]. Recently there has been a surge of interest in the dynamics of systems with long-range interactions, triggered by experiments with ion traps [8,9], where the range of interactions in onedimensional (1D) spin models can be tuned with great accuracy. Other realistic systems that contain long-range interaction include cold atomic clouds [10], natural light-harvesting complexes [11][12][13], helium Rydberg atoms [14], and cold Rydberg gases [15]. Long-range interacting systems display features that are not often observed in other systems, such as broken ergodicity [16][17][18][19] and long-lasting out-of-equilibrium regimes [20].

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

“…(18), points * ), * * ), * * * ), with µ = 1. It is important to notice that for α > 1 the dominating term for g (lat)…”

Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

“…The model then reduces simply to one of non-interacting fermions with a disordered onsite potential and non-random power-law hoppings [61][62][63][64][65][66][67][68]. In such systems, due to a phenomenon termed cooperative shielding [65,66], Anderson localisation is found to persist for all values of the disorder strength and power-law decay exponent α, and for all single-particle states save for a set of measure zero near one edge of the spectrum (which are delocalised for α < 1). This implies that generic many-body states, constructed out of Slater determinants of the localised single-particle eigenstates, are also many-body localised.…”

Long-range topological insulators and weakened bulk-boundary correspondence

“…Independent theoretical studies have shown that LR quantum systems can exhibit various peculiar features, mostly stemming from the breakdown of lattice locality [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. This set includes static correlation functions with hybrid (exponential and algebraic) decay [28][29][30][31], anomalous growth for the entanglement after quenches [32], new constraints on thermalization [33] and on conductivity in NS/NSN junctions [34].…”