Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model

Abstract

We study the ground-state properties of a quantum sunburst model, composed of a quantum Ising spin ring in a transverse field, symmetrically coupled to a set of ancillary isolated qubits, to maintain a residual translation invariance and also a Z 2 symmetry. The large-size limit is taken in two different ways: either by keeping the distance between any two neighboring ancillary qubits fixed or by fixing their number while increasing the ring size. Substantially different regimes emerge, depending on the various Hamiltonian parameters: For small energy scale δ of the ancillary subsystem and small ring-qubit interaction κ, we observe rapid and nonanalytic changes in proximity to the quantum transitions of the Ising ring, both first order and continuous, which can be carefully controlled by exploiting renormalization-group and finite-size scaling frameworks. Smoother behaviors are instead observed when keeping δ > 0 fixed and in the Ising disordered phase. The effect of an increasing number n of ancillary spins turns out to scale proportionally to √ n for sufficiently large values of n.

Liovillian gap and out-of-equilibrium dynamics of a sunburst Kitaev ring: from local to uniform dissipation

“…To model the weak interaction between the open quantum ring and the surrounding environment, we consider n = L/b uniformly spaced local operators that are always commensurate to the number of sites of the chain L. The whole setup is then put in a sunburst geometry, see also Fig. 1, and translation invariance is narrowed down to translations that are multiples of b [16][17][18]. We work under the Born-Markov and secular approximations, so dissipators can be effectively modeled employing Lindblad quantum jump operators Lx .…”

“…We then consider a lattice model tailored to unveil the crossover regime between the dissipation schemes presented. We investigate a (1 + 1)-dimensional Kitaev ring with local particle-decay dissipators arranged in a sunburst geometry [16][17][18]. The whole apparatus is sketched in Fig.…”

Decoherence and energy flow in the sunburst quantum Ising model

“…As mentioned in the introduction, the overall setup realizes the same lattice configuration as the sunburst quantum Ising model, whose equilibrium ground-state properties have been addressed in [33]. In a time-dependent perspective, the equilibrium limit corresponds to an adiabatically slow dynamics for finite-size systems.…”

“…In contrast, here we are going to focus on the out-of-equilibrium decoherence properties and energy exchanges from the point of view of the ancillary spins, aiming at perceiving the capability of these probes to retrieve information on the Ising ring system under study, and in particular its equilibrium quantum phases before the quench. To this purpose, we consider two different dynamic FSS limits, depending on the parameters we decide to maintain fixed with increasing the lattice size L of the ring [33]:…”

“…We probe the system by means of n equally-spaced qubits (being b their interspace distance), completely independent of each other, to which we will refer in the following as the ancillary spins or simply the external spins (red dots). A thorough analysis of the equilibrium ground-state properties of this apparatus has been recently performed in [33]. Here we are interested in investigating the out-of-equilibrium dynamics triggered by a sudden quench of an external parameter κ, which couples the system under study with the monitoring devices.…”