Unified renormalization-group approach to the thermodynamic and ground-state properties of quantum lattice systems

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid

“…Note that here and subsequently the excited states to which we refer are excited states of Liouvillians (evolution operators), rather than Hamiltonians (energy functions). The original RG scheme [22] indeed involved Hamiltonians, whereas the subsequent extension of the scheme to nonequilibrium processes [20], used in this paper, exchanged Hamiltonians for Liouvillians by exploiting the similarity between equations such as (4), and bone fide Schrödinger equations. We require also the left eigenstates of the reference Liouvillian,…”

“…We shall study the attractive East model using a realspace RG developed in the 1980s, and since applied to quantum spin models [22], reaction-diffusion systems [20] and nonequilibrium exclusion models [21]. The procedure is as follows.…”

“…In Section II we define the attractive East model, and for convenience cast its evolution operator in the guise of a quantum spin model. In Section III we explain the RG scheme of References [20,22]. In Section IV we apply this RG to the ordinary East model, emphasising the physical interpretation of the scheme, and in Section V we do the same to its attractive counterpart.…”

“…In this paper we study the attractive East model using the real-space RG scheme of References [20,22]. Our reasons for doing so are twofold.…”

“…The equilibrium behaviour of the attractive East model, modeling a set of experiments in which free volume remains fixed but attraction strength varies, was explored in Reference [1]. Second, we wish to test the utility of the real-space RG scheme, which has previously been applied to quantum spin systems [22], reactiondiffusion systems [20] and simple kinetically constrained models [18].…”