Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes

TL;DR

This study investigates a 2D interacting plaquette model using real space renormalization, revealing a phase transition at a critical coupling where the ground state shifts from deconfined finite clusters to a confined infinite cluster, characterized by gap behavior.

Contribution

It introduces a detailed analysis of the deconfinement transition in a 2D plaquette model using real space RG, identifying the critical coupling and the nature of ground states.

Findings

Critical coupling J_c=0.473528..

Transition from finite to infinite cluster ground states

Singlet-triplet gap vanishes at J_c

Abstract

A two-dimensional model of interacting plaquettes is studied by means of the real space renormalization group approach. Interactions between the plaquettes are mediated solely by spin excitations on the plaquettes. Depending on the plaquette-plaquette coupling $J$, we find two regimes: "confinement" $J_c< J\leq 1$, where the singlet ground state forms an infinite ("confined") cluster in the thermodynamical limit. Here the singlet-triplet gap vanishes, which is the signature for long range spin-spin correlators. "deconfinement" $0\leq J< J_c$, where the singlet ground state "deconfines" - i.e. factorizes - into finite $n$-clusters of size $2^n\times 2^n$, with $n\leq n_c(J)$. Here the singlet-triplet gap is finite. The critical value turns out to be $J_c=0.473528..$.