Critical bifurcation and deconfined quantum criticality in an interacting cluster Ising chain

Abstract:We investigate the cluster Ising chain with an additional nearest-neighbor interaction using tensor-network methods and a weak-coupling field theory. Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains related by an exact $O(3)$ flavor symmetry. Their common mass vanishes at the $SU(2)_2$ Wess-Zumino-Novikov-Witten critical point with central charge $c = 3/2$ separating the symmetry-protected topological cluster phase from a ferromagnet. The interaction reduces $O(3)$ to its cyclic subgroup $C_3$, splitting the triplet into a singlet and a doublet whose gaps close separately, producing a critical bifurcation into Ising ($c = 1/2$) and Gaussian ($c = 1$) critical lines. A second ferromagnetic phase opens between these critical lines for repulsive interactions and a disordered phase for attractive ones. The Gaussian line then separates two Landau-incompatible ferromagnets, realizing a deconfined quantum critical line with emergent $O(2)$ symmetry, along which our independently extracted exponents vary continuously yet satisfy the parameter-free relation $\beta = (2\nu - 1)/4$ of the eight-vertex weak universality class. At stronger repulsion this line opens into an extended gapless floating phase with incommensurate algebraic correlations, entered through Berezinskii-Kosterlitz-Thouless transitions. All of these phases and the transitions between them are captured by the weak-coupling theory. Beyond its regime of validity, our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.

Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2608.24248 [cond-mat.str-el]

(or arXiv:2608.24248v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2608.24248 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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