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

• URL: http://arxiv.org/abs/2608.24248v1
• Date: Tue, 25 Aug 2026 08:48:15 GMT
• Title: Critical bifurcation and deconfined quantum criticality in an interacting cluster Ising chain
• Abstract summary: We investigate a cluster Ising chain with an additional nearest-neighbor interaction.<n>Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains.<n>Our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.
• Score: 35.18016233072556
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $β= (2ν- 1)/4$ 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.

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