Deconfined quantum criticality with internal supersymmetry

Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg–Landau paradigm. In this work we extend the DQCP paradigm to systems with internal supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin $SU(2)$, namely $OSp(1|2)$, we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal $OSp(1|2)$ and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including a heuristic argument for 3D XY critical behavior. Finally, we show that explicitly breaking $OSp(1|2)$ down to $SU(2)$ continuously connects our sDQCP to the conventional DQCP scenario.

💡 Research Summary

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The paper introduces a novel extension of the deconfined quantum critical point (DQCP) framework to lattice systems that possess an internal supersymmetry (SUSY). Traditional DQCP describes a direct, non‑fine‑tuned quantum phase transition between two ordered phases that break distinct symmetries—typically spin‑rotation SU(2) and lattice‑rotation Z₄—through the intertwinement of topological defects (spinons, skyrmions) that carry the charge of the opposite symmetry. The authors ask whether a similar mechanism can operate when the on‑site Hilbert space carries a representation of a Lie superalgebra, i.e., when the system enjoys an internal SUSY.

The minimal supersymmetric generalization of a spin‑½ SU(2) degree of freedom is the orthosymplectic supergroup OSp(1|2). Its five generators consist of three bosonic SU(2) spin operators Sᵃ and two fermionic operators Vα that transform as a spin‑½ doublet under SU(2). The algebra obeys