Supersymmetric Deconfined Quantum Criticality Advances Physics Beyond Ginzburg-Landau Paradigm

Researchers are increasingly focused on understanding deconfined quantum critical points (DQCPs), transitions between ordered states that challenge traditional theories of continuous change. Zhi-Qiang Gao (University of California, Berkeley), Hui Yang (University of Pittsburgh), and Yan-Qi Wang (University of Maryland) et al. now demonstrate a pathway to extend this paradigm by incorporating internal supersymmetry , a powerful symmetry principle , into these critical phenomena. Their work proposes a novel ‘supersymmetric deconfined critical point’ (sDQCP) in a spin-½ system, revealing intricate connections between seemingly disparate symmetries and offering a new framework for describing complex quantum behaviour. By formulating a non-linear sigma model and developing a corresponding gauge theory, the team not only characterises the sDQCP’s properties but also elegantly links it back to established DQCP scenarios, potentially unlocking a deeper understanding of quantum criticality itself.

Supersymmetric Deconfined Quantum Criticality in OSp(1|2) emerges

Scientists have unveiled a novel theoretical framework extending the concept of deconfined quantum criticality to systems possessing internal supersymmetry (SUSY). This breakthrough research proposes a supersymmetric deconfined quantum critical point (sDQCP), a unique phase transition occurring between ordered phases that break distinct symmetries, offering a pathway to continuous transitions beyond conventional paradigms. The team achieved this by focusing on the minimal supersymmetric generalization of SU(2) spin systems, specifically OSp(1|2), and meticulously formulating a non-linear sigma model on a supersphere target space to capture the intricate symmetry intertwinement characteristic of the sDQCP. Researchers developed a gauge theory description to investigate the dynamical properties of this sDQCP, including a compelling heuristic argument suggesting 3D XY critical behaviour.
The study establishes that explicitly breaking the OSp(1|2) symmetry down to SU(2) provides a continuous connection between the newly proposed sDQCP and the well-established conventional DQCP scenario. This connection is crucial, demonstrating a broader applicability of the DQCP paradigm and offering a route to understanding more complex quantum phase transitions. The work opens exciting avenues for exploring novel critical phenomena in systems with enhanced symmetries. Experiments show that the sDQCP arises from a direct, non-fine-tuned quantum phase transition between two distinct ordered phases, each breaking different symmetries.

One phase breaks the internal OSp(1|2) symmetry, while the other breaks lattice rotation symmetry, a configuration that necessitates a careful consideration of symmetry interplay. The researchers formulated a non-linear sigma model on the supersphere to describe this symmetry intertwinement, effectively capturing the complex interactions at the critical point. This model serves as a powerful tool for analysing the behaviour of the system near the sDQCP and predicting its critical properties. The team further refined their analysis by developing a gauge theory formalism to address the dynamical aspects of the sDQCP.

This approach allowed them to explore the behaviour of the system in real-time and gain insights into the nature of the excitations near the critical point. A key finding is the heuristic argument for 3D XY critical behaviour, suggesting a specific universality class for the sDQCP. Finally, the researchers demonstrated that a controlled breaking of the internal SUSY symmetry smoothly connects the sDQCP to the familiar DQCP scenario, solidifying its place within the broader landscape of quantum criticality and offering a pathway for future investigations.

Supersymmetric Deconfined Critical Point Modelling and Gauge Theory

Scientists investigated a deconfined critical point (DQCP) extending the paradigm to systems exhibiting internal supersymmetry (SUSY). This work proposes a supersymmetric deconfined critical point (sDQCP) within the minimal supersymmetric generalization of spin-1/2, specifically the system. Researchers hypothesized a transition between a phase breaking internal symmetry and another breaking lattice rotation symmetry, establishing a novel critical regime. To model this sDQCP, the team formulated a non-linear sigma model residing on the supersphere target space, meticulously capturing the intricate symmetry intertwinement central to the phenomenon.

Experiments employed a gauge theory description to probe the dynamical properties of the sDQCP, including a heuristic argument predicting 3D XY critical behavior. The study pioneered the construction of this gauge theory, enabling detailed analysis of the critical exponents and universality class. Scientists developed a non-linear sigma model on the supersphere, a mathematical space incorporating both bosonic and fermionic degrees of freedom, to accurately represent the system’s complex interactions. This innovative approach allowed them to map the sDQCP onto a geometric framework, revealing its underlying topological properties and facilitating calculations of critical exponents.

Furthermore, the research team demonstrated that explicitly breaking the SUSY down to conventional symmetry continuously connects the sDQCP to the well-established DQCP scenario. This connection was achieved through a controlled perturbation of the Hamiltonian, allowing scientists to trace the evolution of the critical point and confirm its relationship to known physics. The team engineered a pathway to transition between the supersymmetric and non-supersymmetric critical points, validating the robustness of the sDQCP concept. This methodological innovation provides a powerful tool for exploring the interplay between symmetry, criticality, and supersymmetry in condensed matter systems.

The approach enables a deeper understanding of quantum phase transitions and offers a new perspective on the emergence of exotic states of matter. This method achieves a precise characterization of the sDQCP, paving the way for potential applications in quantum information and materials science. The. Focusing on a minimal supersymmetric generalization of spin-1/2, the team proposes an sDQCP mediating a transition between a phase breaking internal SUSY and one breaking lattice rotation symmetry. Experiments revealed the formulation of a non-linear sigma model on a supersphere target space, effectively capturing the symmetry intertwinement characteristic of the sDQCP.

The researchers developed a gauge theory description to investigate the dynamical properties of this critical point, proposing a heuristic argument supporting 3D XY critical behaviour. Measurements confirm that explicitly breaking the OSp(1|2) symmetry down to SU(2) continuously connects the sDQCP to the conventional DQCP scenario previously established in the field. Data shows that within the proposed model, a VBS vortex core carries a spin-1/2 charge under SU(2)S, as it is not bonded to neighbouring sites forming a spin singlet. Consequently, proliferation of these VBS vortices spontaneously breaks SU(2)S and drives the system into a Néel phase.

Similarly, the team recorded that textures in the Néel phase are skyrmions carrying lattice angular momenta, restoring SU(2)S while breaking (Z4)R and driving the system back into the VBS phase. The study details the OSp(1|2) Lie supergroup symmetry, where the five generators, Sa and Vα, satisfy specific commutation and anticommutation relations, defining the system’s conserved quantities. Calculations demonstrate that the Casimir operator of OSp(1|2) equals S(S + 1/2) for a spin-S irrep, providing a crucial parameter for characterizing the system’s behaviour. This breakthrough delivers a deeper understanding of quantum mechanical SUSY and its potential connection to emergent spacetime SUSY, even when the initial SUSY is not exact.