Deconfined quantum critical points: symmetries and dualities (1703.02426v2)

Abstract: The deconfined quantum critical point (QCP), separating the N\'eel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of $2+1$D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher {criticality}. In this work we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to $N_f = 2$ fermionic quantum electrodynamics (QED), which has its own self-duality and hence may have an O(4)$\times Z_2^T$ symmetry. We propose several dualities for the deconfined QCP with ${\mathrm{SU}(2)}$ spin symmetry which together make natural the emergence of a previously suggested $SO(5)$ symmetry rotating the N\'eel and VBS orders. These emergent symmetries are implemented anomalously. The associated infra-red theories can also be viewed as surface descriptions of 3+1D topological paramagnets, giving further insight into the dualities. We describe a number of numerical tests of these dualities. We also discuss the possibility of "pseudocritical" behavior for deconfined critical points, and the meaning of the dualities and emergent symmetries in such a scenario.

• The paper introduces multiple equivalent field theoretic frameworks, demonstrating that deconfined quantum critical points can be described using dualities such as the NCCP1 model and N_f = 2 QED.
• It reveals the emergence of higher symmetries, including O(4)×Z2^T and SO(5), at the critical points that are not apparent in the underlying microscopic models.
• The work provides numerical and theoretical benchmarks that bridge abstract duality concepts with testable predictions for transitions between Néel and valence bond solid phases.

Overview of "Deconfined Quantum Critical Points: Symmetries and Dualities"

The paper "Deconfined Quantum Critical Points: Symmetries and Dualities" addresses the theoretical framework of deconfined quantum critical points (DQCPs), which separate two-dimensional N éel and valence bond solid (VBS) phases in antiferromagnets. This work is pivotal in challenging the traditional Landau-Ginzburg-Wilson paradigm by introducing a conceptually distinct class of criticality in 2+1 dimensions. The paper primarily elucidates multiple equivalent descriptions of DQCPs and explores emergent symmetries in the low-energy regime through dualities.

Key Aspects of the Paper

1. Equivalent Descriptions and Dualities:

• The paper provides multiple formulations for describing DQCPs, particularly focusing on different but equivalent field theoretic representations. These include approaches such as the noncompact CP$^1$ model (NCCP$^1$) and its dual representations.
• A significant portion of the work is dedicated to revealing how dualities, a powerful tool in theoretical physics, can elucidate complex phenomena such as DQCPs. Notably, the easy-plane deconfined QCP is proposed to be dual to $N_f = 2$ fermionic quantum electrodynamics (QED), which itself possesses a self-duality.

2. Emergent Symmetries:

• The concept of emergent symmetries, such as $O(4) \times Z_2^T$ and $SO(5)$ symmetries, is a cornerstone in understanding the critical behavior at DQCPs. These symmetries are not apparent in the microscopic models but emerge at large wavelengths due to the duality and field theoretic structures.
• Dualities not only map one theory to another but also provide clues about these higher symmetries that transcend individual model details.

3. Numerical and Theoretical Validations:

• The paper outlines several numerical tests and theoretical predictions that can validate or challenge the equivalence and duality relationships. These extend the theoretical proposals into the field of testable, empirical science, providing a bridge between the abstract theoretical constructs and computational approaches.

4. Implications for Topological Phases:

• The discussions of dualities and emergent symmetries also have implications for understanding 3+1D topological paramagnets, offering further insight into the description of 2+1D DQCPs as surfaces of topological phases.
• Theoretical constructs are tied to symmetry-protected topological phases, underscoring the importance of anomalies and their cancellation in providing consistent theories.

Implications and Future Directions

The paper's exploration of DQCPs through dualities and emergent symmetries has profound implications for condensed matter physics and quantum field theory. The insights gained could pave the way for understanding new materials with exotic quantum phases and potentially lead to novel applications in quantum computing when dealing with strongly correlated systems.

The theoretical frameworks and dualities proposed require further numerical and experimental validation to fully understand their implications. Future work should focus on computational studies to test the proposed dualities in various lattice models, deepening our understanding of these sophisticated quantum critical phenomena.

Additionally, the exploration of larger symmetry groups and their role in quantum critical phenomena could unlock a deeper understanding of how symmetries emerge in other contexts, such as high-energy physics or beyond-standard-model physics, given the foundational nature of dualities in theoretical physics.