Quantum phase transitions in holographic models of magnetism and superconductors (1003.0010v2)

Abstract: We study a holographic model realizing an "antiferromagnetic" phase in which a global SU(2) symmetry representing spin is broken down to a U(1) by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged AdS black hole. We observe that the phase transition for both neutral and charged (as in the standard holographic superconductor) order parameters can be driven to zero temperature by a tuning of the UV conformal dimension of the order parameter, resulting in a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type. We also characterize the antiferromagnetic phase and an externally forced ferromagnetic phase by showing that they contain the expected spin waves with linear and quadratic dispersions respectively.

Quantum Phase Transitions in Holographic Models of Magnetism and Superconductors

The paper investigates quantum phase transitions within holographic models, offering an exploration of magnetism and superconductors through a theoretical framework grounded in the principles of holography. The core focus is on a particular holographic model that demonstrates an antiferromagnetic phase, arising due to the spontaneous symmetry breaking of a global $SU(2)$ symmetry down to a $U(1)$ symmetry at finite electric charge density.

Key Insights and Findings

1. Holographic Model Implementation: The paper employs a condensation mechanism of a neutral scalar field within a charged AdS black hole. This mechanism forms the backbone for understanding the quantum phase transition, which can be driven to zero temperature by tuning the UV conformal dimension of the order parameter. The model unveils a Berezinskii-Kosterlitz-Thouless (BKT) type transition when approaching criticality.
2. Antiferromagnetic and Ferromagnetic Phases: The characterization of the antiferromagnetic phase, achieved by spontaneous symmetry breaking, results in spin waves with linear dispersion. Conversely, externally induced ferromagnetic phases yield spin waves characterized by quadratic dispersions. These findings align well with the expected theoretical behaviors of these phases, providing credibility to the holographic model.
3. IR Conformal Field Theory Emergence: At low energies, the system transitions to an infrared fixed point depicted by a (0+1)-dimensional conformal field theory, akin to AdS$_2 \times \mathbb{R}^{d-1}$ geometry. This transition encompasses the subtleties of non-Fermi liquid behaviors and superconducting instability, offering a unified understanding from the gravitational perspective.
4. Quantum Criticality and Scaling Behavior: The quantum phase transition showcases exponential scaling characteristically linked to BKT transitions. This arises from a non-linear sensitivity to the UV conformal dimension of the scalar field, as detailed through the expansion and analysis of relevant scalar and spinor operators.
5. Theoretical Implications and Numerical Results: The paper supports its arguments with numerical calculations delineating key exponents such as $\beta$ and $\delta$, confirming mean-field behavior near phase transitions. It also explores quantum critical points across varying parameter spaces, including UV dimension and finite magnetic fields—vital for comprehending the holistic interaction of superconductivity and antiferromagnetism.

Implications and Future Directions

The holographic models presented have broad implications, particularly in modeling many-body systems and understanding the complex interactions that govern quantum phase transitions. By elucidating both superconducting and magnetic ordering phenomena, the paper opens avenues for enhancing the theoretical understanding of condensed matter systems, especially those at critical junctures.

Future research may delve into the granularity of these interactions, extending the models to consider fermionic operators or intricate backreaction mechanisms. Furthermore, the potential competition and coexistence between superconducting and magnetic phases may reveal insights into real-world applications and further theoretical nuances.

Conclusion

Overall, the paper advances theoretical understanding through pioneering applications of holography in studying quantum phase transitions. Its insightful findings on magnetism, superconductors, and the nuances of phase transitions contribute significantly to the field, establishing a robust platform for future exploration. This paper is instrumental for researchers interested in developing comprehensive models of strongly correlated electronic systems and quantum criticality.