We employ a deep learning method to deduce the textit{bulk} spacetime from
textit{boundary} optical conductivity. We apply the neural ordinary
differential equation technique, tailored for continuous functions such as the
metric, to the typical class of holographic condensed matter models featuring
broken translations: linear-axion models. We successfully extract the bulk
metric from the boundary holographic optical conductivity. Furthermore, as an
example for real material, we use experimental optical conductivity of
$text{UPd}_2text{Al}_3$, a representative of heavy fermion metals in strongly
correlated electron systems, and construct the corresponding bulk metric. To
our knowledge, our work is the first illustration of deep learning bulk
spacetime from textit{boundary} holographic or experimental conductivity data.
Deep Learning Bulk Spacetime from Boundary Optical Conductivity
In this study, we employ a deep learning method to deduce the bulk spacetime from boundary optical conductivity in holographic condensed matter models. We specifically focus on linear-axion models featuring broken translations. By applying the neural ordinary differential equation technique, we successfully extract the bulk metric from the boundary holographic optical conductivity.
To validate our approach, we use experimental optical conductivity data of $text{UPd}_2text{Al}_3$, which is a representative of heavy fermion metals in strongly correlated electron systems. Using the experimental data, we construct the corresponding bulk metric. Notably, this is the first time that deep learning has been applied to extract bulk spacetime from either boundary holographic or experimental conductivity data.
Future Roadmap:
1. Refining Deep Learning Models
One of the key challenges going forward is in refining the deep learning models used in this study. The neural ordinary differential equation technique shows promise, but there is room for improvement in accurately deducing the bulk spacetime from the boundary optical conductivity. Further research and development in this area will be crucial.
2. Exploring Other Holographic Condensed Matter Models
While this study focuses on linear-axion models with broken translations, it would be valuable to extend the analysis to other holographic condensed matter models. By applying deep learning techniques to a broader range of models, we can gain deeper insights into the relationship between bulk spacetime and boundary optical conductivity in different physical systems.
3. Investigation of Additional Real Materials
Expanding our analysis to include other real materials will be essential in validating and generalizing the results obtained from $text{UPd}_2text{Al}_3$. By examining the optical conductivity data of different materials, particularly those in strongly correlated electron systems, we can further enhance our understanding of how bulk metric can be extracted using deep learning techniques.
4. Integration with Other Physical Observables
In order to gain a more comprehensive understanding of the relationship between bulk and boundary properties in holographic condensed matter models, it would be worthwhile to explore the integration of deep learning techniques with other physical observables. By considering multiple observables simultaneously, we can strengthen our analysis and potentially uncover new insights.
5. Practical Applications
Finally, as the field of deep learning continues to advance, there may be practical applications for extracting bulk spacetime from boundary optical conductivity data. This could have implications in various fields, such as material science and condensed matter physics, where understanding the underlying spacetime structure is crucial for predicting and designing new materials with specific properties.
In conclusion, this study provides a groundbreaking illustration of deep learning bulk spacetime from boundary optical conductivity. While there are challenges and opportunities ahead, further research in refining models, exploring different models and materials, integrating with other observables, and exploring practical applications will contribute to a deeper understanding of the relationship between bulk and boundary properties in holographic condensed matter models.