Holographic quantum matter (1612.07324v3)

Abstract: We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

• The paper introduces holographic duality as a novel method for probing quantum systems lacking quasiparticles by linking field theories to classical gravitational frameworks.
• It rigorously derives correlators and thermalization timescales, demonstrating how scaling behaviors and holographic horizons characterize quantum critical dynamics.
• The findings provide theoretical insights into non-Fermi liquid behavior and outline potential future applications, including the integration of AI in quantum material design.

Essay on "Holographic Quantum Matter"

The paper "Holographic Quantum Matter" discusses the application of holographic duality in understanding quantum systems devoid of quasiparticle excitations. It explores how gravitational theories with emergent spatial dimensions provide solvable examples of such quantum states. This essay presents an expert overview of the key concepts, results, and implications of this work, aimed at seasoned researchers engaged with quantum field theory (QFT) and holography.

Overview of Key Concepts

The holographic duality, specifically the AdS/CFT correspondence, forms the backbone of this discussion. It relates strongly coupled quantum field theories to classical gravitational systems in higher dimensions, using the language of large-N matrix field theories. Central to this duality is the correspondence between boundary field theories and bulk gravitational dynamics, which allows translating complex quantum phenomena into geometrical descriptions.

This duality is leveraged to paper quantum states without quasiparticles, such as those near quantum critical points or in strange metals, prevalent in cuprate superconductors. Such systems challenge traditional descriptions, as they lack long-lived excitations typical in Fermi liquids. A primary goal of the paper is to explore these complex quantum phases using holography, aiming to uncover insights into non-Fermi liquids and similar non-trivial phases.

Strong Numerical Results and Claims

The authors provide rigorous formulations for correlators in quantum systems, resonating with the structure of large-N theories. Notably, the paper elucidates the intricate relationship between thermalization timescales and holographic horizons, characterizing the dynamics of strongly coupled quantum systems through classical gravity calculations.

Holographic techniques reveal specific transport properties, emphasizing non-quasiparticle dynamics. The paper details how certain scaling behaviors and symmetries observed in condensed matter systems can emerge naturally from their holographic duals. For example, it highlights the robustness of universality classes and scaling dimensions within the holographic framework, consistent with known quantum critical behavior.

Implications and Theoretical Insights

The implications of this work are profound both theoretically and practically. Theoretically, it supports the unification of disparate physical phenomena under a single framework—holography—that can transcend limitations of perturbative techniques. It offers potential resolutions to long-standing problems, such as the nature of non-Fermi liquid states and low-temperature behavior of strongly correlated systems.

Practically, while direct experimental translations of these findings are challenging, the holographic approach provides a novel vantage point to interpret complex data from experiments on correlated electron systems. It suggests pathways to bridge the gap between quantum critical behavior and emergent gravity-like descriptions.

Speculation on Future Developments

The future of AI and holography lies in expanding the data-driven approaches to simulating complex systems and refining the digital tools that translate between QFT phenomena and holographic duals. AI could potentially optimize computations in determining bulk space characteristics, a step pivotal for exploring yet unmapped territories of quantum phase transitions.

Additionally, the integration of holography with machine learning might catalyze breakthroughs in functional materials. Automating the search for ground states or critical points in high-dimension parameter spaces—guided by holographic insights—could innovate material design, notably in superconductors or topological insulators.

Conclusion

"Holographic Quantum Matter" provides an in-depth exploration of non-quasiparticle states in quantum critical systems using holographic duality. The paper's methodological advancements and theoretical foresights offer a cornerstone for ongoing and future investigations in quantum matter without quasiparticles, emphasizing the transformative potential of holographic approaches in theoretical physics and condensed matter research. The critical transition states and unique quantum behaviors characterized in this paper hold promise not only for advancing fundamental physics but for inspiring novel, applied technological advancements.