Spin Glasses Exhibit Emergent Spacetime Via Spectral Functions with Non-Compact Support

The search for a unified theory of gravity and quantum mechanics continues to drive innovation in theoretical physics, and recent work suggests a surprising connection between the complex behaviour of disordered systems and the emergence of spacetime itself. Dimitris Saraidaris and Leo Shaposhnik, both from Freie Universitat Berlin, are now exploring this link by investigating whether certain disordered magnetic systems, known as spin glasses, can exhibit properties mirroring those of a holographic duality, a theoretical framework connecting gravity in one dimension to quantum mechanics in another. Their research demonstrates that the spectral functions of several spin glass models, including the SU Heisenberg chain and the -spin model, develop characteristics remarkably similar to those predicted for systems with emergent spacetime, specifically exhibiting exponential tails indicative of a radial direction. This finding suggests that the seemingly disparate worlds of disordered magnetism and gravitational physics may be more deeply connected than previously thought, potentially offering new avenues for understanding the fundamental nature of spacetime.

Recent work has revealed that the properties of spectral functions are deeply connected to the emergence of semiclassical spacetime and the formation of causal horizons. A key requirement for a radial direction, essential for spacetime to emerge, is that the spectral function exhibits non-compact support. The algebraic structure of the underlying quantum system also appears to play a crucial role in determining the geometry of the resulting spacetime.

This research focuses on the 3D Ising spin glass to explore this connection, analysing the spectral function for evidence of non-compact support which would indicate the emergence of a radial direction and, consequently, a semiclassical spacetime. The team constructs an algebraic framework to describe the spin glass and calculates the spectral function within this framework, allowing for a detailed examination of its properties and potential implications for emergent geometry. The research builds upon conjectures suggesting a duality between complex gravitational configurations and glassy systems, assessing in which parameter regimes these systems might exhibit holographic properties. They compute the spectral functions of the SYK model, the p-spin model, and the SU Heisenberg chain, with quenched disorder, examining their behaviour in various parameter regimes. A significant finding is that the SU Heisenberg chain, in its spin glass phase, exhibits behaviour warranting further investigation.

Spacetime Emerges From Quantum Entanglement

A substantial body of research explores the idea that spacetime itself is not fundamental, but rather emerges from quantum entanglement and quantum information, aiming to reconcile quantum mechanics with general relativity. This research focuses on the holographic principle and the AdS/CFT correspondence, which proposes that a theory of gravity in a higher-dimensional space is equivalent to a quantum field theory without gravity in one fewer dimension, suggesting that the geometry of the higher-dimensional space can be reconstructed from the quantum entanglement of the boundary theory. Entanglement entropy, a measure of the entanglement between regions of the boundary theory, is considered a key ingredient in understanding emergent geometry, with the amount of entanglement dictating the connectivity and geometry of the bulk spacetime. Research also connects this to quantum gravity and the information paradox associated with black holes, exploring how entanglement can resolve the paradox and describe the interior of black holes.

The investigation extends to operator algebras and von Neumann algebras, providing a mathematical framework for describing the local observables and structure of quantum systems, crucial for understanding the emergence of spacetime. Specific areas of investigation include the SYK model, a solvable model of interacting fermions with connections to quantum gravity, and the double-scaled version of this model. Researchers are also exploring the connection between quantum chaos and the emergence of spacetime, using Out-of-Time-Ordered Correlators (OTOCs) to quantify the sensitivity of quantum systems to perturbations. Tools from random matrix theory and free probability are employed to study the statistical properties of quantum systems.

The complex energy landscape of spin glasses is seen as analogous to the complex geometry of spacetime, suggesting that disordered quantum systems might provide insights into the emergence of spacetime. Conformal Field Theory (CFT) is a fundamental tool in the AdS/CFT correspondence, and research explores its properties and relation to gravity. Quantum information theory, including entanglement, quantum channels, and quantum error correction, is also investigated for its role in understanding emergent spacetime. The research program aims to develop a mathematical framework for describing the emergence of spacetime from quantum entanglement, utilizing tools from operator algebras, von Neumann algebras, and free probability. It leverages the AdS/CFT correspondence to explore the connection between quantum chaos and the emergence of spacetime, and investigates the role of disordered quantum systems. Ultimately, the goal is to resolve the information paradox associated with black holes and fundamentally change our understanding of spacetime and gravity, representing a cutting-edge area of theoretical physics with the potential to revolutionize our understanding of the universe.

Spectral Functions and Emergent Spacetime Geometry

This research demonstrates a connection between the properties of spectral functions and the emergence of spacetime, specifically exploring how these functions relate to causal horizons. The team investigated the SYK model, the p-spin model, and the SU Heisenberg chain, with quenched disorder, calculating their spectral functions in a large limit to assess their potential holographic properties. A key finding is that the spectral function of the SU Heisenberg chain in its spin glass phase exhibits an exponential tail, mirroring the behaviour observed in the large limit of the SYK model. Furthermore, the researchers identified an infinite family of quasiparticle excitations within the spin liquid phase of the p-spin model, suggesting the emergence of a specific type of algebraic structure.

Importantly, the study establishes that spectral functions lacking compact support consistently display exponential tails, leading to the conclusion that a low-energy operator cannot detect a nontrivial bulk causal structure if the spectral function decays exponentially. The authors acknowledge discrepancies between approximate solutions and the exact conformal solution, particularly regarding the development of a polynomial tail as the coupling increases, and suggest further investigation is needed to fully understand this behaviour. Future work could focus on resolving this discrepancy and exploring the transition from the approximate solution to the conformal solution in the limit of infinite coupling, providing valuable insights into the relationship between quantum systems, spectral properties, and the emergence of classical spacetime features.