Searching for emergent spacetime in spin glasses

Abstract

Recent work on algebraic formulations of holographic dualities in terms of large $N$ algebras has revealed a deep connection between the properties of the associated spectral functions and the emergence of a semiclassical spacetime and causal horizons therein. One of the main lessons is that, for a radial direction to emerge, the spectral function has to exhibit non-compact support. Furthermore, there exist conjectures upon a possible duality between complex gravitational configurations and glassy systems. The goal of this paper is to combine these ideas by studying many-body quantum-mechanical systems and assess in which parameter regimes they could potentially be holographic. Thus, we compute the spectral functions of three many-body systems with quenched disorder, the SYK model, the $p$-spin model and the SU$(M)$ Heisenberg chain in the large $N$ limit and present results in different parameter regimes. Our main finding is that in the quantum spin glass phase of the SU$(M)$ Heisenberg model, the spectral function develops an exponential tail, similar to the large $q$ limit of SYK. Furthermore, we demonstrate the presence of an infinite family of quasiparticle excitations deep in the spin liquid phase of the $p$-spin model, which could point towards an emergent type I von Neumann algebra. In addition, we demonstrate the presence of an exponential tail in the spectral function for all cases without compact support and conformal symmetry. Motivated by this observation, we prove that no low-energy operator can detect a nontrivial bulk causal structure, if the spectral function has exponentially decaying tails.

33 pages + 32 pages appendix, 12 figures, code/data can be received upon request

References in corpus (54)

• Gauge Theory Correlators from Non-Critical String Theory
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Lectures on holographic methods for condensed matter physics
• Black holes and the butterfly effect
• Cool horizons for entangled black holes
• Fast Scramblers
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Lectures on Holographic Superfluidity and Superconductivity
• Holography from Conformal Field Theory
• Notes on Some Entanglement Properties of Quantum Field Theory
• Anti-de Sitter Fragmentation
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Holographic representation of local bulk operators
• Emergent quantum criticality, Fermi surfaces, and AdS2
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Spin-Glass Theory for Pedestrians
• A Universal Operator Growth Hypothesis
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• The Second Law of Quantum Complexity
• A strongly correlated metal built from Sachdev-Ye-Kitaev models
• Emergent Spacetime and Holographic CFTs
• Chaos, Complexity, and Random Matrices
• What can gauge-gravity duality teach us about condensed matter physics?
• Non-Fermi liquid regime of a doped Mott insulator
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• Semi-Holographic Fermi Liquids
• Gravity and the Crossed Product
• Bounding the Space of Holographic CFTs with Chaos
• Large N algebras and generalized entropy
• Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I)
• The bulk Hilbert space of double scaled SYK
• Algebraic Holography
• The Quantum Spherical p-Spin-Glass Model
• Holographic Lattices, Dimers, and Glasses
• The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
• Generalized free fields and the AdS-CFT correspondence
• A symmetry algebra in double-scaled SYK
• Strange metals and the AdS/CFT correspondence
• Does the SYK model have a spin glass phase?
• Hot Halos and Galactic Glasses
• TASI lectures on complex structures
• Information loss, mixing and emergent type III${}_1$ factors
• Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
• A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC
• Explicit large $N$ von Neumann algebras from matrix models
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Modular Intersections, Time Interval Algebras and Emergent AdS${}_2$