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arXiv:2409.16553

Simulating black hole quantum dynamics on an optical lattice using the complex Sachdev-Ye-Kitaev model

Iftekher S. Chowdhury, Binay Prakash Akhouri, Haque, Shah, Martin H. Bacci, Eric M. Howard

Published Sep 25, 2024• 0 citations
arXivHTMLPDF

Abstract

We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes.

DOI
10.48550/arxiv.2409.16553

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We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes.
We suggest that the holographic principle, combined with recent technological advances in atomic, molecular, and optical physics, can lead to experimental studies of quantum gravity. As a specific example, we consider the Sachdev–Ye–Kitaev (SYK) model, which consists of spin-polarized fermions with an all-to-all complex random two-body hopping and has been conjectured to be dual to a certain quantum-gravitational system. Achieving low-temperature states of the SYK model is interpreted as a realization of a stringy black hole, provided that the holographic duality is true. We introduce a variant of the SYK model, in which the random two-body hopping is real. This model is equivalent to the original SYK model in the large-|NNN| limit. We show that this model can be created in principle by confining ultracold fermionic atoms into optical lattices and coupling two atoms with molecular states via photo-association lasers. This development serves as an important first step towards an experimental realization of such systems dual to quantum black holes. We also show how to measure out-of-time-order correlation functions of the SYK model, which allow for identifying the maximally chaotic property of the black hole.
Abstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.
Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.
The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical many body system with random all-to-all interactions on fermionic N sites (N>>1). This model is shown to saturate the known maximal chaos bound of many body system and then based on this observation it is conjectured to be dual to a quantum black hole in the sense of the AdS/CFT correspondence. In this dissertation, we show that the large N physics of the SYK model is systematically described by a single bi-local field. In particular, we emphasize the appearance of the emergent conformal reparametrization symmetry at the critical IR fixed point and the corresponding divergent contribution of the symmetry modes in the propagator of the bi-local field. We discuss non-linear-level derivation of the zero modes effective action, which is given by the Schwarzian derivative for finite reparametrization symmetry. Besides the symmetry modes, which correspond to the dilaton-gravity sector in the dual AdS theory, the SYK model also predicts an infinite tower of matter fields in AdS_2. We demonstrate that this infinite spectrum can be nicely packaged into a single field in 3-dimensional space-time. Finally, we consider the question of identifying the dual space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green's functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2D string theory.
The realization of quantum field theories on an optical lattice is an important subject toward the quantum simulation. We argue that such efforts would lead to the experimental realizations of quantum black holes. The basic idea is to construct non-gravitational systems which are equivalent to the quantum gravitational systems via the holographic principle. Here the `equivalence' means that two theories cannot be distinguished even in principle. Therefore, if the holographic principle is true, one can create actual quantum black holes by engineering the non-gravitational systems on an optical lattice. In this presentation, we consider the simplest example: the Sachdev-Ye-Kitaev (SYK) model. We design an experimental scheme for creating the SYK model with use of ultra-cold fermionic atoms such as Lithium-6.
With the in-depth subjects chiasma among different research areas, many people are applying concepts and methods in theoretical high-energy physics to condensed matter systems. One of the most intensely studied tools is the Anti-de Sitter space/Conformal Field Theory (AdS/CFT) correspondence. It effectively permits a perturbative treatment of strongly coupled systems. Thus, it has been a focused topic in theoretical physics and high-energy physics. It represents a significant breakthrough in understanding quantum gravity. This paper focuses on the realisation of the duality in Jackiw-Teitelboim (JT) gravity and Sachdev-Ye-Kitaev (SYK) Model. To this end, the author derived the action, free energy, thermal entropy, and low-energy dynamics. The symmetry breaking pattern of the SYK model following previous works are also considered. These results were compared with the counterparts in Euclidean JT theory as a cut-out of the complete nearly AdS space in two dimensions. Based on the similarity in the mathematical form of these quantity and symmetry breaking process, the author concludes that the SYK model, as many believed, is a promising candidate for the holographic dual of the JT theory.