According to the AdS/CFT correspondence, certain quantum many-body systems in d -dimensions are equivalent to gravitational theories in ( d + 1 )-dimensional asymptotically anti–de Sitter (AdS) spacetimes. When a massless particle is sent from the AdS boundary to the bulk curved spacetime, it reaches another point of the boundary after a time lag. In the dual quantum system, it should appear as if quasiparticles have been transferred between two separated points. We theoretically demonstrate that this phenomenon, which we call “spacetime-localized response”, is actually observed in the dynamics of the one-dimensional transverse-field Ising model near the quantum critical point. This result suggests that, if we can realize a holographic spin system in a laboratory, the experimental probing of the emergent extra dimension is possible by applying a designed stimulus to a quantum many-body system, which is holographically equivalent to sending a massless particle through the higher-dimensional curved bulk geometry. We also discuss possible experimental realizations using Rydberg atoms in an optical tweezers array. Published by the American Physical Society 2024
According to the AdS/CFT correspondence, certain quantum many-body systems in d -dimensions are equivalent to gravitational theories in ( d + 1 )-dimensional asymptotically anti–de Sitter (AdS) spacetimes. When a massless particle is sent from the AdS boundary to the bulk curved spacetime, it reaches another point of the boundary after a time lag. In the dual quantum system, it should appear as if quasiparticles have been transferred between two separated points. We theoretically demonstrate that this phenomenon, which we call “spacetime-localized response”, is actually observed in the dynamics of the one-dimensional transverse-field Ising model near the quantum critical point. This result suggests that, if we can realize a holographic spin system in a laboratory, the experimental probing of the emergent extra dimension is possible by applying a designed stimulus to a quantum many-body system, which is holographically equivalent to sending a massless particle through the higher-dimensional curved bulk geometry. We also discuss possible experimental realizations using Rydberg atoms in an optical tweezers array. Published by the American Physical Society 2024
The AdS/CFT correspondence, a remarkable duality between certain gravitational theories in anti-de Sitter (AdS) spacetime and quantum field theories with conformal symmetry (CFT), has had a profound effect on the development of theoretical physics in the past two decades. Recently, many connections of AdS/CFT to quantum information theory have been found, in particular by providing gravitationally dual descriptions of various entanglement measures. Understanding these manifestions of AdS/CFT --- or more generally, the conjectured holographic principle encompassing it --- requires the combination of tools from both high-energy theory and quantum information physics. In this cumulative thesis, the convergence between these two fields is approached from two fronts: First, by calculations within the dual gravitational theory, and second, using a tensor network ansatz to describe the quantum states suspected to possess such a gravitational description. In the first approach, using the gravitational side of AdS/CFT, entanglement entropies of complicated 2+1-dimensional excited CFTs are computed, thus showing how the holographic approach provides access to systems previously out of reach of practical methods, while introducing new numerical methods that this approach necessitates. The second approach is given by tensor networks, a highly successful ansatz for computing properties of one- and two-dimensional quantum systems. Efficiently computable classes of tensor networks are tested in their ability to represent simple holographic systems, successfully reproducing both hyperbolic geometrical features as well as critical boundary states. In addition, the general properties of tensor networks on regular hyperbolic tesselations are considered, leading to new connections to models not previously considered in the context of holography. This interplay of different approaches to quantum information holography showcases the richness of this new field and suggests that a wide range of physical phenomena is accessible via the new tools now at our disposal.
We investigate the phenomenon of spacetime-localized response in a quantum critical spin system, with particular attention to how it depends on the spatial profile and operator content of the applied perturbation, as well as its robustness against increase of amplitude and temporal discretization. Motivated by recent theoretical proposals linking such response patterns to the anti-de Sitter/conformal field theory correspondence, we numerically analyze the real-time dynamics of the one-dimensional transverse-field Ising model at criticality using the time-evolving block decimation algorithm. We find that sharply localized and periodically recurring responses emerge only for specific types of perturbations, namely those that correspond to local density fields in the continuum limit. In contrast, perturbations involving other spin components produce conventional propagating excitations without localization. Furthermore, we demonstrate that the response remains qualitatively robust when the time-dependent perturbation is approximated by a piecewise-linear function, highlighting the practical relevance of our findings for quantum simulation platforms with limited temporal resolution. Our results clarify the operator dependence of emergent bulk-like dynamics in critical spin chains and offer guidance for probing holographic physics in experimental settings.
The AdS/CFT correspondence conjectures a duality between quantum gravity theories in anti-de Sitter (AdS) spacetime and conformal field theories (CFTs) on the boundary. One intriguing aspect of this correspondence is that it offers a pathway to explore quantum gravity through tabletop experiments. Recently, a multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT that can be implemented using contemporary quantum simulators has been proposed [R. Sahay, M. D. Lukin, and J. Cotler, arXiv:2401.13595 (2024)]. Particularly, local bulk excitations (entitled "hologrons") manifesting attractive interactions given by AdS gravity were found. However, the fundamental question concerning the stability of these identified hologrons is still left open. Here, we address this question and find that hologrons are unstable during dynamic evolution. In searching for stable bulk excitations with attractive interactions, we find they can be constructed by the local primary operators in the boundary CFT. Furthermore, we identify a class of boundary excitations that exhibit the bizarre behavior of "holographic transportation", which can be directly observed on the boundary system implemented in experiments.
The goal of these notes is to introduce, in a very elementary way, the idea of the anti de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to condensed matter physicists. This theory relates a gravity theory in a (d+1)- dimensional anti-de Sitter spacetime to a strongly-coupled d- dimensional quantum field theory living on its boundary. The AdS/CFT correspondence can be used to study finite temperature real time processes, such as response functions and dynamics far from equilibrium in quantum critical points in condensed matter systems. Computation of these quantities is reduced to solving classical gravitational equations in one higher dimension than the original theory.
The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error correction, are constructed on regular time-slice discretizations of AdS. In this work, we show that the symmetries of these models are well suited for approximating CFT states, as their geometry enforces a discrete subgroup of conformal symmetries. Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity. We discuss holographic code states and their renormalization group flow as specific implementations of a qCFT with fractional central charges and argue that their behavior generalizes to a large class of existing and future models. Beyond approximating CFT properties, we show that these can be best understood as belonging to a paradigm of discrete holography.
We explore the potential application of quantum computers to the examination of lattice holography, which extends to the strongly coupled bulk theory regime. With adiabatic evolution, we compute the ground state of a spin system on a ( 2 + 1 )-dimensional hyperbolic lattice, and measure the spin-spin correlation function on the boundary. Notably, we observe that with achievable resources for coming quantum devices, the correlation function demonstrates an approximate scale-invariant behavior, aligning with the pivotal theoretical predictions of the anti–de Sitter/conformal field theory correspondence. Published by the American Physical Society 2024