Collective quantum effects have traditionally not received much attention in high energy physics. Recently, however, a model for black hole physics was put forward, in which black holes are described as Bose-condensates of gravitons close to a critical point. In a different line of research, estimates of high-energy collisions in the electro-weak theory have hinted that scattering processes with multiple Higgs or vector Bosons in the final state might be in reach for future particle colliders. In both scenarios, collective quantum effects may be crucial for understanding the physics. In the first part of this thesis, we address the black hole condensate picture of Dvali and Gomez. We study a Bosonic many-body system (attractive Lieb-Liniger) which exhibits a quantum phase transition and was proposed as a model for the graviton condensate. We demonstrate that, even for macroscopic particle number, quantum effects are prominent at the critical point. This becomes especially clear in the entanglement of different momentum modes and in the quantum discord between two successive density measurements. We point out that the leading contribution to these phenomena arises from long-wavelength modes and is therefore insensitive to ultra-violet physics. For black holes in the graviton condensate picture, these findings imply a breakdown of the semiclassical description and may be the key to resolving the long-standing information problem. We then turn our attention to the question of information processing in black holes. Inspired by the properties of three-dimensional attractive Bose condensates, we propose a concrete mechanism for fast scrambling in graviton-condensate black holes. To bolster our claims, we perform simulations of the Lieb-Liniger model in an appropriate regime that reveal entanglement-generation in logarithmic time. We also point out that the idea of instability and possibly chaos as the origin of fast quantum breaking and scrambling may also be relevant for other models of black holes. In the second part of this thesis, we use techniques of integrability (Bethe ansatz) to address the phase transition of the attractive Lieb-Liniger model analytically. We derive the continuum limit of the Bethe equations and solve it for the ground state at arbitrary coupling. We establish an exact equivalence between the Bethe-ansatz description in the large-particle-number limit and the large-N saddle point of Euclidean two dimensional U(N) Yang-Mills theory quantized on a sphere. The transition between the homogeneous and solitonic phases of the Lieb-Liniger model is thus dual to the Douglas-Kazakov confinement-deconfinement transition. In the last part, we consider scattering amplitudes involving many particles. In a simple integral-model, we study in detail the breakdown of perturbation theory and emphasize that the pure tree-level approximation fails earlier, parametrically. We then demonstrate, in three different (integral and quantum mechanical) model systems, that the physical high multiplicity amplitudes can be predicted on the basis of leading-order information from (non-perturbative) saddle points. In the non-Borel summable cases, one non-perturbative saddle contribution alone dominates the amplitudes. We highlight that high-multiplicity amplitudes may thus be a fruitful application for the methods of resurgence theory.
Collective quantum effects have traditionally not received much attention in high energy physics. Recently, however, a model for black hole physics was put forward, in which black holes are described as Bose-condensates of gravitons close to a critical point. In a different line of research, estimates of high-energy collisions in the electro-weak theory have hinted that scattering processes with multiple Higgs or vector Bosons in the final state might be in reach for future particle colliders. In both scenarios, collective quantum effects may be crucial for understanding the physics. In the first part of this thesis, we address the black hole condensate picture of Dvali and Gomez. We study a Bosonic many-body system (attractive Lieb-Liniger) which exhibits a quantum phase transition and was proposed as a model for the graviton condensate. We demonstrate that, even for macroscopic particle number, quantum effects are prominent at the critical point. This becomes especially clear in the entanglement of different momentum modes and in the quantum discord between two successive density measurements. We point out that the leading contribution to these phenomena arises from long-wavelength modes and is therefore insensitive to ultra-violet physics. For black holes in the graviton condensate picture, these findings imply a breakdown of the semiclassical description and may be the key to resolving the long-standing information problem. We then turn our attention to the question of information processing in black holes. Inspired by the properties of three-dimensional attractive Bose condensates, we propose a concrete mechanism for fast scrambling in graviton-condensate black holes. To bolster our claims, we perform simulations of the Lieb-Liniger model in an appropriate regime that reveal entanglement-generation in logarithmic time. We also point out that the idea of instability and possibly chaos as the origin of fast quantum breaking and scrambling may also be relevant for other models of black holes. In the second part of this thesis, we use techniques of integrability (Bethe ansatz) to address the phase transition of the attractive Lieb-Liniger model analytically. We derive the continuum limit of the Bethe equations and solve it for the ground state at arbitrary coupling. We establish an exact equivalence between the Bethe-ansatz description in the large-particle-number limit and the large-N saddle point of Euclidean two dimensional U(N) Yang-Mills theory quantized on a sphere. The transition between the homogeneous and solitonic phases of the Lieb-Liniger model is thus dual to the Douglas-Kazakov confinement-deconfinement transition. In the last part, we consider scattering amplitudes involving many particles. In a simple integral-model, we study in detail the breakdown of perturbation theory and emphasize that the pure tree-level approximation fails earlier, parametrically. We then demonstrate, in three different (integral and quantum mechanical) model systems, that the physical high multiplicity amplitudes can be predicted on the basis of leading-order information from (non-perturbative) saddle points. In the non-Borel summable cases, one non-perturbative saddle contribution alone dominates the amplitudes. We highlight that high-multiplicity amplitudes may thus be a fruitful application for the methods of resurgence theory.
It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one spatial dimension which is known to undergo a quantum phase transition. We demonstrate explicitly that indeed quantum effects are important at the critical point, even if the number of particles is macroscopic. Most prominently, we evaluate the entropy of entanglement between different momentum modes and observe it to become maximal at the critical point. Furthermore, we explicitly see that the leading entanglement is between long-wavelength modes and is hence a feature independent of ultraviolet physics. If applicable to black holes, our findings substantiate the conjectured breakdown of semiclassical physics even for large black holes. This can resolve long-standing mysteries, such as the information paradox and the no-hair theorem.
Recently a quantum portrait of black holes was suggested according to which a macroscopic black hole is a Bose--Einstein condensate of soft gravitons stuck at the critical point of a quantum phase transition. We explain why quantum criticality and instability are the key for an efficient generation of entanglement and consequently of the scrambling of information. By studying a simple Bose--Einstein prototype, we show that the scrambling time, which is set by the quantum break time of the system, goes as logN for N the number of quantum constituents or equivalently the black hole entropy.
Chaos in many-body quantum systems is of great importance to both many-body physics as well as black hole physics. In the field of many-body physics, interactions and disorder in the system can lead to various dynamic phenomena, be it thermalisation, many-body localisation, chaotic behavior and scrambling of quantum information. In the field of high energy physics, the holographic principle connects chaos and scrambling in many-body quantum systems with the information-theoretic properties of black holes. Theoretical quantum physics provides the framework for the models, methods, and results in this thesis, while black hole physics partly provides some motivation and inspiration. First, we introduce a new model for a many-body quantum system based on random quantum circuits. These are a popular framework for theoretic study of disordered spin chains. By drawing the random unitaries in the circuit from different ensembles, we can adjust the disorder strength in the interactions, which in turn leads to a thermal/many-body localisation phase transition. Next, we study the Brownian SYK model, a disordered model of Majorana fermions with all-to-all interactions, motivated by its link to the holographic principle. We develop a new numerical method based on an effective permutational symmetry to reduce computational cost from exponential to linear or quadratic in system size N. As a consequence, we can compute scrambling quantifiers in detail, and find a log N scrambling time, as conjectured in the context of fast scrambling for black holes. Finally, we develop a model based on the continuous-time limit of a random quantum circuit. It serves as a microscopic toy model for the evaporation of a black hole. With a similar method as developed for the Brownian SYK model, we can analyse its information theoretic properties. In particular, we follow established protocols for information retrieval from the Hawking radiation. We find a separation of time scales for entanglement growth and information retrieval, related to the intrinsic black hole dynamics (∝log N) and the coupling to the environment (∝N).
In a previous series of papers it was proposed that black holes can be understood as Bose-Einstein condensates at the critical point of a quantum phase transition. Therefore other bosonic systems with quantum criticalities, such as the Lieb-Liniger model with attractive interactions, could possibly be used as toy models for black holes. Even such simple models are hard to analyse, as mean field theory usually breaks down at the critical point. Very few analytic results are known. In this paper we present a method of studying such systems at quantum critical points analytically. We will be able to find explicit expressions for the low energy spectrum of the Lieb-Liniger model and thereby to confirm the expected black hole like properties of such systems. This opens up an exciting possibility of constructing and studying black hole like systems in the laboratory.
The thesis addresses the fundamental interplay between indistinguishability and interactions in few- and many-body quantum systems, treated in two separate approaches, both analytic in nature, using semiclassical methods. The few-body sector, considering a strictly fixed number of particles, is addressed within the framework of first quantization. By sticking to descriptions as (micro-)canonical ensembles the approach overcomes the inappropriate use of virial expansions. It is based on cluster expansions where quantum statistics are treated exactly and interparticle forces are described non-perturbatively. After a full formal development the cluster expansions are supplemented with short-time dynamical information that is equated with the description of smooth spectral properties or equivalently temperatures above strong quantum degeneracy, which, in the single-particle context, is the essential ingredient to what is known as semiclassical Weyl expansions. This reduction allows for the fully analytical description of universal features of large classes of systems by either truncating to a specific class of allowed collision processes, i.e., two-body collisions, or by extracting higher-order interaction kernels from related integrable models. The consistent combination with scaling considerations, minimal ground-state information and strong-coupling expansions leads to a toolbox providing most of the thermodynamic and spectral properties of one-dimensional systems with short-range interactions, all in terms of the lowest-order interaction kernels. The analytical results are in excellent qualitative and quantitative agreement with extensive numerical simulations for both integrable and non-integrable models of experimental relevance in cold atom physics. The many-body sector is in contrast treated in the second quantized formulation of quantum mechanics making use of the well-known collection of semiclassical methods that are subsumed under the name periodic orbit theory. As these methods apply in a highly system specific manner, the attractive Bose gas on a ring is chosen as exemplary model to show a case where the semiclassical quantization of mean-field dynamics, here considered as the classical analogue, can be used to obtain analytical non-trivial information on correlation-related many-body effects, especially related to quantum critical behavior in this model. After a simplification by truncating to the lowest single-particle momentum modes the consistent application of Einstein-Brillouin-Keller quantization yields a description valid for large numbers of bosons. Besides analytically reproducing numerical spectra to high accuracy, the approach enables one to extract asymptotic scaling laws for level spacings around quantum criticality, representing properties. These (finite) energy differences are intrinsically tied to inter-particle correlations and therefore elude a more conventional description by means of a mean-field theory extended with Bogoliubov quasi particles. An application to the scrambling time of the system, related to a pseudo quantum butterfly effect that stems from a local instability, underlines the importance of the method in the otherwise inaccessible regime of extreme particle numbers.
This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb–Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe's hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb–Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang–Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb–Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability.