If black holes are not to be dreaded sinks of information but rather fully described by unitary evolution, they must scramble in-falling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers; they generate entanglement at a remarkably efficient rate, with the characteristic time scaling logarithmically with the entropy. In this work, we focus on Matrix theory---M-theory in the light-cone frame---and directly probe the conjecture. We develop a concrete test bed for quantum gravity using the fermionic variables of Matrix theory and show that the problem becomes that of chains of qubits with an intricate network of interactions. We demonstrate that the black hole system evolves much like a Brownian quantum circuit, with strong indications that it is indeed a fast scrambler. We also analyze the Berenstein-Maldacena-Nastase model and reach the same tentative conclusion.
If black holes are not to be dreaded sinks of information but rather fully described by unitary evolution, they must scramble in-falling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers; they generate entanglement at a remarkably efficient rate, with the characteristic time scaling logarithmically with the entropy. In this work, we focus on Matrix theory---M-theory in the light-cone frame---and directly probe the conjecture. We develop a concrete test bed for quantum gravity using the fermionic variables of Matrix theory and show that the problem becomes that of chains of qubits with an intricate network of interactions. We demonstrate that the black hole system evolves much like a Brownian quantum circuit, with strong indications that it is indeed a fast scrambler. We also analyze the Berenstein-Maldacena-Nastase model and reach the same tentative conclusion.
BMN Matrix theory admits vacua in the shape of large spherical membranes. Per- turbing around such vacua, the setup provides for a controlled computational frame- work for testing information evolution in Matrix black holes. The theory realizes excitations in the supergravity multiplet as qubits. These qubits are coupled to matrix degrees of freedom that describe deformations of the spherical shape of the membrane. Arranging the ripples on the membrane into a heat bath, we use the qubit system as a probe and compute the associated Feynman-Vernon density matrix at one loop order. This allows us to trace the evolution of entanglement in the system and extract the characteristic scrambling timescale. We find that our numerical analysis is consistent with this time scaling logarithmically with the entropy of the qubit system, in tune with suggestions by Sekino and Susskind.
Many proposed quantum mechanical models of black holes include highly nonlocal interactions.The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity.Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information.It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster.In this article, we address the conjecture from two directions.First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph.Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss.Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian.The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.
BMN Matrix theory admits vacua in the shape of large spherical membranes. Perturbing around such vacua, the setup provides for a controlled computational framework for testing information evolution in Matrix black holes. The theory realizes excitations in the supergravity multiplet as qubits. These qubits are coupled to matrix degrees of freedom that describe deformations of the spherical shape of the membrane. Arranging the ripples on the membrane into a heat bath, we use the qubit system as a probe and compute the associated Feynman-Vernon density matrix at one loop order. This allows us to trace the evolution of entanglement in the system and extract the characteristic scrambling timescale. We find that our numerical analysis is consistent with this time scaling logarithmically with the entropy of the qubit system, in tune with suggestions by Sekino and Susskind.
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).
Abstract In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this entanglement entropy is directly and generally related to the local tidal acceleration experienced by the probe. This establishes a new map between local spacetime geometry and quantum entanglement, suggesting a mechanism through which geometry emerges from Matrix quantum mechanics. We extend this setting to light-cone M-theory in flat space, or the Banks-Fischler-Shenker-Susskind Matrix model, and we conjecture a new general relation between a certain measure of entanglement in Matrix theories and local spacetime geometry. The relation involves a ‘c-tensor’ that measures the evolution of local transverse area and relates to the local energy-momentum tensor measured by a probe.
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large- N matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large- N matrix models, where we provide a gauge invariant entanglement entropy for ‘generalized free fields’, again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.