We study entanglement transfer in a minimal model of two qubits that are coupled with one another through an antiferromagnetic Heisenberg exchange ($\tilde{J}$), and where one of them is additionally coupled to a fermionic environment through another antiferromagnetic Heisenberg exchange ($J_{K}$). By tuning the coupling ratio $J_{K}/\tilde{J}$, the system undergoes a quantum phase transition at $T=0$, accompanied by a redistribution of entanglement from the $d'-d$ qubit-subsystem to the environment. Remarkably, the resulting physics exhibits properties that bear analogy with a quantum-information theoretic perspective of the physics of black hole thermodynamics. Carefully selected bipartite and tripartite mutual information measures displays behaviour analogous to the dynamical evolution of black hole entropy, Hawking entropy, and the Page curve expected during the process of evaporation. An effective temperature scale is obtained from the variation of the ground state energy with respect to changes in the bipartite mutual information between the subsystem and the bath. A steady growth of this temperature with the coupling ratio resembles that of the Hawking temperature with the inverse mass of the black hole. Concomitantly, the emergence of non-Fermi liquid behaviour observed near the quantum critical point and in the strong-coupling phase resembles strange-metal-like physics expected near the event horizon from a holographic duality perspective. Our results establish the minimal model as a platform for studying entanglement transfer and information scrambling within a fully unitary quantum framework, and offer new insights into a resolution of the black hole information paradox.
We study entanglement transfer in a minimal model of two qubits that are coupled with one another through an antiferromagnetic Heisenberg exchange (J~), and where one of them is additionally coupled to a fermionic environment through another antiferromagnetic Heisenberg exchange (JK). By tuning the coupling ratio JK/J~, the system undergoes a quantum phase transition at T=0, accompanied by a redistribution of entanglement from the d′−d qubit-subsystem to the environment. Remarkably, the resulting physics exhibits properties that bear analogy with a quantum-information theoretic perspective of the physics of black hole thermodynamics. Carefully selected bipartite and tripartite mutual information measures displays behaviour analogous to the dynamical evolution of black hole entropy, Hawking entropy, and the Page curve expected during the process of evaporation. An effective temperature scale is obtained from the variation of the ground state energy with respect to changes in the bipartite mutual information between the subsystem and the bath. A steady growth of this temperature with the coupling ratio resembles that of the Hawking temperature with the inverse mass of the black hole. Concomitantly, the emergence of non-Fermi liquid behaviour observed near the quantum critical point and in the strong-coupling phase resembles strange-metal-like physics expected near the event horizon from a holographic duality perspective. Our results establish the minimal model as a platform for studying entanglement transfer and information scrambling within a fully unitary quantum framework, and offer new insights into a resolution of the black hole information paradox.
A bstract We investigate the evolution of entanglement within an open, strongly coupled system interacting with a heat bath as its environment, in the frameworks of both the doubly holographic model and the Sachdev-Ye-Kitaev (SYK) model. Generally, the entanglement within the system initially increases as due to internal interactions; however, it eventually dissipates into the environment. In the doubly holographic setup, we consider an end-of-the-world brane in the bulk to represent an eternal black hole coupled with its radiation and the evolution of the global thermofield double (TFD) state. For small black holes, the reflected entropy between the bipartition exhibits a ramp-plateau-slump behavior, where the plateau arises due to the phase transition of the entanglement wedge cross-section before the Page time. Similarly, the mutual information between the bipartition displays a ramp-slop-stabilizing behavior. In quantum mechanics, we consider a double copy of the SYK-plus-bath system in a global TFD state, resembling an eternal black hole interacting with an environment. The Rényi mutual information within the double-copied SYK clusters exhibits a ramp-plateau-slope-stabilizing behavior. The dynamic behaviors of the entanglement quantities observed in these two models are attributable to the competition between the internal interaction of the system and the external interaction with the baths. Our study provides a fine-grained picture of the entanglement dynamics inside black holes before their Page time.
We study thermodynamic properties and the entanglement island of a black hole in asymptotically safe quantum gravity, analyzing key thermodynamic quantities such as the Hawking temperature, heat capacity, and entropy, as well as the mass-horizon radius relation. Unlike Schwarzschild black holes, the temperature decreases with mass near the evaporation endpoint, signaling a phase transition and possible stable remnant. The entanglement entropy of Hawking radiation is obtained both with and without island contributions. Without islands, the radiation entropy grows linearly indefinitely, leading to the information paradox. By including island contributions and extremizing the generalized entropy functional, we resolve this paradox. At late times, the radiation entropy saturates at the Bekenstein-Hawking entropy, confirming unitary evolution. From this, we derive the Page time and scrambling time by equating early- and late-time entanglement entropies. The result of this study establishes the finiteness of the radiation entropy and consistency with quantum mechanics.
This dissertation presents a comprehensive investigation of fermionic quantum matter into the intricate relationship between quantum chaos, thermalization, and their connection to gravitational duals, with particular emphasis on the Sachdev-Ye-Kitaev (SYK) model and its extensions. Through an integrated approach combining analytical solutions in the large-N limit with advanced numerical techniques, we explore fundamental questions in quantum many-body physics, including the interplay of chaos and ergodicity, universal transport in non-Fermi liquids, and the role of gravitational analogs in strongly correlated systems. We first demonstrate that coupled SYK lattices evade instantaneous thermalization despite weak charge fluctuations, governed by a discrete wave equation dependent solely on hopping strength, independent of on-site interactions. Thermodynamically, coupled SYK models exhibit critical exponents universal to van der Waals fluids and AdS black holes, yet diverge from the Hawking-Page transition at ultralow temperatures, revealing a continuum of first-order phase transitions. They simultaneously retain the quantum chaotic properties of both a single-dot SYK model and black holes. In extended SYK chains, we identify a universal DC conductivity bound across interaction regimes, identifying crossovers between insulating, Fermi liquid, strange metal, and bad metal phases with signatures of holographic insulator behavior. Quench dynamics in mixed SYK systems reveal rapid thermalization without prethermal plateaus, enabling direct observation of thermalization in closed quantum systems in the thermodynamic limit. To diagnose ergodicity-breaking, we introduce the Krylov variance, a probe of operator localization in Krylov space, validated through mass-deformed SYK and quantum East models. Finally, we uncover Page curve entanglement dynamics and temporal quantum phase transitions in entanglement Hamiltonians of interacting fermionic chains, where symmetry-sector crossings highlight limitations of perturbative calculations performed around initial times, such as in Hawking’s analysis of black hole evaporation. We provide a condensed matter analog of the holographic “island formula” — a mechanism invoking quantum extremal surfaces to resolve the black hole information paradox. Methodologically, this work integrates large-N-type expansions, Keldysh contour techniques, and numerical methods to bridge condensed matter physics, quantum information, and gravitational duality. The results establish SYK-type systems as a universal framework for studying non-Fermi liquids, quantum criticality, and black hole analogs, while paving the way for exploring bosonic extensions and generalizations to open quantum systems.
This work explores the hypothesis that time is an emergent phenomenon arising from underlying quantum informational processes. By integrating principles from quantum mechanics, thermodynamics, and general relativity, we develop a comprehensive framework that elucidates the relationship between quantum complexity, entanglement, and the nature of time. We investigate the role of quantum complexity in the evolution of quantum states and demonstrate how the increase in entanglement entropy provides a microscopic basis for the arrow of time. Using the AdS/CFT correspondence and the holographic principle, we establish connections between spacetime geometry and quantum informational measures like entanglement entropy. We address the black hole information paradox within this context, arguing that information is preserved in a highly scrambled form. Additionally, we propose an experimental design using black hole analogues to empirically validate our theoretical predictions, focusing on fast scrambling and the growth of quantum complexity. Our findings suggest that quantum informational dynamics govern the emergence of time and spacetime geometry. This work bridges quantum mechanics, thermodynamics, information theory, and general relativity, offering potential applications in quantum technologies and new insights into the fundamental nature of reality.
The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there has been an intense activity to understand the thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment and the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black holes—which are simple yet macroscopic systems—and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole’s horizon with regard to the system energy. This is yet other numerical evidence leading to understanding the key features of black-hole thermodynamics from the viewpoint of quantum information theory.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signaling, entanglement monogamy, and the equivalence principle. We here show that the Hawking's quantum model for the black hole evaporation is consistent with the above fundamental principles. Our analysis does not involve exotic new physics, but rather uses standard quantum theory, general relativity, and the Einstein–Hilbert action including matter. We explicitly show that the whole state consisting of matter and radiation (in a joint superposition of different energy states) is pure at any stage of the evaporation process, including the particular case of 0 mass. Moreover, after full evaporation the state for radiation at infinity is pure and in one-to-one correspondence with the initial state forming the black hole. Thus there is no information loss upon full evaporation according to the quantum information theory. The original entanglement of the black hole matter (if any) gets transferred to the outgoing particles via a process similar to entanglement swapping, without violation of causality (as proved explicitly). On the other hand, if the initial state is a tensor product state, the entanglement of Hawking particles, present in the intermediate phase, is broken when the black hole evaporates completely. Therefore, the final state (entangled or tensor product depending on the nature of initial state) after the full black hole evaporation is pure without loss of information.