Non-Equilibrating a Black Hole with Inhomogeneous Quantum Quench

Abstract

We study non-equilibrium processes in (1+1)-dimensional conformal field theory (CFT) after quantum quenches starting from the thermal equilibrium (Gibbs) state. Our quench protocol uses spatially inhomogeneous Hamiltonians, the Möbius and sinesquare-deformed (SSD) Hamiltonians. After a quench by the Möbius Hamiltonian, physical quantities such as von Neumann entropy for subsystems exhibit periodic oscillations (quantum revival). On the other hand, there is no quantum revival after a quench using the SSD Hamiltonian. Instead, almost all the degrees of freedom of the system are asymptotically gathered at a single point, the fixed point of the SSD Hamiltonian. This results in a point-like excitation that carries as much information as the total thermal entropy -like a black hole. We call this excitation a black-hole-like excitation. In contrast, parts of the system other than the fixed point approach the low-entropy (low-temperature) state at late times, and the reduced density matrix is given effectively by that of the ground state. When the CFT admits a holographic dual description, these quenches induce inhomogeneous deformations of the black hole in the bulk. In particular, after the quench by the SSD Hamiltonian, at late enough times, the horizon of the bulk black hole asymptotically "touches" the boundary. We also propose and demonstrate that our quench setups can be used to simulate the formation and evaporation processes of black holes, and create low-temperature states.

Quantum hypothesis testing in many-body systems

“…For CFTs with a holographic gravity dual, we develop a dual interpretation of unitary Type I driving, generalizing previous studies [60,61,68,81,[102][103][104]. In our case, the driving starts with the CFT in a thermal state, corresponding to a BTZ black hole in the bulk.…”

“…This has led to an extensive study of so-called rainbow, sine-squared, and Möbius deformations of CFTs [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. By altering the diffeomorphism with time, one obtains non-equilibrium models, e.g., quenches [59][60][61] and Floquet driving [62,63]. While there are many experimental platforms for studying Floquet driving, there are also novel developments in quantum simulating conformal field theories by atomic systems.…”

Entanglement and geometry from subalgebras of the Virasoro

“…21 The techniques and the dual bulk geometries in our work can serve as building blocks for the holographic understanding of the quench dynamics in those deformed models or related questions with excited states. Some progress in this direction has been already reported in [84][85][86][87][88] and more will be presented in the future work [89].…”

Information scrambling versus quantum revival through the lens of operator entanglement

“…We assume that the spatial direction is homogeneous. These assumptions can be relaxed, allowing for a compact spatial extent as well as spatial inhomogeneity [76], with the former being the main subject of this paper. For simplicity, we assume that the state is time-evolved by the unitary operator U (t 1 ) from t = 0 to t = t 1 .…”