[Paper Review] Non-Equilibrating a Black Hole with Inhomogeneous Quantum Quench

Kanato Goto, Masahiro Nozaki+3 more|arXiv (Cornell University)|Dec 29, 2021

Black Holes and Theoretical Physics4 citations

TL;DR

This paper proposes an inhomogeneous quantum quench protocol in 1+1D conformal field theory (CFT) using Möbius and sine-square-deformed (SSD) Hamiltonians to simulate black hole formation and evaporation. While the Möbius quench leads to quantum revivals due to periodic dynamics, the SSD quench concentrates all system degrees of freedom into a point-like, black-hole-like excitation carrying full thermal entropy, while the rest of the system cools to a low-entropy state, mimicking black hole evaporation in holography.

ABSTRACT

We study quantum quench processes in (1+1)-dimensional conformal field theory (CFT) in which the initial thermal equilibrium (Gibbs) state is time-evolved by spatially inhomogeneous Hamiltonians, the so-called Möbius and sine-square-deformed (SSD) Hamiltonians. We found that, when the quench is induced by the SSD Hamiltonian, almost all the degrees of freedom are asymptotically gathered at a single point, resulting in a point-like excitation. This excitation, which we dub black hole-like excitation, carries as much information as the total thermal entropy. In contrast, other parts of the system approach the low-entropy (low-temperature) state at late times. For the quench by the Möbius Hamiltonian, we instead found an eternal periodic oscillation of physical quantities such as von Neumann entropy for subsystems. When the CFT admits a holographic dual description, the SSD quench induces a time-dependent, inhomogeneous deformation of the bulk black hole horizon, which, at late enough times, ``touches'' the boundary. Our quench setups can be used as a way to create low-temperature states, and, also, simulate the formation and evaporation processes of black holes.

Motivation & Objective

• To explore non-equilibrium dynamics in 2D CFTs after inhomogeneous quantum quenches, particularly focusing on non-thermalizing and information-localizing behaviors.
• To investigate how inhomogeneous Hamiltonians—specifically Möbius and SSD deformations—induce non-equilibrium states with distinct entanglement and energy dynamics.
• To demonstrate that the SSD quench can simulate black hole formation and evaporation, including the emergence of a point-like excitation with full thermal entropy.
• To establish a connection between inhomogeneous quenches and holographic bulk geometry, showing that the black hole horizon asymptotically touches the boundary in the bulk.
• To propose a quantum simulation platform for low-temperature state preparation and black hole dynamics using experimentally accessible inhomogeneous quench protocols.

Proposed method

• The study employs sudden quantum quenches from a thermal Gibbs state to inhomogeneous Hamiltonians: the Möbius and SSD Hamiltonians, which are spatially varying deformations of the original CFT Hamiltonian.
• The time evolution is analyzed in the Schrödinger picture using exact solutions for 2D CFTs, particularly for free fermion and holographic CFTs.
• Entanglement entropy and energy-momentum tensor are computed using the Heisenberg picture and conformal mapping techniques to extract dynamical behavior.
• The quasiparticle picture is applied to describe early-time entanglement dynamics, while its breakdown at late times is analyzed for subsystems excluding the fixed point.
• Holographic duals are constructed via conformal mapping to the bulk AdS geometry, showing that the SSD quench induces a black hole horizon that approaches the boundary.
• Mutual information and two-point functions are computed to probe the structure of the late-time density matrix and distinguish between integrable and chaotic CFTs.

Experimental results

Research questions

• RQ1 Can inhomogeneous quantum quenches in 2D CFTs lead to non-thermalizing dynamics where information is localized rather than delocalized?
• RQ2 How does the SSD quench lead to a point-like excitation that carries the full thermal entropy of the system, resembling a black hole?
• RQ3 What is the holographic dual of the SSD quench, and how does the bulk black hole geometry evolve to have its horizon touch the boundary?
• RQ4 Can the quasiparticle picture adequately describe entanglement dynamics in inhomogeneous quenches, and if not, what breaks it?
• RQ5 Can these quench protocols be used to simulate black hole formation and evaporation, and to prepare low-temperature states in quantum simulators?

Key findings

• After an SSD quench, the entire thermal entropy is concentrated at a single fixed point, forming a black-hole-like excitation that carries the full information of the initial thermal state.
• The rest of the system, excluding the fixed point, asymptotically approaches a low-entropy state described effectively by the ground state density matrix.
• In contrast to the SSD quench, the Möbius quench leads to periodic quantum revivals in subsystem entanglement entropy due to unitary periodicity.
• The late-time reduced density matrix for subsystems not containing the fixed point is well-approximated by the ground state density matrix, indicating effective cooling.
• In the holographic dual, the SSD quench causes the black hole horizon to asymptotically touch the boundary, consistent with the formation and evaporation of a black hole.
• The quasiparticle picture fails to describe entanglement dynamics for subsystems excluding the fixed point at late times, indicating a breakdown due to strong inhomogeneity and information localization.