Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe

Abstract

The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational recipes in molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving non-autonomous time evolution in a large Hilbert space. We illustrate our general results by analyzing conditions for the transport quantization in a topological Thouless pump.

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Cited by in corpus (30)

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• Adiabatic Theorem for Quantum Spin Systems
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• Breakdown of topological Thouless pumping in the strongly interacting regime
• Bounds in Nonequilibrium Quantum Dynamics
• The impact of the injection protocol on an impurity's stationary state
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Quantum speed limit for thermal states
• Adiabatic theorem for closed quantum systems initialized at finite temperature
• Loschmidt-amplitude wave function spectroscopy and the physics of dynamically driven phase transitions
• Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system
• Quantum lower and upper speed limits
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• An ideal rapid-cycle Thouless pump
• Measuring adiabaticity in non-equilibrium quantum systems
• Bounds on quantum adiabaticity in driven many-body systems from generalized orthogonality catastrophe and quantum speed limit
• Adiabatic time evolution of highly excited states
• A necessary condition for quantum adiabaticity applied to the adiabatic Grover search
• Bounds for nonadiabatic transitions
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Lower bounds for adiabatic quantum algorithms by quantum speed limits
• Merits of using density matrices instead of wave functions in the stationary Schrödinger equation for systems with symmetries
• Quantum speed limits for adiabatic evolution, Loschmidt echo and beyond
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Adiabatic state distribution using anti-ferromagnetic spin systems
• Quantum speed limits for an open system in contact with a thermal bath
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Rate Function Modelling of Quantum Many-Body Adiabaticity
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe
• Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace