Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits

Abstract

In this work, we examine the validity of quantum adiabatic theorem in thermodynamic systems. For a $d$-dimensional quantum many-body system, we show that the duration time ${\tau }_0$ required by its ground-state adiabatic process does not depend on the microscopic details, but the scaling dimension of the fidelity susceptibility $d_a$. Our result, therefore, provides a quantitative time scale of the quantum adiabatic theorem in thermodynamic systems. The quantum adiabatic theorem might be violated in case that the scaling dimension of the fidelity susceptibility is larger than the system's real dimension ($d_a>d$).

4 pages, final version accepted by PRE

References in corpus (12)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Sufficiency Criterion for the Validity of the Adiabatic Approximation
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Direct observation of quantum criticality in Ising spin chains
• Operator fidelity susceptibility: an indicator of quantum criticality
• Quantum phase transition in the one-dimensional period-two and uniform compass model
• Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation

Cited by in corpus (13)

• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Fidelity approach to quantum phase transitions
• Quantum Critical Scaling of Fidelity Susceptibility
• The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Oscillating fidelity susceptibility near a quantum multicritical point
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Quantum phase transition between topologically distinct quantum critical points
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Nonadiabatic transition at a band-touching point