Quantum quenches from integrability: the fermionic pairing model

Abstract

Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from both the vanishing time scale of the quench event, which can thus create arbitrarily high energy modes, and its non-local nature, which curtails the utility of local excitation bases. We here show that nonperturbative methods based on integrability can prove sufficiently powerful to completely characterize quantum quenches: we illustrate this using a model of fermions with pairing interactions (Richardson's model). The effects of simple (and multiple) quenches on the dynamics of various important observables are discussed. Many of the features we find are expected to be universal to all kinds of quench situations in atomic physics and condensed matter.

10 pages, 7 figures

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• The Quench Action
• Quantum Quenches in Integrable Field Theories
• What is an integrable quench?
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• Quantum quench dynamics of the sine-Gordon model in some solvable limits
• Quantum Quench from a Thermal Initial State
• Dynamics after a sweep through a quantum critical point
• Interaction quenches in the 1D Bose gas
• Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects
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• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
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• Finite-size corrections vs. relaxation after a sudden quench
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• Exact formulas for the form factors of local operators in the Lieb-Liniger model
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• A semiclassical study of the Jaynes-Cummings model
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• Spin 1 microcondensate in a magnetic field: semiclassics and exact solution
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