Quenching the magnetic flux in 1d fermionic ring: Loschmidt echo and edge singularity

Abstract

We consider the non-equilibrium dynamics of a system of interacting massless fermions in a ring threaded by a magnetic flux. We focus on the quench where the flux is initially vanishing and is then turned on. We show that the definition of the limit of abrupt quench is problematic due to the presence of gauge invariance that has to be taken into account. We then propose a specific protocol where the dynamics is non-trivial. Employing techniques coming from the Algebraic Bethe-Ansatz, we present an exact formula for the Loschmidt echo valid at all times as a Fredholm determinant at the free fermionic point. From the analysis of the asymptotic behavior of the Fredholm determinant, we show that the distribution of work done at small energies present an edge singularity whose exponent can be explicitly computed. Using the correspondence between the edge singularity and the decay of the fidelity at finite-size we propose a general formula for the exponent valid also in the interacting case.

4 pages, 1 figure, 3 pages supplemental material

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Fluctuation theorems: Work is not an observable
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Work distribution and edge singularities for generic time-dependent protocols in extended systems
• Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
• Universal energy distribution of quasi-particles emitted in a local time dependent quench

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• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Integrability-protected adiabatic reversibility in quantum spin chains
• Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Quench echo and work statistics in integrable quantum field theories
• Non-linear current and dynamical quantum phase transitions in the flux-quenched Su-Schrieffer-Heeger model
• Exact work statistics of quantum quenches in the anisotropic XY model
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Effects of the Dzyaloshinsky-Moriya interaction on nonequilibrium thermodynamics in the $XY$ chain in a transverse field
• Superluminal moving defects in the Ising spin chain
• Lack of thermalization for integrability-breaking impurities
• Flux quench in a system of interacting spinless fermions in one dimension
• Return amplitude after a quantum quench in the XY chain
• Entanglement front generated by an impurity travelling in an isolated many-body quantum system
• Bosonization with a background $U(1)$ gauge field
• Floquet dynamical quantum phase transitions in periodically flux-quenched systems