Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons

Abstract

We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb-Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there exists a mapping between the bosonic wavefuntions and the free fermionic ones but this does not help the computation of the one-body density matrix which is sensitive to particle statistics. The final expression, given in terms of the difference of the square root of two Fredholm determinants, can be numerically evaluated and is valid in the thermodynamic limit and for all times after the quench.

24 pages, 2 figure

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Cited by in corpus (12)

• Generalized Gibbs Ensembles for Quantum Field Theories
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Pre-relaxation in weakly interacting models
• Exact solution for the quench dynamics of a nested integrable system
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Density form factors of the 1D Bose gas for finite entropy states
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Effective free-fermionic form factors and the XY spin chain