Solution for an interaction quench in the Lieb-Liniger Bose gas

By J. Nardis, B. Wouters, M. Brockmann, J. Caux. 2013

185 citations recorded by the source corpus.

We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $\ensuremath{\delta}$-interacting repulsive bosons. By using a recently proposed variational method, we here obtain the exact nonthermal steady state of the system in the thermodynamic limit and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a standard implementation of the generalized Gibbs ensemble fails.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3175a978a2893b0c0008de784a532ea9ac9c0244

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In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. M. Fagotti
3. V. Alba
4. F. Essler
5. J. Caux
6. L. Vidmar
7. B. Doyon
8. Marcos Rigol

Citations in the corpus

• The Quench Action (2016, methodology): “Amazingly, for the BEC state, at any value of the interaction parameter, a dramatic simplification in fact turns out to be possible: one finds [36, 94] that the exact overlaps (which are only nonvanishing for parity-symmetric states, namely states in which the rapidity distribution is mirror-symmetr”
• Drude Weight for the Lieb-Liniger Bose Gas (2017, background): “There are bona fide GGE states for which local densities have diverging averages [48], although this does not imply divergence of their two-point correlation functions.”
• Generalized Gibbs ensemble in integrable lattice models (2016, methodology): “We note that related ideas have been discussed in the context of the so-called quench-action method [67, 68, 69, 113, 114] (see also the review by Caux in this volume [115]).”
• Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “Progress has however been made in cases where the initial state has a simpler structure, in particular for (matrix) product states in either position [58, 63, 65, 66, 68, 69] or momentum/rapidity space [95, 97, 105, 107, 111, 113, 114].”
• Entanglement dynamics after quantum quenches in generic integrable systems (2017, background): “1 Repulsive case The quench action solution for the quench in the repulsive Lieb-Liniger has been provided in [141].”