Momentum-space entanglement and Loschmidt echo in Luttinger liquids after a quantum quench

TL;DR

This paper investigates the universal features of momentum-space entanglement in Luttinger liquids, revealing connections to the Loschmidt echo and contrasting behavior with spatial bipartitioning after a quantum quench.

Contribution

It uncovers universal properties of momentum-space entanglement spectrum and entropy in Luttinger liquids, linking the largest eigenvalue to the Loschmidt echo and analyzing entanglement dynamics post-quench.

Findings

Momentum-space entanglement spectrum has universal features.

Largest eigenvalue equals the Loschmidt echo.

Entanglement entropy saturates quickly and is extensive.

Abstract

Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e. the overlap of the disentangled and final wavefunctions of the system. The second largest eigenvalue is the overlap of the first excited state of the disentangled system with zero total momentum and the final wavefunction. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.