Density matrix of electrons coupled to phonons and the electron-phonon entanglement content of excited states

Abstract

We derive the exact reduced density matrix for the electrons in an analytically solvable electron-phonon model. Here, the electrons are described as a Luttinger liquid that is coupled to Einstein phonons. We further derive analytical expressions for the electron-phonon entanglement, its spectrum and mutual information at finite and zero temperature as well as for excited states. The entanglement entropy is additive in momentum for the quasi-particle excited states, but not in the electron-phonon coupled eigenmodes of the system.

9 pages, 4 figures

References in corpus (7)

• Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
• Entanglement negativity in the harmonic chain out of equilibrium
• Diagrammatic Monte Carlo method for many-polaron problems
• Bound states and entanglement in the excited states of quantum spin chains
• Quantum-entanglement aspects of polaron systems
• Phase diagram and phonon-induced backscattering in topological insulator nanowires
• Entanglement of electrons and the lattice in a Luttinger system

Cited by in corpus (2)

• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Spectral features of polaronic excitations in a superconducting analog simulator