Entanglement of electrons and the lattice in a Luttinger system
arXiv:2009.03274 · doi:10.1103/PhysRevB.104.035405
Abstract
The coupling between electronic and lattice degrees of freedom lies at the core of many important properties of solids. Nevertheless, surprisingly little is know about the entanglement between these degrees of freedom. We here calculate the entanglement entropy at zero temperature as well as the mutual information and the entanglement negativity at finite temperatures between the electrons and the lattice of a one-dimensional chain. The electrons are described within Luttinger-liquid theory. Our results show that the entanglement entropy diverges when one approaches the limit of stability, the so-called Wentzel-Bardeen singularity. We have found that the mutual information and the entanglement negativity decrease with the temperature. The mutual information reaches a finite value in the infinite-temperature limit, which is the consequence of the infinite linear electron spectrum of Luttinger theory. The entanglement negativity becomes exactly zero above a certain temperature, i.e., the lattice and the electrons become non-entangled above this temperature. If the electron-electron interaction is unscreened or weakly screened, this characteristic temperature diverges with the system size. However, if the interaction is strongly screened the characteristic temperature is finite and independent of the system size.
arXiv comment11 pages, 4 figures
References in corpus (33)
- A computable measure of entanglement
- Concentrating Partial Entanglement by Local Operations
- Area laws for the entanglement entropy - a review
- Many-body localization, thermalization, and entanglement
- Electron-phonon interactions from first principles
- The Role of Relative Entropy in Quantum Information Theory
- Coulomb Interactions and Mesoscopic Effects in Carbon Nanotubes
- Classical simulation of quantum many-body systems with a tree tensor network
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Effective low-energy theory for correlated carbon nanotubes
- Bound entangled Gaussian states
- Entanglement Properties of the Harmonic Chain
- Polaron Problem by Diagrammatic Quantum Monte Carlo
- Quantum inseparability as local pseudomixture
- Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
- Entanglement in solvable many-particle models
- Entanglement negativity in the harmonic chain out of equilibrium
- Real-Space Tailoring of the Electron-Phonon Coupling in Ultra-Clean Nanotube Mechanical Resonators
- Entanglement negativity after a global quantum quench
- Tensor network simulation of non-Markovian dynamics in organic polaritons
- Quantum information dynamics in multipartite integrable systems
- Diagrammatic Monte Carlo method for many-polaron problems
- Wentzel-Bardeen singularity and phase diagram for interacting electrons coupled to acoustic phonons in one dimension
- Acoustic phonon exchange, attractive interactions, and the Wentzel-Bardeen singularity in single-wall nanotubes
- The correlation theory of the chemical bond
- Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
- Entanglement entropy between two coupled Tomonaga-Luttinger liquids
- The von Neumann entropy asymptotics in multidimensional fermionic systems
- Entanglement and classical fluctuations at finite-temperature critical points
- Electron-phonon coupling in metallic carbon nanotubes: Dispersionless electron propagation despite dissipation
- Phase diagram and phonon-induced backscattering in topological insulator nanowires
- Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
- Distilling momentum-space entanglement in Luttinger liquids at finite temperature