Bound excited states of Fröhlich polarons in one dimension

Abstract

The one-dimensional Fröhlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the existence of an arbitrarily large number of bound excited states in the strong coupling limit and calculate their excitation energies. Numerical simulations of a discretized model demonstrate the complete amelioration of the projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert space. They reveal the threshold for the occurrence of the first bound excited states at a value of $\alpha \approx 1.73$ for the dimensionless coupling constant. This puts the threshold into the regime of intermediate interaction strength. We find a significant spectral weight and increased phonon number of the bound excited state at threshold.

arXiv comment11 pages, 9 figures

References in corpus (31)

• Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate
• Bose polarons in the strongly interacting regime
• Froehlich Polaron and Bipolaron: Recent Developments
• A Constrained Path Monte Carlo Method for Fermion Ground States
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Electron-phonon effects and transport in carbon nanotubes
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• The Holstein Polaron
• Semistochastic Projector Monte Carlo Method
• The Green's Function of the Holstein Polaron
• Erratum: Exact Ground State Energy of the Strong-Coupling Polaron
• An excited-state approach within full configuration interaction quantum Monte Carlo
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
• Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
• Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron
• Polarons in Carbon Nanotubes
• Diagrammatic Monte Carlo study of the Fröhlich polaron dispersion in 2D and 3D
• The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function
• Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra
• Free energy of the Fröhlich polaron in two and three dimensions
• Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
• Quantum corrections to the Pekar asymptotics of a strongly coupled polaron
• Improved walker population control for full configuration interaction quantum Monte Carlo
• Grid-based diffusion Monte Carlo for fermions without the fixed-node approximation
• Optical signatures of exciton-polarons from diagrammatic Monte Carlo
• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• Lattice Bose polarons at strong coupling and quantum criticality
• Approximating matrix eigenvalues by subspace iteration with repeated random sparsification
• Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces
• Ubiquity of bound states for the strongly coupled polaron
• Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling