Holstein model

Holstein model
Name	Holstein model
Field	Condensed matter physics
Introduced	1959
Author	Theodore Holstein

Holstein model The Holstein model is a theoretical lattice model introduced to describe interactions between electrons and local vibrational modes in crystalline solids. It captures essential features of polaron formation, charge-density waves, and superconducting tendencies in materials through a minimal set of parameters, and it has been studied using techniques developed in Cambridge University, Harvard University, Massachusetts Institute of Technology, Stanford University, Princeton University, California Institute of Technology, ETH Zurich, University of Oxford, University of Cambridge, Columbia University, University of Chicago, University of Tokyo, University of California, Berkeley, Max Planck Society, Los Alamos National Laboratory, Argonne National Laboratory, CERN, IBM Research, Bell Labs, Microsoft Research, Google Research, Duke University, Yale University, University of Illinois Urbana–Champaign, University of Pennsylvania, Rutgers University, University of Michigan, Cornell University, University of California, Santa Barbara.

Introduction

The Holstein model was proposed by Theodore Holstein in 1959 to address small-polaron physics in molecular crystals and narrow-band materials; it complements earlier work by Lev Landau, Soviet Academy of Sciences, Herbert Fröhlich, and Rudolf Peierls. Early developments connected it to experimental studies at Bell Labs and theoretical frameworks at Princeton University and Harvard University; subsequent influential work involved researchers at Max Planck Institute for Solid State Research and Institute Laue–Langevin. The model has been a focus in conferences at American Physical Society, European Physical Society, International Centre for Theoretical Physics, Joint Quantum Institute, and at schools hosted by ICTP and Les Houches.

Model Definition

The Holstein Hamiltonian describes spinful or spinless fermions on a discrete lattice coupled locally to dispersionless Einstein phonons; it is parameterized by electronic hopping, phonon frequency, and electron–phonon coupling constants. Its minimal form is studied on one-dimensional chains, two-dimensional square lattices, and three-dimensional cubic lattices frequently used in studies at Los Alamos National Laboratory and ETH Zurich; variants appear in works from Columbia University, University of Cambridge, and University of Tokyo. The model contrasts with the Hubbard model and the Fröhlich model in emphasizing local coupling and has been compared to the t–J model and Holstein–Hubbard model in theoretical studies at University of Oxford and Stanford University.

Methods of Solution

Exact diagonalization, quantum Monte Carlo, density matrix renormalization group, dynamical mean-field theory, variational Lang–Firsov transformations, and diagrammatic Monte Carlo are standard techniques used to solve or approximate the Holstein model. These methods have been developed and refined at institutions including Harvard University, Princeton University, Yale University, University of California, Berkeley, University of Illinois Urbana–Champaign, Cornell University, Duke University, Rutgers University, University of Pennsylvania, and Caltech. Quantum Monte Carlo implementations draw on algorithms from groups at Argonne National Laboratory and Oak Ridge National Laboratory, while dynamical mean-field theory connections were advanced at Rutgers University and ETH Zurich. Matrix product state and tensor network approaches have been advanced at University of Vienna, University of Bath, and Max Planck Institute for the Physics of Complex Systems.

Physical Properties and Phases

The Holstein model exhibits polaron formation, charge-density-wave order, superconducting correlations, and metal–insulator transitions depending on coupling strength, adiabaticity ratio, carrier concentration, and lattice dimensionality. Phase diagrams and critical behavior have been mapped in one dimension, two dimensions, and three dimensions by research groups at University of Cambridge, University of Oxford, Stanford University, University of Tokyo, Nagoya University, Tata Institute of Fundamental Research, University of São Paulo, University of British Columbia, and McGill University. Relations to bipolaron formation and Bose–Einstein condensation have been explored in contexts associated with Rice University, Princeton University, and University of Chicago. Comparisons to charge ordering in transition-metal oxides studied at Argonne National Laboratory and Oak Ridge National Laboratory link the model to experimental probes such as angle-resolved photoemission spectroscopy at SLAC National Accelerator Laboratory and inelastic neutron scattering at Institut Laue–Langevin.

Extensions and Generalizations

Generalizations include the Holstein–Hubbard model, multi-orbital Holstein models, disordered Holstein lattices, long-range electron–phonon coupling variants, and models with dispersive phonons or anharmonic phonon potentials. These extensions have been pursued at Max Planck Institute for Solid State Research, University of Cologne, CNRS, CEA Saclay, Paul Scherrer Institute, Lawrence Berkeley National Laboratory, Brookhaven National Laboratory, National Institute for Materials Science, RIKEN, Seoul National University, Peking University, Tsinghua University, Indian Institute of Science, University of Melbourne, Monash University, University of Sydney, and University of New South Wales. Connections to polaronic transport in organic semiconductors have been informed by collaborations with Samsung Advanced Institute of Technology and Nokia Bell Labs.

Applications and Experimental Relevance

The Holstein model informs understanding of transport and optical properties in organic crystals, molecular solids, transition-metal dichalcogenides, cuprate-related compounds, and fullerene materials investigated at Bell Labs, IBM Research, MIT Lincoln Laboratory, SLAC National Accelerator Laboratory, Brookhaven National Laboratory, Argonne National Laboratory, Oak Ridge National Laboratory, Max Planck Society, CNRS, RIKEN, National Institute of Standards and Technology, Toyota Research Institute, Samsung Electronics, Hitachi, Panasonic, Sony Corporation, LG Electronics, Siemens, BASF, Pfizer, Boehringer Ingelheim, Novartis, Johnson & Johnson, and GlaxoSmithKline. Experimental observables predicted by the model include spectral functions, optical conductivity, isotope effects, and phonon softening measured via angle-resolved photoemission, Raman spectroscopy, infrared spectroscopy, and inelastic neutron scattering at facilities such as ISIS Neutron and Muon Source and European Synchrotron Radiation Facility.

Category:Condensed matter physics models