Polarons—quantum particles dressed by a cloud of bath excitations—arise whenever a particle interacts strongly with its host medium. Electron and hole polarons, formed when carriers bind to a phonon cloud through electron-phonon (e-ph) interactions, govern charge transport in transition metal oxides, organic semiconductors, and halide perovskites. The concept generalizes to exciton-phonon interactions, giving rise to exciton polarons that produce the large Stokes shifts and broad photoluminescence (PL) lineshapes central to light-emitting applications. A predictive treatment of polarons has remained elusive. Numerically exact methods such as diagrammatic Monte Carlo (DMC) have been restricted to simplified model Hamiltonians, while first-principles approaches based on density functional theory provide material-specific e-ph interactions but treat the e-ph correlation approximately. This thesis bridges that gap by developing first-principles diagrammatic Monte Carlo (FPDMC), which stochastically sums all e-ph Feynman diagrams using accurate ab-initio interactions, yielding numerically exact polaron properties in real materials. Two methodological advances make FPDMC possible. A matrix-product formalism sums over electronic band indices exactly, alleviating the multi-band sign problem in realistic band structures. A data-driven compression of e-ph interactions based on singular-value decomposition (SVD) in the Wannier basis then accelerates the method by more than 10³×. The SVD compression also reveals a hidden low-dimensional structure of quantum interactions, maintaining accuracy across charge transport, spin relaxation, band renormalization, and superconductivity calculations. Extending this philosophy to phonon-phonon interactions via a permanent CP (PCP) decomposition yields 10³–10⁴× compression of anharmonic force constants and orders-of-magnitude speedups in thermal conductivity calculations. Applying FPDMC, we study polarons in LiF, SrTiO₃, and TiO₂, finding excellent agreement with experimental mobilities and resolving the contrasting small- and large-polaron transport in the two TiO₂ polymorphs. To make the microscopic picture concrete, we introduce an e-ph correlation function that visualizes lattice distortion and polaron orbital character. Extending FPDMC to exciton polarons, we obtain first-principles exciton-phonon interactions from finite-momentum Bethe-Salpeter equation calculations and derive a Fermi-golden-rule PL theory. Applied to CrBr₃, FPDMC predicts a broad PL spectrum agreeing with experiment in both peak position and lineshape.
Polarons—quantum particles dressed by a cloud of bath excitations—arise whenever a particle interacts strongly with its host medium. Electron and hole polarons, formed when carriers bind to a phonon cloud through electron-phonon (e-ph) interactions, govern charge transport in transition metal oxides, organic semiconductors, and halide perovskites. The concept generalizes to exciton-phonon interactions, giving rise to exciton polarons that produce the large Stokes shifts and broad photoluminescence (PL) lineshapes central to light-emitting applications. A predictive treatment of polarons has remained elusive. Numerically exact methods such as diagrammatic Monte Carlo (DMC) have been restricted to simplified model Hamiltonians, while first-principles approaches based on density functional theory provide material-specific e-ph interactions but treat the e-ph correlation approximately. This thesis bridges that gap by developing first-principles diagrammatic Monte Carlo (FPDMC), which stochastically sums all e-ph Feynman diagrams using accurate ab-initio interactions, yielding numerically exact polaron properties in real materials. Two methodological advances make FPDMC possible. A matrix-product formalism sums over electronic band indices exactly, alleviating the multi-band sign problem in realistic band structures. A data-driven compression of e-ph interactions based on singular-value decomposition (SVD) in the Wannier basis then accelerates the method by more than 10³×. The SVD compression also reveals a hidden low-dimensional structure of quantum interactions, maintaining accuracy across charge transport, spin relaxation, band renormalization, and superconductivity calculations. Extending this philosophy to phonon-phonon interactions via a permanent CP (PCP) decomposition yields 10³–10⁴× compression of anharmonic force constants and orders-of-magnitude speedups in thermal conductivity calculations. Applying FPDMC, we study polarons in LiF, SrTiO₃, and TiO₂, finding excellent agreement with experimental mobilities and resolving the contrasting small- and large-polaron transport in the two TiO₂ polymorphs. To make the microscopic picture concrete, we introduce an e-ph correlation function that visualizes lattice distortion and polaron orbital character. Extending FPDMC to exciton polarons, we obtain first-principles exciton-phonon interactions from finite-momentum Bethe-Salpeter equation calculations and derive a Fermi-golden-rule PL theory. Applied to CrBr₃, FPDMC predicts a broad PL spectrum agreeing with experiment in both peak position and lineshape.
Strong coupling between mobile charge carriers or excitons and lattice vibrations gives rise to polarons: quasiparticles formed by charge carriers dressed by a cloud of phonon excitations. Polaron formation determines transport properties of systems ranging from transition-metal oxides and organic semiconductors to light-harvesting complexes. In excitonic systems that admit a hard-core boson description, mapping the excitations to pseudospins provides a natural framework for studying polaron physics, including the nonperturbative regime in which hopping amplitudes, phonon energies, and coupling strengths are comparable. Here, we propose a trapped-ion blueprint for realizing spin-phonon Hamiltonians with programmable spatial coupling between excitation density and phonon displacements, encompassing local Holstein and long-range Fröhlich-type interactions. To access strongly dressed quasiparticles whose bare spectral weight is suppressed, we introduce displaced Green's functions implemented through spin-dependent phonon displacements. Their spectral response reveals the polaron band spectrum, including binding energies and phonon-excitation sidebands, while spatially resolved measurements probe the structure of the phonon dressing cloud, providing a route to polaron tomography. We further complement this spectroscopy with direct and ancilla-assisted measurements of spin-phonon correlations that track the coupled dynamics of the excitation and its environment. These approaches connect the emergent quasiparticle spectrum to the microscopic buildup of its dressing cloud, enabling controlled studies of how the spatial range of coupling shapes polaron formation and mobility.
This article reviews recent theoretical developments in the ab initio study of polarons in materials. The polaron is an emergent quasiparticle that arises from the interaction between electrons and phonons in solids, and consists of an electron or a hole accompanied by a distortion of the crystal lattice. Recent advances in experiments, theory, and computation have made it possible to investigate these quasiparticles with unprecedented detail, reigniting the interest in this classic problem of condensed matter physics. Recent theoretical and computational advances include ab initio calculations of polaron spectral functions, wavefunctions, lattice distortions, and transport and optical properties. These developments provide new insight into polaron physics, but they have evolved somewhat independently from the earlier effective Hamiltonian approaches that laid the foundation of the field. This article aims to bridge these complementary perspectives by placing them within a single unified conceptual framework. To this end, we start by reviewing effective Hamiltonians of historical significance in polaron theory, ab initio techniques based on density functional theory, and many-body first-principles approaches to polarons. After this survey, we outline a general field-theoretic framework that bridges between these diverse approaches to polaron physics. For completeness, we also review recent progress in the study of exciton polarons and self-trapped excitons and their relations to polarons. Beyond the methodology, we discuss recent applications to several classes of materials that attracted attention in the context of polaron physics.
Electron-phonon interactions underpin a variety of phenomena, ranging from transport and superconductivity to polarons and ultrafast carrier dynamics. Despite being one of the most intensely studied subjects in condensed matter physics, research on electron-phonon physics mostly focused on linear, first-order couplings. Second- and higher-order nonlinear couplings are commonly ignored because their calculations are too demanding and we lack computational frameworks that can provide both diagonal and off-diagonal coupling matrix elements. In this work, we report a theory and computational method for computing nonlinear electron-phonon interactions of any order in real materials. Our approach combines the advantages of unit-cell calculations of electron wavefunctions and supercell calculations of phonon perturbations, is systematically improvable, can be used with either semilocal or nonlocal exchange-correlation functionals, and is amenable to Wannier-Fourier interpolation. As a first proof of concept, we illustrate this method by computing second-order electron-phonon coupling matrix elements in diamond, lithium fluoride, and graphite as representative nonpolar semiconductors, polar semiconductors, and metals, respectively. Furthermore, we generalize the ab initio polaron equations to second-order electron-phonon couplings, and we show that second-order couplings are essential to achieve quantitative accuracy in polaron formation energies and hopping barriers. The present methodology will find application in the study of all properties and phenomena that are currently being investigated within the linear electron-phonon coupling approximation, from phonon-mediated superconductivity to excited-states dynamics, both in harmonic and anharmonic systems.
Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo (DiagMC) data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109 (2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.
Achieving materials-specific predictions for large, realistic molecules and solids with strong electron correlations remains a long-standing challenge in quantum chemistry. This dissertation develops scalable ab initio quantum many-body methods for crystalline materials, demonstrating that rigorous optimization of theoretical approximations and numerical algorithms enables predictive computation even in strongly correlated systems. The work tackles three interconnected challenges, namely describing material-specific properties of strongly correlated superconductors, achieving linear scaling with k-points for large-scale periodic calculations, and establishing reliable methods for electron-phonon interactions. The following chapters address each challenge in turn. Chapter 2 demonstrates that ab initio density matrix embedding theory, combined with symmetry-breaking strategies for superconducting order parameters, reproduces experimental trends in cuprate superconductivity, including pressure and layer effects on transition temperatures. By directly solving the electronic Schrödinger equation from material structures, these calculations capture multi-orbital covalency effects that simplified model Hamiltonians neglect, revealing their essential role in the spin fluctuations driving pairing. This predictive capability establishes a foundation for efficient computational screening of superconducting materials. Extending these calculations to larger k-point meshes and broader phase diagram explorations, however, demands more efficient computational algorithms. To overcome this computational bottleneck, Chapter 3 introduces interpolative separable density fitting framework. This development enables thermodynamic limit calculations with up to 1000 k-points, as validated on diamond, carbon dioxide, nickel monoxide, and cuprate systems. Integration with density matrix embedding theory and local natural orbital methods further yields converged ground-state energies from accurate correlated wavefunction methods such as CCSD(T) for crystalline materials in the thermodynamic limit. With computational efficiency established, the remaining challenge lies in extending the theoretical framework beyond purely electronic degrees of freedom. Chapter 4 addresses this need by establishing exponential ansatz wavefunctions as competitive approaches for electron-phonon systems. Unlike previous treatments based on perturbation theory, systematic benchmarking of coupled cluster theory and variational Lang-Firsov methods on the Holstein model demonstrates, for the first time, that these approaches accurately describe polaron formation across coupling regimes when combined with appropriate reference state optimization. These results provide a foundation for incorporating phonon effects into ab initio studies of superconducting materials. In addition to these methodological advances, GPU acceleration and MPI parallelization enhance computational throughput, enabling efficient large-scale calculations. Together, these developments constitute a computational framework for predictive ab initio quantum many-body calculations in crystalline materials, opening new avenues for understanding and designing strongly correlated quantum materials.