Diagrammatic Monte Carlo method for many-polaron problems

Metal-insulator transition of spinless fermions coupled to dispersive optical bosons

Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model.

Revealing the Polaron State at the MoS2/TiO2 Interface

Interfacial polarons determine the distribution of free charges at the interface and thus play important roles in manipulating the physicochemical properties of hybridized polaronic materials. In this work, we investigated the electronic structures at the atomically flat interface of the single-layer MoS₂ (SL-MoS₂) on the rutile TiO₂ surface using high-resolution angle-resolved photoemission spectroscopy. Our experiments directly visualized both the valence band maximum and the conduction band minimum (CBM) of SL-MoS₂ at the K point, which clearly defines a direct bandgap of ∼2.0 eV. Detailed analyses corroborated by density functional theory calculations demonstrated that the CBM of MoS₂ is formed by the trapped electrons at the MoS₂/TiO₂ interface that couple with the longitudinal optical phonons in the TiO₂ substrate through an interfacial Fröhlich polaron state. Such an interfacial coupling effect may register a new route for tuning the free charges in the hybridized systems of two-dimensional materials and functional metal oxides.

Vertex-Based Diagrammatic Treatment of Light-Matter-Coupled Systems

We propose a diagrammatic Monte Carlo approach for quantum impurity models, which can be regarded as a generalization of the strong-coupling expansion for fermionic impurity models. The algorithm is based on a self-consistently computed three-point vertex and a stochastically sampled four-point vertex, and it allows one to obtain numerically exact results in a wide parameter regime. The performance of the algorithm is demonstrated with applications to a spin-boson model representing an emitter in a waveguide. As a function of the coupling strength, the spin exhibits a delocalization-localization crossover at low temperatures, signaling a qualitative change in the real-time relaxation. In certain parameter regimes, the response functions of the emitter coupled to the electromagnetic continuum can be described by an effective Rabi model with appropriately defined parameters. We also discuss the spatial distribution of the photon density around the emitter.

Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions

It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.

Fermi blockade of the strong electron-phonon interaction in modelled optimally doped high temperature superconductors

We study how manifestations of strong electron-phonon interaction depend on the carrier concentration by solving the two-dimensional Holstein model for the spin-polarized fermions using an approximation free bold-line diagrammatic Monte Carlo method. We show that the strong electron-phonon interaction, obviously present at very small Fermion concentration, is masked by the Fermi blockade effects and Migdal's theorem to the extent that it manifests itself as moderate one at large carriers densities. Suppression of strong electron-phonon interaction fingerprints is in agreement with experimental observations in doped high temperature superconductors.

Formation of Plasmonic Polarons in Highly Electron-Doped Anatase TiO2

The existence of various quasiparticles of polarons because of electron-boson couplings plays important roles in determining electron transport in titanium dioxide (TiO₂), which affects a wealth of physical properties from catalysis to interfacial superconductivity. In addition to the well-defined Fröhlich polarons whose electrons are dressed by the phonon clouds, it has been theoretically predicted that electrons can also couple to their own plasmonic oscillations, namely, the plasmonic polarons. Here we experimentally demonstrate the formation of plasmonic polarons in highly doped anatase TiO₂ using angle-resolved photoemission spectroscopy. Our results show that the energy separation of plasmon-loss satellites follows a dependence on √n, where n is the electron density, manifesting the characteristic of plasmonic polarons. The spectral functions enable to quantitatively evaluate the strengths of electron-plasmon and electron-phonon couplings, respectively, providing an effective approach for characterizing the interplays among different bosonic modes in the complicate many-body interactions.

Strong long-range electron-phonon interaction as possible driving force for charge ordering in cuprates

A model resulting in charge ordering (CO) similar to that observed in cuprate superconductors is under study. It includes strong long-range electron-phonon interaction (EPI) and high density of correlated carriers. Coexistence of large bipolarons and delocalized carriers is a feature of such system. We develop generalized variation method to calculate the bipolaron size (CO period) in the ground normal state of such system at various doping. The approach allows the revealing of a possible physical reason of strongly different doping behavior of the CO wave vector in different cuprates. Obtained doping dependences of the CO period and temperature of the CO decay demonstrate quantitative agreement with those observed in cuprates. Predicted in the suggested approach ratio of the CO wave vector to the wave vector of the high-energy anomaly (HEA) in ARPES spectrum is in consent with that in cuprates. Calculated resonant x-rays scattering on the CO emerging in the model is in good agreement with experiments on cuprates including the asymmetry of the CO peaks' cross-section. A gap arises in the spectrum of delocalized carriers near antinodal direction due to their scattering on the periodic potential created by autolocalized carriers, analogously to photon crystal effect.

Diagrammatic Monte Carlo Approach to Angular Momentum in Quantum Many-Particle Systems

We introduce a diagrammatic Monte Carlo approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite-size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model; however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.

Resummation of Diagrammatic Series with Zero Convergence Radius for Strongly Correlated Fermions

We demonstrate that a summing up series of Feynman diagrams can yield unbiased accurate results for strongly correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of nonrelativistic fermions in three-dimensional continuous space. Diagrams are built from partially dressed or fully dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient.

Holstein polaron in a valley-degenerate two-dimensional semiconductor

Two-dimensional (2D) crystals have emerged as a class of materials with tunable carrier density¹. Carrier doping to 2D semiconductors can be used to modulate many-body interactions² and to explore novel composite particles. The Holstein polaron is a small composite particle of an electron that carries a cloud of self-induced lattice deformation (or phonons)^3-5, which has been proposed to play a key role in high-temperature superconductivity⁶ and carrier mobility in devices⁷. Here we report the discovery of Holstein polarons in a surface-doped layered semiconductor, MoS₂, in which a puzzling 2D superconducting dome with the critical temperature of 12 K was found recently^8-11. Using a high-resolution band mapping of charge carriers, we found strong band renormalizations collectively identified as a hitherto unobserved spectral function of Holstein polarons^12-18. The short-range nature of electron-phonon (e-ph) coupling in MoS₂ can be explained by its valley degeneracy, which enables strong intervalley coupling mediated by acoustic phonons. The coupling strength is found to increase gradually along the superconducting dome up to the intermediate regime, which suggests a bipolaronic pairing in the 2D superconductivity.

Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit

We present a simple trick that allows us to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models, such that the thermodynamic limit can be taken analytically. With our approach one can achieve superior performance compared to conventional diagrammatic Monte Carlo algorithm, while rendering the algorithmic part dramatically simpler. By considering the sum of all connected diagrams at once, we allow for massive cancellations between different diagrams, greatly reducing the sign problem. In the end, the computational effort increases only exponentially with the order of the expansion, which should be contrasted with the factorial growth of the standard diagrammatic technique. We illustrate the efficiency of the technique for the two-dimensional Fermi-Hubbard model.

Tailoring the nature and strength of electron-phonon interactions in the SrTiO3(001) 2D electron liquid

Surfaces and interfaces offer new possibilities for tailoring the many-body interactions that dominate the electrical and thermal properties of transition metal oxides. Here, we use the prototypical two-dimensional electron liquid (2DEL) at the SrTiO3(001) surface to reveal a remarkably complex evolution of electron-phonon coupling with the tunable carrier density of this system. At low density, where superconductivity is found in the analogous 2DEL at the LaAlO3/SrTiO3 interface, our angle-resolved photoemission data show replica bands separated by 100 meV from the main bands. This is a hallmark of a coherent polaronic liquid and implies long-range coupling to a single longitudinal optical phonon branch. In the overdoped regime the preferential coupling to this branch decreases and the 2DEL undergoes a crossover to a more conventional metallic state with weaker short-range electron-phonon interaction. These results place constraints on the theoretical description of superconductivity and allow a unified understanding of the transport properties in SrTiO3-based 2DELs.

Polaronic metal state at the LaAlO3/SrTiO3 interface

Interplay of spin, charge, orbital and lattice degrees of freedom in oxide heterostructures results in a plethora of fascinating properties, which can be exploited in new generations of electronic devices with enhanced functionalities. The paradigm example is the interface between the two band insulators LaAlO3 and SrTiO3 that hosts a two-dimensional electron system. Apart from the mobile charge carriers, this system exhibits a range of intriguing properties such as field effect, superconductivity and ferromagnetism, whose fundamental origins are still debated. Here we use soft-X-ray angle-resolved photoelectron spectroscopy to penetrate through the LaAlO3 overlayer and access charge carriers at the buried interface. The experimental spectral function directly identifies the interface charge carriers as large polarons, emerging from coupling of charge and lattice degrees of freedom, and involving two phonons of different energy and thermal activity. This phenomenon fundamentally limits the carrier mobility and explains its puzzling drop at high temperatures.