Abstract: Precise calculations of dynamics in the homogeneous electron gas (jellium model) are of fundamental importance for design and characterization of new materials. We introduce a diagrammatic Monte Carlo technique based on algorithmic Matsubara integration that allows us to compute frequency and momentum resolved finite temperature response directly in the real frequency domain using a series of connected Feynman diagrams. The data for charge response at moderate electron density are used to extract the frequency dependence of the exchange-correlation kernel at finite momenta and temperature. These results are as important for development of the time-dependent density functional theory for materials dynamics as ground state energies are for the density functional theory.

Link: https://doi.org/10.1103/PhysRevLett.129.246401

Data: https://drive.google.com/drive/u/1/folders/1QzZo0TG-hgpSCtO-hfBoZXUjjLDVsCQ6

Codes: https://github.com/jpfleblanc/hf_cuba_mpi

Authors: I. S. Tupitsyn, A. M. Tsvelik, R. M. Konik, and N. V. Prokof’ev

Abstract: Building on previous developments [1-3], we show that the Diagrammatic Monte Carlo technique allows to compute finite temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system’s action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon line-width in a homogeneous electron gas (jellium).

Link: https://doi.org/10.1103/PhysRevLett.127.026403

Data: TBA

Authors: Pengcheng Hou, Xiansheng Cai, Tao Wang, Youjin Deng, Nikolay V. Prokof’ev, Boris V. Svistunov, Kun Chen

Abstract: We investigate the temperature dependence of the linear response of a generic Fermi liquid to a pair-creating perturbation, referred to as precursory Cooper flow. We show that the form of this dependence allows for an unbiased prediction of the BCS transition temperature, Tc, from data collected at temperatures dramatically higher than Tc. We employ this technique to calculate the phase diagram of superconducting states with multiple orbital channels in a moderately interacting two-dimensional uniform electron gas. Our analysis of the leading correction to the pair susceptibility reveals the possibility of predicting the temperature evolution of pairing correlations and Tc in low-temperature superconductors through the analysis of DC I-V characteristics of tunnel junctions at high temperatures.

Data availability: https://drive.google.com/drive/folders/1pIjPDrc7J7nhdT_7X0TZOMh1rfFVndFT?usp=drive_link

Code availability: https://github.com/numericalEFT/ElectronGas.jl

Authors: Tao Wang, Xiansheng Cai, Kun Chen, Boris V. Svistunov, Nikolay V. Prokof’ev

Abstract: We address the outstanding problem of electron pairing in the presence of strong Coulomb repulsion at small to moderate values of the Coulomb parameter, rs?2, and demonstrate that the pseudopotential framework is fundamentally biased and uncontrolled. Instead, one has to break the net result into two distinctively different effects: the Fermi liquid renormalization factor and the change in the effective low-energy coupling. The latter quantity is shown to behave non-monotonically with an extremum at rs?0.75. Within the random-phase approximation, Coulomb interaction starts to enhance the effective pairing coupling at rs>2, and the suppression of the critical temperature is entirely due to the renormalized Fermi liquid properties. Leading vertex corrections change this picture only quantitatively. Our results call for radical reconsideration of the widely accepted repulsive pseudopotential approach and show the need for precise microscopic treatment of Coulomb interactions in the problem of superconducting instability.

Link: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.L140507

Data availability: https://drive.google.com/drive/folders/1YgRC6gGsf5cDVwvOwDifZYeGD3SSpI7S?usp=drive_link

Code availability: https://github.com/iintSjds/QuantumStatistics.jl, https://github.com/numericalEFT/ElectronGas.jl

Authors: C. Zhang, J. Sous, D.?R. Reichman, M. Berciu, A.?J. Millis, N.?V. Prokof’ev, and B.?V. Svistunov

Abstract: Electron-lattice interactions play a prominent role in quantum materials, making a deeper understanding of direct routes to phonon-mediated high-transition-temperature (Tc) superconductivity desirable. However, it has been known for decades that weak electron-phonon coupling gives rise to low values of Tc, while strong electron-phonon coupling leads to lattice instability or formation of bipolarons, generally assumed to be detrimental to superconductivity. Thus, the route to high-Tcmaterials from phonon-mediated mechanisms has heretofore appeared to be limited to raising the phonon frequency as in the hydrogen sulfides. Here we present a simple model for phonon-mediated high-Tc superconductivity based on superfluidity of light bipolarons. In contrast to the widely studied Holstein model where lattice distortions modulate the electron’s potential energy, we investigate the situation where lattice distortions modulate the electron hopping. This physics gives rise to small-size, yet light bipolarons, which we study using an exact sign-problem-free quantum Monte Carlo approach demonstrating a new route to phonon-mediated high-Tc superconductivity. We find that Tc in our model generically and significantly exceeds typical upper bounds based on Migdal-Eliashberg theory or superfluidity of Holstein bipolarons. The key ingredient in this bipolaronic mechanism that gives rise to high Tc is the combination of light mass and small size of bipolarons. Our work establishes principles for the design of high-Tc superconductors via functional material engineering.

DOI: https://doi.org/10.1103/PhysRevX.13.011010

Data availability: https://drive.google.com/drive/folders/1MyzLIH6XlE0fbtaS8xjo_gTV7yxJsTc-?usp=share_link

Authors: Chao Zhang, Nikolay V. Prokof’ev, and Boris V. Svistunov

Abstract: Polarons originating from phonon displacement modulated hopping have relatively light masses and thus are of significant current interest as candidates for the bipolaron mechanism of high-temperature superconductivity [Sous  et al., Phys. Rev. Lett. 121, 247001 (2018)]. We observe that the bond model, when the dominant coupling comes from atomic vibrations on lattice bonds, can be solved by efficient sign-free Monte Carlo methods based on the path-integral formulation of the particle sector in combination with either the (real-space) diagrammatic or Fock-path-integral representation of the phonon sector. We introduce the corresponding algorithms and provide illustrative results for singlet bipolarons in two dimensions. The data suggest that the route towards high-temperature superconductivity (if any) in the multiparametric space of the model lies between the Scylla of large size of moderately light bipolarons and the Charybdis of large mass of compact bipolarons. As a result, on-site repulsion is helping s-wave superconductivity in sharp contrast with existing expectations.

DOI: https://doi.org/10.1103/PhysRevB.105.L020501

Data availability: https://drive.google.com/drive/folders/1DBYwQ7oxYfd5HzRMgk2YF7KhTSuL1b39?usp=share_link

Authors: Chao Zhang, Nikolay V. Prokof’ev, and Boris V. Svistunov

Abstract: Polarons with different types of electron-phonon coupling have fundamentally different properties. When the dominant interaction is between the electron density and lattice displacement, the momentum of the ground state does not change and the polaron gets exponentially heavy at strong coupling. In contrast, one-dimensional Peierls/Su-Schrieffer-Heeger (PSSH) polarons with interaction originating from displacement-modulated hopping feature a shift of the ground-state momentum to finite values and moderate values of effective mass as coupling is increased [D. J. J. Marchand  et al., Phys. Rev. Lett. 105, 266605 (2010)]. Based on Diagrammatic Monte Carlo method, we investigate whether unusual properties of PSSH polarons depend on the type of the displacement-modulated hopping and to what degree they survive in higher dimension. We study two different PSSH models: with bosonic degrees of freedom residing on sites (model A) and bonds (model B) of the two-dimensional square lattice. For model A, we find that in both adiabatic and intermediate regimes, the momentum of the ground state experiences a continuous transition from zero to a finite value as a function of coupling strength. The transition is driven by quadratic instability of the dispersion function, implying that effective mass diverges at the critical point, and then decreases in an anisotropic fashion with increasing coupling. Unexpectedly, for model B, the momentum of the ground state always stays at zero and the effective mass increases monotonously with coupling. The increase is far from exponential and tends to level off at strong interaction, resulting in relatively light polarons. Having light polarons in the strong coupling regime is crucial for the bipolaron mechanism of high-temperature superconductivity [J. Sous, M. Chakraborty, R. V. Krems, and M. Berciu, Phys. Rev. Lett.121, 247001 (2018).]

DOI: https://doi.org/10.1103/PhysRevB.104.035143

Data availability: https://drive.google.com/drive/folders/19RnxNhgjgyPsUfaZoZ887cpImKlhx_5J?usp=share_link

Authors: Xiansheng Cai, Tao Wang, Nikolay V. Prokof’ev, Boris V. Svistunov, and Kun Chen

Abstract: We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter rs?2. We confirm that superconductivity naturally emerges from purely repulsive interactions described by the Kukkonen-Overhauser vertex function. By employing the implicit renormalization approach and the discrete Lehmann representation we reveal that even in the small-rs limit, the dominant mechanism behind Cooper instability is based on dynamic screening of the Coulomb interaction—accurately captured by the random phase approximation, whereas the Kohn-Luttinger contribution is negligibly small and, thus, not relevant.

Link: https://doi.org/10.1103/PhysRevB.106.L220502

Data availability: https://drive.google.com/drive/folders/1psLvj3zmW4oG4qmSUFZPTOmpJ0_OsZ9d?usp=drive_link

Code availability: https://github.com/iintSjds/QuantumStatistics.jl

Authors: TBA

Abstract: TBA

doi: xx.xx/xx.xx.xx

Link to the data: https://drive.google.com/file/d/1VjTuYQEXntqhOQrUWDRryc4sv79bR6CV/view?usp=drive_link