Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model

Symmetry-Broken Perturbation Theory to Large Orders in Antiferromagnetic Phases

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Riccardo Rossi, Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett. 119, 045701 (2017).PRLTAO0031-900710.1103/PhysRevLett.119.045701]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the Néel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O(3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U/t=4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.

Local and Nonlocal Electronic Correlations at the Metal-Insulator Transition in the Two-Dimensional Hubbard Model

Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.

Optimizing Superconductivity: From Cuprates via Nickelates to Palladates

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in the single-band Hubbard model. We calculate the spectrum and superconducting transition temperature T_{c} as a function of filling and Coulomb interaction for a range of hopping parameters, using the dynamical vertex approximation. We find the sweet spot for high T_{c} to be at intermediate coupling, moderate Fermi surface warping, and low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close to this optimum within the single-band description. Instead, we identify some palladates, notably RbSr_{2}PdO_{3} and A_{2}^{'}PdO_{2}Cl_{2} (A^{'}=Ba_{0.5}La_{0.5}), to be virtually optimal, while others, such as NdPdO_{2}, are too weakly correlated.

Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model

Diagrammatic Monte Carlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.

Efficient world-line-based quantum Monte Carlo method without Hubbard-Stratonovich transformation

By precisely writing down the matrix element of the local Boltzmann operator (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{e}}^{-\tau h}$$\end{document}e-τh, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h$$\end{document}h is the Hermitian conjugate pairs of off-diagonal operators), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With the current formula, the Hubbard–Stratonovich transformation is not necessary, accordingly the determinant calculation is not needed, which can improve the computational efficiency. The results show that, the simulation time has the square-law scaling with system sizes, which is comparable with the usual first-principles calculations. The current formula also improves the accuracy of the Suzuki–Trotter decomposition. As an example, we have studied the one-dimensional half-filled Hubbard model at finite temperature. The obtained results are in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be applied to various studies in future.

How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger-Dyson (or the Bethe-Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.

Entropy in the Non-Fermi-Liquid Regime of the Doped 2D Hubbard Model

We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.

Spin and Charge Correlations across the Metal-to-Insulator Crossover in the Half-Filled 2D Hubbard Model

The 2D Hubbard model with nearest-neighbor hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using the diagrammatic Monte Carlo approach in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and nonlocal fluctuations in both channels are essential.