Exploring nonequilibrium phases of photo-doped Mott insulators with generalized Gibbs ensembles

Many experiments show that strong excitations of correlated quantum materials can cause non-thermal phases without equilibrium analogues. Understanding the origin and properties of these nonequilibrium states has been challenging due to the limitations of theoretical methods for nonequilibrium strongly correlated systems. In this work, we introduce a generalized Gibbs ensemble description that enables a systematic analysis of the long-time behavior of photo-doped states in Mott insulators based on equilibrium methods. We demonstrate the power of the method by mapping out the nonequilibrium phase diagram of the one-dimensional extended Hubbard model, which features η-pairing and charge density wave phases in a wide photo-doping range. We furthermore clarify that the peculiar kinematics of photo-doped carriers, and the interaction between them, play an essential role in the formation of these non-thermal phases. Our results establish a new path for the systematic analysis of nonequilibrium strongly correlated systems.

Importance of charge self-consistency in first-principles description of strongly correlated systems

First-principles approaches have been successful in solving many-body Hamiltonians for real materials to an extent when correlations are weak or moderate. As the electronic correlations become stronger often embedding methods based on first-principles approaches are used to better treat the correlations by solving a suitably chosen many-body Hamiltonian with a higher level theory. The success of such embedding theories, often referred to as second-principles, is commonly measured by the quality of self-energy Σ which is either a function of energy or momentum or both. However, Σ should, in principle, also modify the electronic eigenfunctions and thus change the real space charge distribution. While such practices are not prevalent, some works that use embedding techniques do take into account these effects. In such cases, choice of partitioning, of the parameters defining the correlated Hamiltonian, of double-counting corrections, and the adequacy of low-level Hamiltonian hosting the correlated subspace hinder a systematic and unambiguous understanding of such effects. Further, for a large variety of correlated systems, strong correlations are largely confined to the charge sector. Then an adequate nonlocal low-order theory is important, and the high-order local correlations embedding contributes become redundant. Here we study the impact of charge self-consistency within two example cases, TiSe2 and CrBr3, and show how real space charge re-distribution due to correlation effects taken into account within a first-principles Green’s function-based many-body perturbative approach is key in driving qualitative changes to the final electronic structure of these materials.

Regularized Second-Order Correlation Methods for Extended Systems

While many-body wavefunction theory has long been established as a powerful framework for highly accurate molecular quantum chemistry, these methods have only fairly recently been applied to extended systems in a significant scale. This is due to the high computational cost of such calculations, requiring efficient implementations and ample computing resources. To further aggravate this, second-order Møller-Plesset perturbation theory (MP2) (the most cost effective wavefuntion method) is known to diverge or fail for some prototypical condensed matter systems like the homogeneous electron gas (HEG). In this paper, we explore how the issues of MP2 for metallic and strongly correlated systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillioun-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model and the graphene-water interaction energy. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for metallic and strongly correlated systems, respectively.

Chebyshev matrix product states with canonical orthogonalization for spectral functions of strongly correlated systems

We propose a method to calculate the spectral functions of strongly correlated systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. We demonstrate for the first time that Chebyshev MPS can be used in quantum chemistry. We also caution the application for electron-phonon system with densed density of states.