Frontiers of Computational Approaches to Correlated Matter

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Background

The development of novel analytical and numerical methods, specifically designed to study correlated electronic materials and their many body ground states, now forms an important pillar of quantum condensed matter physics. Several electronic and thermodynamic properties of innumerable exotic phenomena such as metal-insulator transitions, strange metal phases and non-Fermi liquid behavior, unconventional superconductivity, multi-ferro and magnetoelectricity, nematic and related symmetry broken orders, spin/orbital liquids, spin charge separation, many body localization etc. have now been either well established or studied with an enormous assistance from computation. Many of these phenomena have been observed in materials such as high temperature superconductors, heavy fermion systems, one dimensional copper oxides, Vanadium and Iridium oxides, to name a few.

Over the last couple of decades, the evolution of diverse numerical techniques and the increased availability of computational muscle has brought an unprecedented level of possibilities to attack research problems in condensed matter physics. Among the class of stochastic methods, Quantum Monte Carlo (QMC) provides a very promising avenue to extract reliable ground state and thermodynamic information due to its exactness and ability to scale up calculations to large system sizes. Several flavors of QMC such as Diffusion MC, Variational MC, Path Integral MC and Cluster MC have made major inroads and have enabled better descriptions of the system's observable properties. However, QMC simulations suffer from the Fermionic sign problem and there have been considerable efforts to circumvent the issue. Density Matrix Renormalization Group (DMRG) provides an efficient representation of the ground state solution in terms of matrix product states for 1D/quasi-1D systems with local interactions. On the down side, DMRG works best only for one dimensional systems or systems that can be effectively reduced to one dimension. Other iterative approaches such as Dynamical Mean Field Theory (DMFT), Hierarchical MFT and Numerical Renormalization Group (NRG) have become popular but are seriously limited by the size of the clusters chosen. In certain cases, not all spatial correlations are present, and one needs to take special care in incorporating these effects especially when the correlation lengths are larger than the cluster sizes. Other variational methods like the use of Tensor networks, where one allows greater flexibility for optimization by a Hilbert space expansion, has aided greater accuracy in computing ground state properties.

A basic knowledge of these techniques, their capabilities, the class of problems they are most suited to solve, along with an appreciation of their advantages and limitations, is a crucial aspect that this Research Topic will address. Many researchers in different branches of condensed matter physics and statistical mechanics have little or no experience with each and every technique that has been listed here; therefore, a Research Topic section devoted to 'Frontiers of computational approaches to correlated matter' is highly called for. We hope that this effort will hugely benefit researchers who have novel ideas to attack outstanding physical problems, but lack the necessary expertise to quickly narrow down on what methods could best enable them to achieve their objectives.

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