# TurboRVB and the legacy of P. W. Anderson

Two months ago P.W. Anderson died, one of the greatest physicists of the past century[1]. Anderson made contributions in different subjects of physics from electron-localization, that earned him the Nobel Prize in 1977, to anti-ferromagnetism, high-Tc superconductivity and symmetry breaking, that years later will inspire the Higgs mechanism in particle physics.

Among all his contributions we want to remember the Resonant Valence Bond (RVB) theory to explain high-Tc superconductivity. In this theory the ground state wave-function is written as a superposition of resonant states in lattice Hamiltonian. This wave-function found many application in spin-liquids and frustrated magnets. In our work, we extended the application of this wave-function to real-space space Hamiltonians, in particular to molecular systems and periodic solids. This wave-function is implemented in a very efficient code TurboRVB[2], and we released this month. In molecular systems, this wave-function has a structure similar to the valence bond theory proposed by L. Pauling in 1987[3]. It can be expressed as a single determinant of electron-pairs and evaluated in an efficient way by means of stochastic approaches. TurboRVB implements RVB wave-function and its extensions to polarized systems, triplet states. The code includes also different Jastrow factors to deal with double occupations and Van-der Waals interaction. All these wave-function can be evaluated within Variation-Monte Carlo or with Diffusion Monte Carlo that includes also a lattice regularization to deal with non-local pseudo-potentials. For more detail on the code see Ref. [2].

References:

[1] P. W. Anderson on Wiki

[2] TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo J. Chem. Phys. 152, 204121 (2020), https://arxiv.org/abs/2002.07401

[3] L. Pauling on Wiki