My Random Walks in Anderson's Garden

TL;DR

This paper narrates the author's journey with Anderson's garden metaphor, detailing contributions to RVB theory of high-temperature superconductivity and quantum spin liquids, and extending the theory to recent high Tc superconductors.

Contribution

The paper presents a personal account of developing RVB theory for quantum spin liquids, emergent Fermi surfaces, and high Tc superconductivity, including recent extensions to H2S.

Findings

First RVB mean field theory for quantum spin liquids

Prediction of superconducting dome in cuprates

Extension of RVB theory to high-pressure H2S superconductivity

Abstract

Anderson's Garden is a drawing presented to Philip W. Anderson on the eve of his 60th birthday celebration, in 1983. This cartoon (Fig. 1), whose author is unknown, succinctly depicts some of Anderson's pre-1983 works, as a blooming garden. As an avid reader of Anderson's papers, random walk in Anderson's garden had become a part of my routine since graduate school days. This was of immense help and prepared me for a wonderful collaboration with the gardener himself, on the resonating valence bond (RVB) theory of High Tc cuprates and quantum spin liquids, at Princeton. The result was bountiful - the first (RVB mean field) theory for i) quantum spin liquids, ii) emergent fermi surfaces in Mott insulators and iii) superconductivity in doped Mott insulators. Beyond mean field theory - i) emergent gauge fields, ii) Ginzbuerg Landau theory with RVB gauge fields, iii) prediction of superconducting dome, iv) an early identification and study of a non-fermi liquid normal state of cuprates and so on. Here I narrate this story, years of my gardening attempts and end with a brief summary of my theoretical efforts to extend RVB theory of superconductivity to encompass the recently observed very high Tc ~ 203 K superconductivity in molecular solid H2S at high pressures ~ 200 GPa.