Dual vortex theory of doped Mott insulators

TL;DR

This paper develops a comprehensive theoretical framework for understanding the quantum phases of doped Mott insulators on a square lattice, emphasizing the role of projective symmetry groups (PSG) in constraining the effective actions of excitations.

Contribution

It introduces a PSG-based approach to describe doped Mott insulators and extends the effective action framework across various quantum phase transitions.

Findings

Doped insulators share PSG with bosons at the same density as Cooper pairs.

The framework applies to transitions to supersolid or insulating states.

Analysis of the d-wave superconductor derived from a staggered-flux spin liquid.

Abstract

We present a general framework for describing the quantum phases obtained by doping paramagnetic Mott insulators on the square lattice. The undoped insulators are efficiently characterized by the projective transformations of various fields under the square lattice space group (the PSG). We show that the PSG also imposes powerful constraints on the doped system, and on the effective action for the vortex and Bogoliubov quasiparticle excitations of superconducting states. This action can also be extended across transitions to supersolid or insulating states at nonzero doping. For the case of a valence bond solid (VBS) insulator, we show that the doped system has the same PSG as that of elementary bosons with density equal to the density of electron Cooper pairs. We also discuss aspects of the action for a d-wave superconductor obtained by doping a ``staggered-flux'' spin liquid state.