Competing Orders and non-Landau-Ginzburg-Wilson Criticality in (Bose) Mott transitions

TL;DR

This paper reviews a non-Landau-Ginzburg-Wilson approach to superfluid-Mott insulator transitions in 2D bosonic systems, emphasizing vortex duality, competing orders, and deconfined quantum criticality, challenging traditional criticality theories.

Contribution

It introduces a dual vortex field theory framework that unifies competing insulating orders and offers new insights into quantum criticality beyond LGW theory.

Findings

Re-examination of LGW theory and its limitations

Unification of competing orders via vortex duality

Connection to deconfined quantum criticality

Abstract

This paper reviews a recent non-Landau-Ginzburg-Wilson (LGW) approach to superfluid to Mott insulator transitions in two dimensional bosonic lattice systems, using a dual vortex field theory (cond-mat/0408329). The physical interpretation of conventional LGW theory of quantum criticality is re-examined and similarities and differences with the vortex picture are discussed. The ``unification'' of various competing (insulating) orders, and the coincidence of these orders with the Mott transition are readily understood in this formulation. Some aspects of the recent theory of ``deconfined'' quantum criticality, which are to an extent subsumed in this approach, are discussed. A pedagogical presentation of the ``nuts and bolts'' of boson-vortex duality at the hamiltonian level is included, tailored to a condensed matter audience.