Featureless Mott Insulators

TL;DR

This paper constructs a family of pair hopping models in various dimensions that exhibit incompressible quantum liquids at fractional fillings, demonstrating their unique ground states and finite excitation energies.

Contribution

It introduces new lattice models with a novel symmetry and rigorously proves the uniqueness of their ground states across different dimensions.

Findings

Ground states are unique under open boundary conditions.

Models exhibit finite excitation energy.

Constructs generalized lattices like tetrahedral in 3D.

Abstract

A family of the pair hopping models exhibiting the incompressible quantum liquid at fractional filling $1/m^D$ is constructed in $D$ dimensional lattice. Except in one dimension, the lattice is the generalized edge-shared triangular lattice, for example the triangular lattice in two dimensions and tetrahedral lattice in three dimensions. They obey the new symmetry, conservation of the center-of-mass position proposed by Seidel et al..\cite{Seidel2005} The uniqueness of the ground state is proved rigorously in the open boundary condition. The finiteness of the excitation energy is calculated by the single mode approximation.