Unavoidable Gapless Boundary State and Boundary Superfluidity of Trapped Bose Mott States in Two-Dimensional Optical Lattices

TL;DR

This paper demonstrates that trapped bosonic Mott insulators in two-dimensional optical lattices always feature a gapless boundary mode with superfluidity, regardless of boundary width, revealing fundamental boundary properties of these quantum states.

Contribution

It provides the first quantum Monte Carlo evidence that gapless boundary modes and superfluidity are intrinsic to trapped bosonic Mott insulators in optical lattices.

Findings

Finite superfluid density appears at the boundary regardless of boundary width.

Boundary correlation functions exhibit power-law decay below a certain temperature.

Gapless boundary modes are a universal feature of atomic Mott insulators.

Abstract

We study the boundary nature of trapped bosonic Mott insulators in optical square lattices, by performing quantum Monte Carlo simulation. We show that a finite superfluid density generally emerges in the incommensurate-filling (IC) boundary region around the bulk Mott state, irrespectively of the width of the IC region. Both off-diagonal and density correlation functions in the IC boundary region exhibit a nearly power-law decay. The power-law behavior and superfluidity are well developed below a characteristic temperature. These results indicate that a gapless boundary mode always emerges in any atomic Mott insulators on optical lattices. This further implies that if we consider a topological insulating state in Bose or Fermi atomic systems, its boundary possesses at least two gapless modes (or coupled modes) of an above IC edge state and the intrinsic topologically-protected edge state.