# Agenda

# Tuesday 12 September 2017

### The extended Bose-Hubbard model in 1D: new results to an old problem

#### B. Grémaud (LKB, ENS Paris et UMI MajuLab Singapour)

### Orateur :

B. Grémaud (LKB, ENS Paris et UMI MajuLab Singapour)

### Titre :

The extended Bose-Hubbard model in 1D: new results to an old problem

### Résumé :

In a first part, I will present the phase diagram of the one-dimensional bosonic Hubbard model with contact ($U$) and near neighbor ($V$) interactions: (i) reviewing the well-known phases, such as the Mott insulating phase, the Haldane insulating phase and the charge density wave (ii) discuss new phases, in particular the supersolid (SS) phase, .i.e, depicting both a diagonal long range order and an off-diagonal (quasi-) long range order. In addition, I will show that, at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane. Our results have been obtained with the Stochastic Green Function quantum Monte Carlo algorithm as well as the density matrix renormalization group.

In a second part, I will present the excitation spectrum above the ground state in different phases, obtained with the time evolving block decimation method. At unit filling, I will discuss the properties of the structure factor across the Mott insulating phase, the Haldane insulating phase and the charge density wave phase. In the supersolid phase appearing by doping the charge density wave phase, I’ll show that the structure factor depicts additional gapless modes at a finite momentum that depends on the density. This feature and the low energy spectrum can be explained by a mapping of the system onto the Heisenberg model for a spin 1/2 chain in a finite magnetic field.