4.5. Phase diagram of the hardcore boson model on a trianglar lattice¶
Finally, let us consider a zero-temperature phase diagram of the hardcore boson model on a trianglar lattice. The Hamiltonian of this model is given as
where
To perform calculation for this system, the user can use toml files named basic.toml
, nn_obs.toml
and a python script file run.py
in the direction sample/05_hardcore_boson_triangular
.
Here, basic.toml
specifies the model and its parameters.
This file is almost the same as the triangular Heisenberg model described in the previous section and differs from it only in the section model
in the last part, where the line type = "boson"
specifies the hardcore boson model and t = 0.1
, V = 1
determines the strength of the hopping and nearest-neighbor interaction.
To calculate the structure factor tenes_simple
, users should define them by themselves.
nn_obs.toml
specifies them for std__XXX_YYY.toml
in run.py
.
For larger unitcell, the computational cost increases, and hence the calculatation of the structure factor gets difficult.
On the other hand, TeNeS can calculate the correlation functions along the x and y directions (in the square lattice iTPS) at a low cost.
Structure factor can be calculated using these correlation functions.
Additionally, the Fourier transform of the density operator
Let us execute calculation using the script run.py
.
After setting of the paths, execute calculation by typing the following command:
python run.py
The calculation will finish within several minutes or several tens of minutes.
After the calculation, start gnuplot
and execute the following command:
load 'plot.gp'
Then, we obtain a graph as shown in Fig. 4.7.
run.py
, we can perform more accurate calculation at the expense of execution time.
From these figures, we find that there exists three phases for the ground state, i.e., (a) a superfluid phase (

Fig. 4.7 Phase diagram of the hardcore boson model on a triangular lattice. Inset shows a particle pattern in a solid phase.¶
Reference
[Wessel] S. Wessel, M. Troyer, Supersolid hard-core bosonson the triangular lattice, Phys. Rev. Lett. 95, 127205 (2005). link.