controlling particle number of independent species
Posted: 25 Sep 2024, 16:07
I got the following question by email:
I encountered some difficulties when setting conserved quantities. I filled two types of bosons in a two-dimensional bosonsite, and I want to control the filling numbers for each boson. Usually, I control the filling number by controlling their chemical potential, for example, for a two-dimensional bosonsite with Lx=20 and Ly=4, the upper part with Lx=20 and Ly=2 is set to chemical potential \(\mu_{up}\), and the other part is set to \(\mu_{down}\).
However, controlling the filling through chemical potential is always inconvenient. The spinhalf model in the fermion system can directly achieve different fillings between different fermions through Sz conservation. But the boson system in the two-dimensional bosonsite is difficult to transform to spinhalf model through the Jordan Wigner transformation. So I want to ask if there are any good ways to control the filling number of different bosons separately or set their corresponding particle number conservation, and if you could help me?
I encountered some difficulties when setting conserved quantities. I filled two types of bosons in a two-dimensional bosonsite, and I want to control the filling numbers for each boson. Usually, I control the filling number by controlling their chemical potential, for example, for a two-dimensional bosonsite with Lx=20 and Ly=4, the upper part with Lx=20 and Ly=2 is set to chemical potential \(\mu_{up}\), and the other part is set to \(\mu_{down}\).
However, controlling the filling through chemical potential is always inconvenient. The spinhalf model in the fermion system can directly achieve different fillings between different fermions through Sz conservation. But the boson system in the two-dimensional bosonsite is difficult to transform to spinhalf model through the Jordan Wigner transformation. So I want to ask if there are any good ways to control the filling number of different bosons separately or set their corresponding particle number conservation, and if you could help me?