Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$ where $c^\dagger (c)$ are creation (annihilation) operators, $n$ is number operator, $t$ is hopping parameter, $V$ is nearest-neighbor interaction, $L$ is the total number of sites and $\mu$ is chemical potential.

What I understand by chemical potential is, if we set $μ=$some constant, then no matter how many sites ($L$) we add to the system, the number of particles will always be conserved. (Please correct me if I am wrong)

QUESTION: What is the relation between chemical potential and the number of particles? i.e. if I set $μ = 10$ then how many particles are allowed in the system?

Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$ where $c^\dagger (c)$ are creation (annihilation) operators, $n$ is number operator, $t$ is hopping parameter, $V$ is nearest-neighbor interaction, $L$ is the total number of sites and $\mu$ is chemical potential.

What I understand by chemical potential is, if we set $μ=$some constant, then no matter how many sites ($L$) we add to the system, the number of particles will always be conserved. (Please correct me if I am wrong)

QUESTION:

What is the relation between chemical potential and the number of particles? i.e. if I set $μ = 10$ then how many particles are allowed in the system?