"Grand Canonical" Finite Size Numerical Approaches : a Route to Measuring Bulk Properties under Applied Field

We exploit a prescription to observe directly the physical properties of the thermodynamic limit under continuously applied field in one-dimensional quantum finite lattice systems. By systematically scaling down the energy of the Hamiltonian of the open system from center toward both ends, one could adopt the edge sites with negligibly small energy scale as a "grand canonical" small particle bath, and an equilibrium states with non-integer arbitrary conserved numbers, e.g., electron numbers or sz, are realized in the main part of the system. This will enable the evaluation of the response functions under continuously varying external field in a small lattice without any fine tuning or scaling of parameters while keeping the standard numerical accuracy. Demonstrations are given on quantum spin systems as well as on a Hubbard model by the density matrix renormalization group calculation.