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

TL;DR

This paper introduces a novel finite size numerical method that uses a 'grand canonical' approach to directly measure bulk properties under applied fields in one-dimensional quantum systems, avoiding fine tuning.

Contribution

The method employs energy scaling of edge sites to simulate a particle bath, enabling accurate response function calculations without parameter fine tuning.

Findings

Effective in quantum spin systems and Hubbard models

Allows direct measurement of bulk responses under external fields

Maintains numerical accuracy without parameter scaling

Abstract

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.