Gap Estimation by means of Hyperbolic Deformation

Understand

We present a way of numerical gap estimation applicable for one-dimensional infinite uniform quantum systems.

• Using the density matrix renormalization group method for a non-uniform Hamiltonian, which has deformed interaction strength of $j$-th bond proportional to $\cosh \lambda j$, the uniform Hamiltonian is analyzed as a limit of $\lambda \to 0$.
• As a consequence of the deformation, an excited quasi-particle is weakly bounded around the center of the system, and kept away from the system boundary.
• Therefore, insensitivity of an estimated excitation gap of the deformed system to the boundary allows us to have the bulk excitation gap $\Delta(\lambda)$, and shift in $\Delta(\lambda)$ from $\Delta(0)$ is nearly linear in $\lambda$ when $\lambda \ll 1$.