Speaker

Dr. Tsutomu Momoi / Condensed Matter Theory Laboratory, RIKEN

Title

Numerical Approaches to Low-Energy Effective Hamiltonians in Many-Body Systems: Applications to Spin Excitations

Abstract

Low-energy states in many-body systems are confined to a specific subspace of the Hilbert space, where the low-energy effective Hamiltonian is defined. The derivation of this effective Hamiltonian involves block-diagonalizing the Hilbert space to isolate this subspace. A widely used technique for block-diagonalization is perturbative expansion, which iteratively block-diagonalizes at each order of the perturbation parameter. However, this method becomes unstable in parameter regimes where the perturbative expansion fails to converge. This limitation necessitates the development of non-perturbative approaches for deriving effective Hamiltonians. We present a numerical block-diagonalization method for deriving effective Hamiltonians and demonstrate its application. This approach is particularly advantageous for systems with an open energy gap and provides a versatile framework. As an example, we analyze spin excitations in spin systems to illustrate the effectiveness of this method.

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Meeting ID: 934 3647 7810

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