Theoretical Solid State Physics

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Machine learning Schrieffer-Wolff transformation (SWT) and its applications

Schrieffer-Wolff transformation (SWT) [1] is a standard theoretical technique to derive a low-energy effective Hamiltonian from the original Hamiltonian of a given system. The SWT is approximative in that only the low-order terms, typically up to the second order, are considered. Thus the effective and original Hamiltonians may result in quantitatively (or even qualitatively) different behaviors at lowest temperatures. Recently, Rigo and Mitchell proposed a "machine learning" approach to the SWT, which optimizes the parameters for the effective Hamiltonian with respect to the cost function based on partition functions. They showed that their approach provides an effective Hamiltonian which accurately reproduces the low-energy behavior. This project aims at two goals:
(i) Implement the method of Rigo and Mitchell, and then (ii) apply this to develop a new Hilbert space truncation scheme in the numerical renormalization group (NRG) method.


[1] J. R. Schrieffer and P. A. Wolff, Phys. Rev. 149, 491 (1966).
[2] J. B. Rigo and A. K. Mitchell, <>