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On this page we provide links and some details to open source code bases developed by members of the Pixley group.


Kernel Polynomial Method (KPM)

The KPM is a general approach to compute spectral properties of Hamiltonians that admit a sparse matrix representation. We have shared an easy to use package through our Github collaboration.


Kernel Polynomial Method combined with Wilson’s Numerical Renormalization Group (KPM+NRG)

The development of the KPM+NRG appeared in Phys. Rev. B 106, 165123 (2022) To describe quantum impurities in hosts that lack translational symmetry

Here we write the local density of states and the resulting hybridization function as a Chebyshev expansion and are able to analytically evaluate the Wilson chain coefficients. The code base to evaluate these coefficients using this KPM based expansion is given in the Github repo below


Nonlinear response

Here we provide the code base used to compute the circular photogalvanic effect (CPGE) in chiral Weyl semimetals as described in arXiv:2312.14244. While in principle the full second order tensor can be computed, here we focus on the second order response only of the CPGE.

Link: To appear after publication

Scaling collapse

The general application of the scaling hypothesis to critical phenomena underlies how we analyze data to draw universal conclusions. The estimate of critical exponents computed from the finite size scaling hypothesis applied to data obtained from finite size simulations is an essential part of this theoretical analysis. In this package we provide a general approach to obtaining an unbiased estimate of critical eponents.

Link: To Appear