What is LDA?

Dear Diary,

I learned about another way to use DFT today called the Local Density Approximation.

Normally quantum mechanics works by solving a Hamiltonian for a wave function and then determining all the properties from that wave function.  If you take the modulus of the wave function, you can find the density of the electrons in the system.

Now, Density Functional Theory relies on having the density and plugging that into something called a functional which takes a function (here, our density) to a number.  If you write down an approximation to a functional using only powers of the density (and not the derivatives), then you're using a Local Density Approximation (LDA).