I have read that carrots prefer an acidic soil, and that this is why they are so good at removing iron from your body. I have a carrot patch in my garden, and I don't fertilize it with anything. The soil is clayey, but also has a lot of sand mixed in.
The pH of the soil has some effect on how many carrots a plant will produce. Carrots prefer a pH that's somewhere between 6 and 7.
However, it is also true that carrots are very sensitive to changes in soil pH.