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I have some questions about the point density analysis in ArcGIS. I am interested to know the concept and formula about how to come out with all the break point values and ranges of the different colour bands for point density heatmap. I hope any of you can provide me a rough idea about the concept and the formula to use. I want to know the rough Value/Range I can get using the formula.

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You should check the How Hot Spot Analysis (Getis-Ord Gi*) works page of the ArcGIS online help for the formula. The symbology is based on the Gi_Bin field of the output feature class, see the Hot Spot Analysis (Getis-Ord Gi*) (Spatial Statistics) tool reference page.

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