Not exactly. I mean, in the US, as far as I know in all/most jurisdictions you don't get a different tax rate depending on whether the property is vacant or not. But in many places you can get a sizable property tax deduction for historic designated properties, sometimes equal to 100% of the value of the structure. Note that in the UK "listed building" means the property is registered as being historically significant, https://en.wikipedia.org/wiki/Listed_building.

That's pretty rare though, especially in the US. And generally afaik, historic listings here impose a cost on the homeowner but not a benefit (i.e. a tax break).