I'm an archaeologist (or was?) who's specifically done work on the Neolithic transition. I don't know much about art history, so I couldn't say whether they'd use a similar definition.
What's often taught in introductory classes is usually more of a basic outline of actual archaeological thought rather than a perfect reflection of literature. Not knowing your curriculum, level, or when you were in school, but it probably came up with either Childe's 10 traits or from Trigger's definition. Childe's definition is basically anything that shows off power. Trigger's definition is anything that's elaborated beyond practical function, either in size or ornamentation. The common examples when teaching both of these are large structures, but that's mainly a bias in common examples. Size isn't the sole factor, just one of several and the easiest to observe because of the inherent labor costs. It also makes for a nice exercise to have students wander around campus looking for monumental architecture and explaining why different structures are or aren't.
Over the last 20ish years people have moved away from emphasizing the size aspect because it doesn't encompass what we want to include, particularly as we look at things a little more exotic than classical centers like southern Mesopotamia. Joyce Marcus had an explicit response to Trigger that's pretty well known de-emphasizing size, Rosemary Joyce (unrelated) argued that the size aspect was a category error in monumentality of early mesoamerican pyramid construction, and Osborne gave a definition that's very similar to what I said above. I'm doing the same thing here to make it clear that the actual physical size of the structure isn't what's important, the intangible mental aspects are.
I still don't understand your intangible mental aspects claim. That seems a nonphysical, and really nonscientific subjective evaluation. You didn't go back in time and interview the builders, so how do you know what the intangible mental aspects were? It's guesswork.
Physical size isn't necessary, and I didn't mean to clean that it was. The more fundamental connection would be labor expenditure, and directed organization. There's a bunch of old cities in the Levant that were occupied for thousands of years and which developed into very large beehive-like structures. These aren't monumental architecture in the way a smaller, but purpose-built temple or city walls would be.
The connection to 'civilization', as I understand it, is that a social organization beyond mere family units making incremental home improvements over generations is required to build monumental architecture, so it directly implies the existence of some form of societal structure to organize the work. That's what turns a 'culture' into a 'civilization.'
That seems a nonphysical, and really nonscientific subjective evaluation.
We're talking past each other a bit because we're referring to different things with our use of "monumental" though. I'm talking about monumental as a way of understanding how the structure was perceived and used by humans. You're using monumental as a way of understanding to the social organization of the society that constructed it. This is much more in line with Childe's use that I mentioned earlier.
Part of the problem is that the scale and sophistication of social organization associated with the classical mesopotamian states is not at all reflective of what would have been going on with Gobekli Tepe. In other words, we wouldn't traditionally call the GT builders a "civilization" (civilization being a bad word that makes archaeologists cry).
So let's go back to the scale and grandeur thing. If we have to understand the intention, that's one of the tangibles encapsulated in my definition. What I'm saying is that it's the mental relationship between the human, the structure and the context that gives rise to monumentality. The physical structure can facilitate that creation by intentional design (e.g. large imposing size, etc), but it can also arise naturally or change over time.
We don't actually understand enough of the ancient world to definitively establish monumentality everywhere because our understanding of those intangibles is so patchy. The tower of Jericho was thought to be monumental for many years because of the obvious size and labor investment it represents. The thinking nowadays is that it had more utilitarian purposes and probably wasn't monumental. The structure is the same either way, the only thing that's changed there is our understanding of how ancient people would have engaged with it.