Infrared quartz heaters are generally effective at heating a single room, similar to other space heaters. They are also reasonably energy-efficient, but many marketers overstate the energy savings they provide.
Infrared quartz heaters provide radiant heat, which is different than the convection heat that many space heaters use. Radiant heat warms objects and people near the heater instead of just heating the air, which can make these heaters very effective and efficient in the right circumstances. However, they can only heat things that are in a direct line with them, so they may not be as effective for larger rooms or if they need to be placed in a hidden area.
There is some evidence that quartz heaters reach a higher temperature than other radiant heaters, so they may be more effective. However, radiant heaters have to be hot on the outside to work, so they also may be a fire or burn hazard. They do tend to heat the area more quickly than other types of space heaters and can generally provide the same level of comfort with less heat.
Although many quartz heater manufacturers claim that they can cut a home's heating bill in half, these claims are probably exaggerated. It may be true for a few very limited circumstances, but most people see more modest savings if they see any at all.