Client FPS drops to 0 in certain areas

My client is lagging and becoming unplayable in certain areas underground around caves. During the lag FPS and Chunk Updates drops to 0 and Tick task is taking up to 70% of game CPU time (while normally taking around 7%). Javaw process itself is sometimes marked as "not responding" by Windows.

It happens on the same map in the same place on both singleplayer modes and multiplayer (when I move world to the server).

The screenshot itself doesn't show 0 FPS but the moment right after the lag spike (increased game tick cpu time is visible on profiling chart)

Edit: I have uploaded the faulty world there - https://dl.dropboxusercontent.com/u/32145655/world.zip