Lieb-Schultz-Mattis Theorem in Higher Dimensions from Approximate Magnetic Translation Symmetry
Lieb-Schultz-Mattis Theorem in Higher Dimensions from Approximate Magnetic Translation Symmetry
We prove the Lieb-Schultz-Mattis (LSM) theorem on the energy spectrum of a general two or three-dimensional quantum many-body system with the U(1) particle number conservation and translation symmetry. Especially, it is demonstrated that the theorem holds in a system with long-range interactions. To this end, we introduce approximate magnetic translation …