Loading Events

Non-zero momentum requires long-range entanglement

CMSA EVENTS: CMSA QUANTUM MATTER IN MATH & PHYSICS SEMINAR

When: March 23, 2022
10:30 am - 12:00 pm
Where: Virtually

I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.


For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/