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DTSTART;TZID=America/New_York:20220323T103000
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DTSTAMP:20260717T143942
CREATED:20240214T103754Z
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UID:10002677-1648031400-1648036800@cmsa.fas.harvard.edu
SUMMARY:Non-zero momentum requires long-range entanglement
DESCRIPTION:Youtube Video \n  \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/3-23-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.23.2022-1583x2048-1.png
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