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Institute for Condensed Matter Theory Seminar: Momentum creates long-range entanglement and quantum anomalies

Event Type
The Institute for Condensed Matter Theory
190 ESB
Sep 26, 2022   12:00 pm  
Lei Gioia Yang, Perimeter Institute
Janice K Benner
Originating Calendar
Physics - Institute for Condensed Matter Theory Seminar

In this talk, I will show how crystalline momentum holds a deep connection to quantum entanglement and quantum anomalies. First I will demonstrate that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero crystalline momentum [1]. The statement can also be generalized to fermion systems, and all dimensions. I will present several non-trivial consequences that follow from our theorem:

          • Several different types of Lieb-Schultz-Mattis-Oshikawa-Hastings theorems, including a previously unknown version involving only a discrete symmetry;

             • 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;

             • Quantum anomalies associated to momentum are described by a Chern-Simons term that emerges in physical systems such as the time-reversal invariant Weyl semimetals [2].

 I conclude by presenting some potential generalisations of this statement, and work that remains to be done especially regarding the possible roles of momentum in emergent symmetries.

[1] Lei Gioia, Chong Wang, Phys. Rev. X 12, 031007 (2022)

[2] Lei Gioia, Chong Wang, A. A. Burkov, Phys. Rev. R 3, 043067 (2021)

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