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

- Event Type
- Seminar/Symposium
- Sponsor
- The Institute for Condensed Matter Theory
- Location
- 190 ESB
- Date
- Sep 26, 2022 12:00 pm
- Speaker
- Lei Gioia Yang, Perimeter Institute
- Contact
- Janice K Benner
- jbenner@illinois.edu
- Views
- 93
- 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)