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One of the most important implications of symmetry in a physical system is the existence of conservation laws, which holds irrespective of whether the theory is local or not. On the other hand, while locality leads to the Lieb-Robinson bound on the propagation speed of information, it does not impose any conservation laws without symmetry. Therefore, it is very natural and interesting to ask, in the presence of symmetry, does locality lead to any new conservation laws? Surprisingly, the answer is yes, as demonstrated in our work 2105.12877, which shows that indeed new conservation laws arise in systems with 2-local interactions and SU(d) symmetry for d≥3. In this talk, I will explain how these new conservation laws arise and show some examples.
I did my undergrad at Nanjing University and currently pursuing PhD study at Duke University focusing on quantum critical phenomena and quantum information theory.