Tensor networks meet quantum field theory: first steps
Date : November 2, 2022 16:00 ~
Speaker : 이승섭 (서울대학교 물리천문학부)
Professor : Prof. Dohun Kim, Prof. Sunghoon Jung
Location : 56동105호 +온라인 중계 (코로나 방역 상황에 따라 변동 가능)
The quantum many-body problem is usually approached from one of two perspectives: the first is based on correlation functions represented by Feynman diagrams, and the second deals with quantum states and operators. Tensor network (TN) methods in the latter category rank among the most successful theories, as they are the gold standards in solving quantum impurity problems and one-dimensional systems. Despite various successes of the TN methods as well as so-called (Feynman) diagrammatic methods from the former category, two-dimensional strongly correlated lattices, such as the models of high-temperature superconductors, remain unsolved; all these approaches encounter obstacles, originating from their intrinsic shortcomings. Interestingly, many of the pros and cons of the TN methods and those of the diagrammatics are complementary. In this talk, I will explain our first steps towards combining the TN and diagrammatic approaches, in which one's weakness is supplemented with the other's strength. One step is the derivation of "spectral representations," which represent generic correlation functions in terms of quantum states and operators ; and the other is the development of a TN method for correlation functions, whose accuracy and availability go beyond the reach of the other state-of-the-art approaches . I will conclude the talk with a brief mention of the current status of this "TNs meet quantum field theory" agenda.
 F. B. Kugler*, S.-S. B. Lee*, and J. von Delft, Phys. Rev. X 11, 041006 (2021). (*: equal contribution)
 S.-S. B. Lee, F. B. Kugler, and J. von Delft, Phys. Rev. X 11, 041007 (2021).