Hidden supersymmetry in the Fateev-Zamolodchikov spin chain

by Chihiro Matsui (The University of Tokyo)

Tuesday 6 Jun 2017, 13:30 → 14:30 Asia/Tokyo

Room 433, Main Research Building (RIKEN Wako)

Date: June 6 (Tue) Time: 13:30 - Place: Main Research bldg. 433 Speaker: Chihiro Matsui (The University of Tokyo) Title: Hidden supersymmetry in the Fateev-Zamolodchikov spin chain Abstract: The low-energy regime of a massless quantum spin chain is described by a quantum field theory (QFT). The derivation of the corresponding QFT from the spin chain is often achieved by utilizing the bosonization. Inversely, the corresponding spin chain is obtained from the QFT through the discretization of the Minkowski space-time called “the light-cone lattice regularization”. What is interesting is that the supersymmetric QFT sometimes arises from the non-supersymmetric spin chain. This fact motivates us to study whether the hidden supersymmetry exists behind the non-supersymmetric spin chains. Yang and Fendley introduced the discrete analog of the supersymmetry on the non-supersymmetric integrable spin chains [1]. Since the supercharges exchange a boson and a fermion, they defined the supercharges in such a way that change the length of the spin chain [1-3]. In the talk, I discuss how the discrete analog of the supersymmetry is connected to the conventional supersymmetry via the spinon basis of the spin chain. As an illustration, by focusing on the correspondence between the Fateev-Zamolodchikov spin chain and the supersymmetric sine-Gordon model, I show that the length-change action of the supercharge is essential to connect the non-supersymmetric spin chain to the supersymmetric QFT [4]. References: [1] X. Yang and P. Fendley, “Non-local spacetime supersymmetry on the lattice”, J. Phys. A: Math. Gen., 37:8937–8948, 2004. [2] C. Hagendorf and P. Fendley, “The eight-vertex model and lattice supersymmetry”, J. Stat. Phys., 146:1122–1155, 2012. [3] C. Hagendorf, “Spin chains with dynamical lattice supersymmetry”, J. Stat. Phys., 150:609–657, 2013. [4] C. Matsui, “Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry”, Nucl. Phys. B913:15–33, 2016. QHP seminars