VENUE APCTP HQ, Pohang & Online via ZOOM
PERIOD Oct. 14 (Wed.), 2020 / 16:00 (KST)
ZOOM LINK https://zoom.us/meeting/register/tJcpc-qqzMpGtOBaCBYQ3oV7yULDvLC4Rlk
ABSTRACT
Our group has been exploring the idea of writing down variational wave functions for spin-½ and spin-1 Heisenberg chains in the framework of matrix product states (MPS). The ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) is famously known to have a very simple MPS form with the bond dimension (matrix dimension) of two. The ground state of the pure spin-1 Heisenberg model is not exactly known. Using the variation MPS (vMPS) approach, we were able to find nearly exact ground state for the bilinear-biquadratic spin-1 model in the so-called Haldane phase, encompassing both the AKLT and the Heisenberg models as special cases. The strategy for deriving such vMPS is then applied to the more challenging task of writing down the ground state of the spin-½ Heisenberg model. Our approach differs dramatically from the century-old tactic of Bethe ansatz, and starts from the well-known ground state of the Majumdar-Ghosh (MG) Hamiltonian. By proliferating the MG state with various long-ranged dimers in a manner consistent with the resonating valence bond (RVB) picture and writing down MPS tensor accordingly, we could show that a vMPS state with excellent energetics and entanglement properties can indeed be derived. This confirms the picture of the gapless ground state of the spin-½ chain as an example of RVB. Spinon spectrum can be worked out with a slight modification of our vMPS tensor, in good agreement with exact results.
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APCTP