Seminarium Fizyki Materii Skondensowanej
sala 1.02, ul. Pasteura 5
2026-05-29 (12:15) 
Jędrzej Wardyn (IFT FUW)
Systematic construction of exact valence bond ground state Hamiltonians
The usual method of investigating quantum systems starts with some Hamiltonian for which we identify the ground state, correlations, and more.What if instead, we approached the same problem in reverse?Can we systematically construct Hamiltonians with exactly solvable ground states?
We consider the dimer ground state present in the Majumdar-Ghosh (MG) model, a special case of the Heisenberg chain with the antiferromagnetic nearest neighbor J_1>0 and next-to-nearest neighbor J_2>0 interactions, where J_2/J_1=1/2.
In our work using analytical, ED, and DMRG methods, we show that the dimer ground state is supported in a large class of Hamiltonians: models with arbitrarily long-distance interactions, with broken translational invariance, as well as with XXZ or XYZ anisotropies.
Studying this class of systems lays the groundwork for understanding novel magnetic materials as well as quantum information systems realized with valence bond states.
We consider the dimer ground state present in the Majumdar-Ghosh (MG) model, a special case of the Heisenberg chain with the antiferromagnetic nearest neighbor J_1>0 and next-to-nearest neighbor J_2>0 interactions, where J_2/J_1=1/2.
In our work using analytical, ED, and DMRG methods, we show that the dimer ground state is supported in a large class of Hamiltonians: models with arbitrarily long-distance interactions, with broken translational invariance, as well as with XXZ or XYZ anisotropies.
Studying this class of systems lays the groundwork for understanding novel magnetic materials as well as quantum information systems realized with valence bond states.