Tensor Product State Approach to Strongly Correlated Systems: From Spin Liquid to Doped-Mott-Insulator
Landua's paradigm, as a foundation of traditional condensed matter physics builds up on two theories: symmetry breaking theory for phases and phase transitions, and Fermi liquid theory for metals. Both symmetry breaking theory and Feimi liquid theory build up on special classes of variational wave functions: the direct product states and the slater determinate states. However, in the last three decades, more and more evidences show such a paradigm fails for strongly correlated systems. A major reason is that new orders of matter, topological order will emergy in strongly correlated systems at low energy. The most famous example is the fractional quantum hall effect(FHQE). It is believed such kind of new orders exists in general strongly correlated systems, such as frustrated spin systems, electron systems with strong interactions. In this talk, I will introduce a new class of variational states: tensor product states. The unique advantage of these new states is that we can use a local tensor to describe both symmetry breaking order and topological order. The local tensor can be regarded as a natural generalization of the order parameters(complex numbers) in the symmetry breaking theory. Thus, the tensor product states provide us a unified variational approach to study both symmetry breaking and topologically ordered states. Finally, I will show some non-trivial applications for this new method in many interesting strongly correlated systems, such as square lattice J1-J2 model and honeycomb lattice Hubbard/t-J model.
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