Critical role of the sign structure in the doped Mott insulator: Luther-Emery versus Fermi-liquid-like state in quasi-one-dimensional ladders

The mechanism of superconductivity in a purely interacting electron system has been one of the most challenging issues in condensed matter physics. In the BCS theory, the Landau's Fermi liquid is the ground state of weakly interacting fermions dictated by the fermion sign structure, and the superconducting instability only occurs when an additional pairing force is added. By contrast, as shown by density matrix renormalization group calculation, a quasi-one-dimensional superconducting state (specifically a Luther-Emery state) is an intrinsic ground state of the t-J two-leg ladder and four-leg cylinder at finite doping. Such a Luther-Emery state with pairing can be directly turned into a Fermi-gas-like normal state without pairing by merely switching off the phase-string signs hidden in the model via two schemes, which reduce the sign structure to the trivial fermion signs associated with doped holes. It thus demonstrates a new pairing paradigm in a model-doped Mott insulator as due to the generic phase-string sign structure. Finally, as an example, the latter is explicitly shown to lead to a "stringlike" pairing force after adiabatically connecting to a strong anisotropic limit of the model.