Abstract
How the ground state nature can be dramatically changed by the distinct underlying spin correlation is a central issue of doped Mott insulators. The two-leg XXZ ladder provides a prototypical spin background, which can be tuned from a long-range N\'{e}el order to a short-range ``spin liquid'' via the superexchange anisotropy, giving rise to a complex phase diagram at finite doping. By density matrix renormalization group method, we show that although the charge is always self-localized in the N\'{e}el ordered phase, a second insulating phase emerges, in which the doped holes become paired but remain localized while the transverse spin-spin correlation reduces to short-ranged one to make the N\'{e}el order classical. Only when the N\'{e}el order totally disappears by further reducing anisotropy, does the pairing become truly coherent as characterized by a Luther-Emery state. In sharp contrast, the pairing is totally absent in the in-plane ferromagnetic XXZ regime, where a direct transition from the charge self-localization in the N\'{e}el ordered phase to a Fermi-gas-like state in the spin liquid phase is found. A consistent physical picture is briefly discussed.
Highlights
As one of the simplest models describing the doped Mott insulator, the t-J model has attracted intense attention due to its potential to characterize systematically a complex phase diagram composed of a long-range Néel state, pseudogap, and superconducting (SC) states, etc., as a function of doping [1]
Such a model can be accurately investigated by density matrix renormalization group (DMRG) method [2] in quasione-dimensional (1D) square lattice cases, which do exhibit quasi-1D SC behavior [3,4,5,6,7] known as the Luther-Emery (LE) state, characterized by an exponential decay of spin correlations and power-law decays of SC and charge density wave (CDW) correlations [6,8,9]
Given the same resonance valence bond (RVB) or gapped spin background, the LE ground state can be replaced by a Luttinger-liquid-like state with the exponent very close to that of the free Fermi gas (FG) [6] at finite doping, if the hopping term is modified to result in the so-called σ · t-J ladders [15,16]
Summary
As one of the simplest models describing the doped Mott insulator, the t-J model has attracted intense attention due to its potential to characterize systematically a complex phase diagram composed of a long-range Néel state, pseudogap, and superconducting (SC) states, etc., as a function of doping [1]. Given the same RVB or gapped spin background, the LE ground state can be replaced by a Luttinger-liquid-like state with the exponent very close to that of the free Fermi gas (FG) [6] at finite doping, if the hopping term is modified to result in the so-called σ · t-J ladders [15,16]. Top panel at > 0, two insulating phases separated by a solid line: CL/SDW I denotes the charge localization with an SDW of wavelength λSDW = 1/δ, while LPP/SDW II refers to the lower pseudogap phase with an SDW of wavelength λSDW = 2/δ The latter is further separated from a quasi-1D SC (LE) phase at > c2 by a dashed vertical line; Bottom panel at < 0: CL/SDW I persists to c3 (dashed vertical line) to reduce to a Luttinger liquid phase in the Fermi gas limit.
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