Sign structure of the $t$-$t^{\prime }$-$J$ model and its physical consequences

Abstract

Understanding the doped Mott insulator is a central challenge in condensed matter physics. In this work, we first explicitly identify a new sign structure in the $t$-$t^{\prime }$-$J$ model on the square lattice that replaces the conventional Fermi statistics for weakly interacting electrons. Then we show that the singular, i.e., the phase-string part of the sign structure in the partition function can be precisely turned off in a modified model. The density matrix renormalization group method is then employed to study these two models comparatively on finite-size systems, which is designed to unveil the consequences of the phase-string component. We find that the hole pairing is present not only in the quasi-long-range superconducting phase but also in the stripe phase of the $t$-$t^{\prime }$-$J$ model. However, once the phase-string is switched off, both the superconducting and stripe orders together with the underlying hole pairing disappear. The corresponding ground state reduces to a trivial Fermi-liquid-like state with small hole Fermi pockets that is decoupled from the antiferromagnetic spin background. It is in sharp contrast to the original $t$-$t^{\prime }$-$J$ model where large Fermi surfaces can be restored in the stripe phase found at $t^{\prime }/t<0$ or the superconducting phase at $t^{\prime }/t>0$ in the six-leg ladder calculation. Our study clearly demonstrates that the strong correlation effect in doped Mott insulator should be mainly attributed to the long-range quantum entanglement between the spin and charge, which is, non-perturbatively, beyond a simple spin-charge separation under the no double occupancy constraint.

19 pages, 16 figures

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Cited by in corpus (8)

• Global Phase Diagram of D-wave Superconductivity in the Square-Lattice $t\text{-}J$ Model
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Two-dopant origin of competing stripe and pair formation in Hubbard and $t$-$J$ models
• Electric transport in doped Mott insulators dictated by a non-Ioffe-Larkin composition rule and spinons
• Tuning competition between charge order and superconductivity in the square-lattice $t$-$t^{\prime }$-$J$ model
• Quantum colored strings in the hole-doped $t$-$J_z$ model
• Unveiling Stripe-shaped Charge Density Modulations in Doped Mott Insulators
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach