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

TL;DR

This paper identifies a new sign structure in the $t$-$t'$-$J$ model affecting doped Mott insulators, and shows that removing this structure leads to a trivial Fermi-liquid state, highlighting the importance of quantum entanglement in strong correlations.

Contribution

The study reveals a novel sign structure in the $t$-$t'$-$J$ model and demonstrates its crucial role in the emergence of superconductivity and stripe phases in doped Mott insulators.

Findings

Hole pairing exists in both superconducting and stripe phases.

Removing the phase-string sign structure results in a Fermi-liquid-like state.

The strong correlation effects are mainly due to long-range quantum entanglement.

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 $t$-$t'$-$J$ 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 $t$-$t'$-$J$ 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 $t$-$t'$-$J$ model where large Fermi surfaces can be restored in the stripe phase found at $t'/t<0$ or the superconducting phase at $t'/t>0$ 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.