Sign structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mtext>−</mml:mtext> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> <mml:mtext>−</mml:mtext> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> </mml:math> model and its physical consequences
Xin Lu, Jiaxin Zhang, Shou-Shu Gong, D. N. Sheng, Zheng-Yu Weng
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 $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ 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 $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ 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 $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model where large Fermi surfaces can be restored in the stripe phase found at ${t}^{\ensuremath{'}}/t<0$ or the superconducting phase at ${t}^{\ensuremath{'}}/t>0$ 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, nonperturbatively, beyond a simple spin-charge separation under the no double occupancy constraint.