Incipient Order in the $t\mathrm{\text{−}}J$ Model at High Temperatures

We analyze the high-temperature behavior of the susceptibilities towards a number of possible ordered states in the $t$-$J$-$V$ model using the high-temperature series expansion. From all diagrams with up to ten edges, reliable results are obtained down to temperatures of order $J$, or (with some optimism) to $J/2$. In the unphysical regime, $t<J$, large superconducting susceptibilities are found which, moreover, increase with decreasing temperatures, but for $t>J$, these susceptibilities are small and decreasing with decreasing temperature; this suggests that the $t$-$J$ model does not support high-temperature superconductivity. We also find modest evidence of a tendency toward nematic and $d$-density wave orders.

Figure 1

AF susceptibility vs temperature for $t=J/2$ (dashes, $x=1\%$, $16\%$, $31\%$) and $t=2J$ (dot-dash, $x=1\%$, $6\%$) from the HTS to $1/T^{11}$ (diagrams with $N_E\le 10$). Shading represents the standard deviation of nondefective Padé approximants as discussed in text.

Figure 2

Superconducting ($d$-wave) susceptibility ${\chi }_{d\mathrm{-}\mathrm{S}\mathrm{C}}$ for $t=J/2$ with $V=0$ (dashes) and $V=J/4$ (dot-dash) from the HTS to $1/T^9$ (diagrams with $N_E\le 10$). Shading as in Fig. 1. Pairing fluctuations are strong at $V=0$, but are strongly suppressed already at $V=J/4$.

Figure 3

Same as Fig. 2 for $t=2J$. Pairing fluctuations are weak already at $V=0$ (dashes), and decrease further with introduction of weak NN repulsion (dot-dash).

Figure 4

Staggered-flux susceptibility ${\chi }_{d\mathrm{-}\mathrm{D}\mathrm{W}}$ for $t=2J$, at $V=0$ (dashes) and $V=J/4$ (dot-dash) obtained from HTS to $1/T^9$ ($N_E\le 10$). Shading as in Fig. 1.

Figure 5

Nematic susceptibility ${\chi }_{\mathrm{N}}$ for $t=2J$ and $V=0$ (dashes) and $V=J/4$ (dot-dash) obtained from HTS to $1/T^9$ ($N_E\le 10$). Shading as in Fig. 1. The NN repulsion term $V$ has virtually no effect on ${\chi }_{\mathrm{N}}$.