Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting $\text{SU}\left(2N\right)$ Dirac fermions

We investigate the $\mathrm{SU}\left(2N\right)$ symmetry effects with $2N>2$ on the two-dimensional interacting Dirac fermions at finite temperatures, including the valence-bond-solid transition, the Pomeranchuk effect, the compressibility, and the uniform spin susceptibility, by performing the determinant quantum Monte Carlo simulations of the half-filled $\mathrm{SU}\left(2N\right)$ Hubbard model on a honeycomb lattice. The columnar valence-bond-solid (cVBS) phase only breaks the threefold discrete symmetry and thus can survive at finite temperatures. The disordered phase in the weak coupling regime is the thermal Dirac semi-metal state, while in the strong coupling regime it is largely a Mott state in which the cVBS order is thermally melted. The calculated entropy-temperature relations for various values of the Hubbard interaction $U$ show that the Pomeranchuk effect occurs when the specific entropy is below a characteristic value of $S^{*}$—the maximal entropy per particle from the spin channel of local moments. The $\mathrm{SU}\left(2N\right)$ symmetry enhances the Pomeranchuk effect, which facilitates the interaction-induced adiabatic cooling. Our work sheds light on future explorations of novel states of matter with ultracold large-spin alkaline fermions.

Figure 1

The cVBS (a) and pVBS (b) configurations break the threefold discrete symmetry and exhibit a $\sqrt{3}\times \sqrt{3}$ superunit cell. (This figure is taken from Ref. [16].)

Figure 2

Finite-size scalings of the VBS dimer parameter $|D_K|$ for the half-filled $\mathrm{SU}\left(6\right)$ Hubbard model at different values of $U$ and $\beta$ close to the phase boundary: (a) $\beta =10$ with different values of $U$; (b) $\beta =17$ with different values of $U$; (c) $U=12$ with different $\beta$; (d) $U=14$ with different $\beta$. The linear fitting is used starting from $L=9$, and error bars are smaller than data points.

Figure 3

Finite-size scalings of $W\left(L\right)$ for the half-filled $\mathrm{SU}\left(6\right)$ Hubbard model at $U/t=12$ with different values of the inverse temperature $\beta$.

Figure 4

The finite-temperature phase diagram of the half-filled SU(6) Hubbard model on a honeycomb lattice. The black and the blue lines represent the upper and lower boundaries of the transition temperatures determined by the DQMC simulations. The zero-temperature results are extracted from Ref. [16]. With denser $U$ and $T$, the two boundaries should merge into one. The red dashed line represents the isoentropy curve of $S_{SU\left(6\right)}=0.1$.

Figure 5

The entropy per particle as a function of $T$ at different values of $U$ in (a) $\mathrm{SU}\left(4\right)$ and (b) $\mathrm{SU}\left(6\right)$ Hubbard models. Note that the $S-T$ curve for $U=0$ is calculated in Appendix pp1. The lattice size is $L=9$.

Figure 6

$D$ as a function of temperature $T$ for (a) $\mathrm{SU}\left(4\right)$ and (b) $\mathrm{SU}\left(6\right)$ Hubbard models at half filling. The system size is $L=9$. Error bars are smaller than the data points.

Figure 7

The probability distributions $P\left(n\right)$ of the on-site particle numbers (a) $P\left(2\right)$, (b) $P\left(1\right)$, and (c) $P\left(0\right)$ versus entropy $S$ at different values of $U$ in the half-filled $\mathrm{SU}\left(4\right)$ Hubbard model. The lattice size is $L=9$. The lines serve as a guide to the eye, and error bars are smaller than the data points.

Figure 8

The density compressibility $\kappa$ versus $T$ at various values of $U$ in the half-filled (a) SU(4) and (b) SU(6) Hubbard models. The lattice size is $L=9$.

Figure 9

The uniform spin susceptibilities $\chi$ versus temperature $T$ at various values of $U$ in the half-filled (a) $\mathrm{SU}\left(4\right)$ and (b) $\mathrm{SU}\left(6\right)$ Hubbard models. The lattice size is $L=9$. Error bars are smaller than the data points.

Figure 10

The finite-size dependence of entropy per particle of the half-filled SU(6) Hubbard model with parameters (a) $U=0$, (b) $U=6$, and (c) $U=12$.

Figure 11

The imaginary part of compressibility $\mathrm{Im}\left(\kappa \right)$ versus $T$ with different $U$ and $2N$: (a) $\mathrm{SU}\left(4\right)$ case with different $U$; (b) $\mathrm{SU}\left(6\right)$ case with different $U$; (c) $\mathrm{SU}(6)$ case with $U=4$; (d) $\mathrm{SU}\left(6\right)$ case with $U=12$.

Figure 12

The average sign as a function of $T$ for various chemical potentials at (a) $U=12$ and (b) $U=14$ in the $\mathrm{SU}\left(6\right)$ Hubbard model on a honeycomb lattice with $L=9$. Error bars are smaller than the data points.

Figure 13

The AF structure factors $S_{AF}$ versus temperature $T$ at various values of $U$ in the half-filled (a) $\mathrm{SU}\left(4\right)$ and (b) $\mathrm{SU}\left(6\right)$ Hubbard models. The lattice size is $L=9$. Error bars are smaller than the data points.

Figure 14

The AF structure factor $S_{AF}$ of the $\mathrm{SU}\left(6\right)$ Hubbard model with $U=14$ is plotted as a function of $\beta$ for different lattice sizes $L$. The dashed lines serve as a guide to the eye, and error bars are smaller than the data points.

Figure 15

The nearest-neighbor spin-spin correlation $S_{nn}$ versus temperature $T$ at various values of $U$ in the half-filled (a) $\mathrm{SU}\left(4\right)$ and (b) $\mathrm{SU}\left(6\right)$ Hubbard models. The lattice size is $L=9$. Error bars are smaller than the data points.