We investigate the
SU(2N) 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
SU(2N) 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
SU(2N) 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.
We study generalizations of the singlet-sector amplitude-product (AP) states in the valence-bond basis of
S=1/2 quantum spin systems. In the standard AP states, the weight of a tiling of the system into valence bonds (singlets of two spins) is a product of amplitudes depending on the length of the bonds. We here introduce correlated AP (CAP) states, in which the AP is further multiplied by factors depending on two bonds connected to a pair of sites (here nearest neighbors). While the standard AP states can describe a phase transition between an antiferromagnetic (N\'eel) state and a valence-bond solid (VBS) in one dimension (which we also study here), in two dimensions it cannot describe VBS order. With the CAP states, N\'eel-VBS transitions are realized as a function of some parameter describing the bond correlations. We here study such phase transitions of CAP wave functions on the square lattice. We find examples of direct first-order N\'eel-VBS transitions, as well as cases where there is an extended U(1) spin liquid phase intervening between the N\'eel and VBS states. In the latter case the transitions are continuous and we extract critical exponents and address the issue of a possible emergent U(1) symmetry in the near-critical VBS. We also consider variationally optimized CAP states for the standard Heisenberg model in one and two dimensions and the
J-
Q model in two dimensions, with the latter including four-spin interactions (
Q) in addition to the Heisenberg exchange (
J) and harboring VBS order for large
Q/J. The optimized CAP states lead to significantly lower variational energies than the simple AP states for these models.
We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.