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Register a new userBound state of a hole and a triplet spin in the $t_1$-$t_2$-$J_1$-$J_2$ model
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We show that a hole and a triplet spin form a bound state in a nearly half-filled band of the one- and two-dimensional $t_1$-$t_2$-$J_1$-$J_2$ models. Numerical calculation indicates that the bound state is a spatially small object and moves as a composite particle with spin 1 and charge $+e$ in the spin-gapped background. Two bound states repulsively interact with each other in a short distance and move independently as long as they keep their distance. If a finite density of bound states behave as bosons, the system undergoes the Bose-Einstein condensation which means a superconductivity with charge $+e$.
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We study the ground state and the magnetization process of a spin-1/2 $J_1$-$J_2$ model with a plaquette structure by using various methods. For small inter-plaquette interaction, this model is expected to have a spin-gap and we computed the first- and the second excitation energies. If the gap of the lowest excitation closes, the corresponding particle condenses to form magnetic orders. By analyzing the quintet gap and magnetic interactions among the quintet excitations, we find a spin-nematic phase around $J_1/J_2sim -2$ due to the strong frustration and the quantum effect. When high magnetic moment is applied, not the spin-1 excitations but the spin-2 ones soften and dictate the magnetization process. We apply a mean-field approximation to the effective Hamiltonian to find three different types of phases (a conventional BEC phase, ``striped supersolid phases and a 1/2-plateau). Unlike the BEC in spin-dimer systems, this BEC phase is not accompanied by transverse magnetization. Possible connection to the recently discovered spin-gap compound (CuCl)LaNb2O7 is discussed.
The pseudofermion functional renormalization group (pf-FRG) has been put forward as a semi-analytical scheme that, for a given microscopic spin model, allows to discriminate whether the low-temperature states exhibit magnetic ordering or a tendency towards the formation of quantum spin liquids. However, the precise nature of the putative spin liquid ground state has remained hard to infer from the original (single-site) pf-FRG scheme. Here we introduce a cluster pf-FRG approach, which allows for a more stringent connection between a microscopic spin model and its low-temperature spin liquid ground states. In particular, it allows to calculate spatially structured fermion bilinear expectation values on spatial clusters, which are formed by splitting the original lattice into several sublattices, thereby allowing for the positive identification of a family of bilinear spin liquid states. As an application of this cluster pf-FRG approach, we consider the $J_1$-$J_2$ SU($N$)-Heisenberg model on a square lattice, which is a paradigmatic example for a frustrated quantum magnet exhibiting quantum spin liquid behavior for intermediate coupling strengths. In the well-established large-$N$ limit of this model, we show that our approach correctly captures the emergence of the $pi$-flux spin liquid state at low temperatures. For small $N$, where the precise nature of the ground state remains controversial, we focus on the widely studied case of $N=2$, for which we determine the low-temperature phase diagram near the strongly-frustrated regime after implementing the fermion number constraint by the flowing Popov-Fedotov method. Our results suggest that the $J_1$-$J_2$-Heisenberg model does not support the formation of a fermion bilinear spin liquid state.
The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combining with Monte Carlo sampling techniques, we are able to obtain the ground states energies that are competitive to the best results. The calculations show that there is no Neel order, dimer order and plaquette order in the region of 0.42 $lesssim J_2/J_1lesssim$ 0.6, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer and plaquette correlation functions all have power law decay behaviours, which provide strong evidences that the intermediate nonmagnetic phase is a single gapless spin liquid state.
The one-dimensional spin-S $J_1-J_2$ XY model is studied within the bosonization approach. Around the two limits ($J_2/J_1 ll 1,J_2/J_1 gg 1$) where a field theoretical analysis can be derived, we discuss the phases as well as the different phase transitions that occur in the model. In particular, it is found that the chiral critical spin nematic phase, first discovered by Nersesyan et al. (Phys. Rev. Lett. {bf 81}, 910 (1998)) for $S=1/2$, exists in the general spin-S case. The nature of the effective field theory that describes the transition between this chiral critical phase and a chiral gapped phase is also determined.
We study the phase diagram of the 2D $J_1$-$J_1$-$J_2$ spin-1/2 Heisenberg model by means of the coupled cluster method. The effect of the coupling $J_1$ on the Neel and stripe states is investigated. We find that the quantum critical points for the Neel and stripe phases increase as the coupling strength $J_1$ is increased, and an intermediate phase emerges above the region at $J_1 approx 0.6$ when $J_1=1$. We find indications for a quantum triple point at $J_1 approx 0.60 pm 0.03$, $J_2 approx 0.33 pm 0.02$ for $J_1=1$.
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