We have realized that the transition between the up-up-down and 0-coplanar states near the Ising limit is actually of the first order, although the hysteresis region is very narrow. In Fig. 1(a), we present the corrected quantum phase diagram, in which the boundary of the corresponding transition for 0 < J=J z < 0.437 is replaced by a thick blue line. This minor correction does not affect the rest of the phase diagram and the main conclusions of our Letter, including the novel degeneracy-lifting mechanism that gives rise to the new π-coplanar state.A recent theoretical work based on the density matrix renormalization group method has suggested the existence of the first-order transition for 0 < J=J z ≲ 0.4 [3]. Therefore, we reexamined the magnetization curve m z ðHÞ ¼ P i hŜ z i i=M for small positive values of the anisotropy J=J z . As shown in Fig. 1(b), the magnetization curve is three valued in a finite range of H=J z near the end point of the plateau (H ¼ H c2 ), which implies that the transition is of the first order. When J=J z increases, the sign of the susceptibility χ c2 ≡ dm z =dHj H¼H c2 just above the plateau changes from negative to positive; i.e., there is a tricritical point (TCP) where the transition nature changes from first order to second order. In Fig. 1(c), we show the extrapolation of the inverse of χ c2 with respect to the scaling parameter λ for different values of J=J z . The location of the TCP is estimated to be ðJ=J z Þ TCP ≈ 0.437, for which the extrapolated value of χ −1 c2 is 0. This result is consistent with Ref.[3].[1] S. Wessel and M. Troyer, Phys. Rev. Lett. 95, 127205 (2005).[2] L. Bonnes and S. Wessel, Phys. Rev. B 84, 054510 (2011).[3] D. Sellmann, X.-F. Zhang, and S. Eggert, arXiv:1403.0008.FIG . 1 (color online). (a) Ground-state phase diagram of the spin-1=2 triangular-lattice XXZ model obtained by the cluster mean-field method combined with a scaling scheme (CMF þ S) (J z > 0). The thick blue (thin black) solid curves correspond to first-(second-)order transitions. The dot marks the tricritical point. The latest quantum Monte Carlo data [1,2] are shown by the red dashed (first-order) and dotted (second-order) curves. The symbol (×) is the value from the dilute Bose gas expansion. (b) An example of the magnetization curve that exhibits a first-order transition. We show the magnetization m z divided by the saturation value S ¼ 1=2 as a function of the magnetic field H=J z . The vertical dashed line marks the first-order transition point. (c) Cluster-size scalings of the CMF data for the inverse susceptibility χ −1 c2 just above the plateau. The lines indicate linear fits to the data obtained from the three largest clusters for each J=J z .

We study phase transitions and hysteresis in a system of dipolar bosons loaded into triangular optical lattices at zero temperature. We find that the quantum melting transition from supersolid to superfluid phase is first order, in contrast with the previous report. We also find that due to strong quantum fluctuations the supersolid (or solid)-superfluid transition can exhibit an anomalous hysteretic behavior, in which the curve of density versus chemical potential does not form a standard loop structure. Furthermore, we show that the transition occurs unidirectionally along the anomalous hysteresis curve.

We study the ground-state phase diagrams of hardcore bosons with long-range interactions on a square lattice using the linear spin-wave theory and a cluster mean-field method. Specifically, we consider the two types of long-range interaction: One consists only of the nearest-and nextnearest-neighbor interactions, and the other is the dipole-dipole interaction that decays with the interparticle distance r as ∼ r −3 . It is known from previous analyses by quantum Monte Carlo methods that a checkerboard supersolid (CSS) is absent in the ground-state phase diagram of the former case while it is present in the latter. In the former, we find that quantum fluctuations around mean-field solutions are enhanced by the direct competition between the checkerboard and striped solid orders and that they destabilize the CSS phase. On the other hand, the emergence of the CSS phase in the latter case can be attributed to the absence of such a competition with other solid orders. We also show that the cluster mean-field method allows for the determination of phase boundaries in a precise quantitative manner when scaling with respect to the cluster size is taken into account. It is found that the phase transition between the superfluid and the solid (or CSS) is of the first order in the vicinity of the particle-hole symmetric line.

Magnetization processes of spin-1/2 layered triangular-lattice antiferromagnets (TLAFs) under a magnetic field H are studied by means of a numerical cluster mean-field method with a scaling scheme. We find that small antiferromagnetic couplings between the layers give rise to several types of extra quantum phase transitions among different high-field coplanar phases. Especially, a field-induced first-order transition is found to occur at H≈0.7H_{s}, where H_{s} is the saturation field, as another common quantum effect of ideal TLAFs in addition to the well-established one-third plateau. Our microscopic model calculation with appropriate parameters shows excellent agreement with experiments on Ba_{3}CoSb_{2}O_{9} [T. Susuki et al., Phys. Rev. Lett. 110, 267201 (2013)]. Given this fact, we suggest that the Co^{2+}-based compounds may allow for quantum simulations of intriguing properties of this simple frustrated model, such as quantum criticality and supersolid states.

Electric transport of a zigzag graphene nanoribbon through a steplike potential and a barrier potential is investigated by using the recursive Green's function method. In the case of the steplike potential, we demonstrate numerically that scattering processes obey a selection rule for the band indices when the number of zigzag chains is even; the electrons belonging to the "even" ("odd") bands are scattered only into the even (odd) bands so that the parity of the wave functions is preserved. In the case of the barrier potential, by tuning the barrier height to be an appropriate value, we show that it can work as the "band-selective filter", which transmits electrons selectively with respect to the indices of the bands to which the incident electrons belong. Finally, we suggest that this selection rule can be observed in the conductance by applying two barrier potentials.

The triangular lattice of S=1/2 spins with XXZ anisotropy is a ubiquitous model for various frustrated systems in different contexts. We determine the quantum phase diagram of the model in the plane of the anisotropy parameter and the magnetic field by means of a large-size cluster mean-field method with a scaling scheme. We find that quantum fluctuations break up the nontrivial continuous degeneracy into two first-order phase transitions. In between the two transition boundaries, the degeneracy-lifting results in the emergence of a new coplanar phase not predicted in the classical counterpart of the model. We suggest that the quantum phase transition to the nonclassical coplanar state can be observed in triangular-lattice antiferromagnets with large easy-plane anisotropy or in the corresponding optical-lattice systems.

We study the stability of superfluid Fermi gases in deep optical lattices in the BCS-Bose-Einstein condensation (BEC) crossover at zero temperature. Within the tight-binding attractive Hubbard model, we calculate the spectrum of the low-energy Anderson-Bogoliubov (AB) mode as well as the single-particle excitations in the presence of superfluid flow in order to determine the critical velocities. To obtain the spectrum of the AB mode, we calculate the density response function in the generalized random-phase approximation applying the Green's function formalism developed by Côté and Griffin to the Hubbard model. We find that the spectrum of the AB mode is separated from the particle-hole continuum having the characteristic rotonlike minimum at short wavelength due to the strong charge-density-wave fluctuations. The energy of the rotonlike minimum decreases with increasing the lattice velocity and it reaches zero at the critical velocity which is smaller than the pair breaking velocity. This indicates that the superfluid state is energetically unstable due to the spontaneous emission of the short-wavelength rotonlike excitations of the AB mode instead due to pair-breaking. We determine the critical velocities as functions of the interaction strength across the BCS-BEC crossover regime.PACS numbers:where c jσ is the annihilation operator of a fermion on the jth site with pseudospin σ =↑, ↓.Here, J is the nearest-neighbor hopping energy, U is the on-site interaction energy, and µ is the chemical potential. We assume an attractive interaction between atoms (U < 0).In order to calculate the density response function, we introduce a fictitious timedependent external field P j (t) which is coupled with the density. The Hamiltonian with

We study the first-order quantum phase transitions of Bose gases in optical lattices. A special emphasis is placed on an anomalous hysteresis behavior, in which the phase transition occurs in a unidirectional way and a hysteresis loop does not form. We first revisit the hardcore Bose-Hubbard model with dipole-dipole interactions on a triangular lattice to analyze accurately the ground-state phase diagram and the hysteresis using the cluster mean-field theory combined with cluster-size scaling. Details of the anomalous hysteresis are presented. We next consider the two-component and spin-1 Bose-Hubbard models on a hypercubic lattice and show that the anomalous hysteresis can emerge in these systems as well. In particular, for the former model, we discuss the experimental feasibility of the first-order transitions and the associated hysteresis. We also explain an underlying mechanism of the anomalous hysteresis by means of the Ginzburg-Landau theory. From the given cases, we conclude that the anomalous hysteresis is a ubiquitous phenomenon of systems with a phase region of lobe shape that is surrounded by the first-order boundary.