We determine the quantum phase diagram of the antiferromagnetic spin-1/2 XXZ model on the triangular lattice as a function of magnetic field and anisotropic coupling Jz. Using the density matrix renormalization group (DMRG) algorithm in two dimensions we establish the locations of the phase boundaries between a plateau phase with 1/3 Néel order and two distinct coplanar phases. The two coplanar phases are characterized by a simultaneous breaking of both translational and U(1) symmetries, which is reminiscent of supersolidity. A translationally invariant umbrella phase is entered via a first order phase transition at relatively small values of Jz compared to the corresponding case of ferromagnetic hopping and the classical model. The phase transition lines meet at two tricritical points on the tip of the lobe of the plateau state, so that the two coplanar states are completely disconnected. Interestingly, the phase transition between the plateau state and the upper coplanar state changes from second order to first order for large values of Jz > ∼ 2.5J.PACS numbers: 75.10. Jm, 67.80.kb, 05.30.Jp Competing interactions between quantum spins can prevent conventional magnetic order at low temperatures. In the search of interesting and exotic quantum phases frustrated systems are therefore at the center of theoretical and experimental research in different areas of physics . One of the most straight-forward frustrated system is the spin-1/2 antiferromagnet (AF) on the triangular lattice, which was also the first model to be discussed as a potential candidate for spin-liquid behavior without conventional order by Anderson [2]. It is now known that the isotropic Heisenberg model on the triangular lattice is not a spin liquid and does show order at zero temperature [3]. Nonetheless, the phase diagram as a function of magnetic field is still actively discussed with recent theoretical calculations [4,5] as well as experimental results [6-9] on Ba 3 CoSb 2 O 9 , which appears to be very well described by a triangular AF. Interesting phases have also been found for anisotropic triangular lattices [11][12][13] and for the triangular extended Hubbard model [14]. Hard-core bosons with nearest neighbor interaction on a triangular lattice correspond to the xxz model with ferromagnetic exchange in the xy-plane, which has been studied extensively [15][16][17][18][19][20]. In this case a so-called supersolid phase near half-filling has been established for large interactions [15], which is characterized by two order parameters, namely a superfluid density and a √ 3 × √ 3 charge density order. Impurity effects show that the two order parameters are competing [17] and the transition to the superfluid state is first order [19,20].However, surprisingly little attention has been paid to the role of an antiferromagnetic anisotropic exchange interaction away from half-filling [24][25][26][27], even though the XXZ model on the triangular lattice H = J ij (Ŝ x iŜ x j +Ŝ y iŜ y j ) + J z ij Ŝ z iŜ z j − B iŜ z i , (1) is arguable one of the...

The spin-1/2 J1-J2 antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin liquid phase. The generalization of this system on the anisotropic square lattice is given by the J1-J2-J In the search of exotic quantum states and quantum phase transitions, frustrated antiferromagnetic systems have increasingly become the center of attention [1,2]. The competing interactions between spins potentially lead to a large entropy even at low temperatures, which together with quantum fluctuations may give rise to quantum phases with unconventional or topological order parameters [3][4][5]. In particular, the so-called spin liquid state without long range order of a conventional (local) order parameter has been much discussed in the literature ever since Anderson related this phase to hightemperature superconductivity [6]. A solid proof for a system which shows a spin liquid ground state has long been elusive, due to inherent numerical and analytical problems in frustrated systems. Nonetheless, some good evidence for possible spin liquid states has recently been presented for the Hubbard model on the honeycomb [7] and the anisotropic triangular lattice [8], as well as for for the Heisenberg model on a Kagome lattice [1, 9-11], and on the J 1 -J 2 frustrated square lattice [12][13][14].In particular, the J 1 -J 2 Heisenberg model has been treated with a vast array of theoretical methods , which is also the model originally considered by Anderson [6]. Early numerical works have shown an intermediate phase between ordinary Néel order for J 2 0.4J 1 and collinear Néel order for J 2 0.6J 1 [15], but the underlying correlations in this phase remain hotly debated. Most works have predicted a plaquette or columnar dimer order as the most likely scenario [16][17][18][19][20][21][22][23][24][25][26], but more recent numerical works have again proposed a spin liquid [12][13][14]. Unfortunately, the issue may never be conclusively solved using numerical methods, since convergence with finite size and/or temperature of data from density matrix renormalization group (DMRG) or tensor matrix methods is very slow. In particular, it was shown recently for the related two-dimensional (2D) J-Q model that the finite size scaling on moderate lengths would lead to the prediction of a spin liquid, even though the system orders in the thermodynamic limit [44]. In general, the slow convergence is related to the observation that spin liquid states are often very close in energy to competing states with dimer order [10,11].In light of the disappointing numerical situation, analytical methods become very important, but the problem is difficult since series expansions [16,36], chain meanfield theories [45], spin wave theories [23] or coupled cluster methods [25,40,41] have to incorporate frustrating

Publisher's Note: Spin-liquid versus dimer phases in an anisotropicJ 1 -J 2 frustrated square antiferromagnet [Phys. Rev. B 89, 241104(R) (2014)]