Motivated by a recent experiment on the rare-earth material
YbMgGaO4 [Y. Li et al., Phys. Rev. Lett. 115, 167203 (2015)], which found that the ground state of
YbMgGaO4 is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-
1/2 model that was proposed to describe
YbMgGaO4. Using the density matrix renormalization-group method in combination with the exact-diagonalization method, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram, there is a ${120}^{\ensuremath{\circ}}$ phase and two distinct stripe phases. The transitions from the two stripe phases to the ${120}^{\ensuremath{\circ}}$ phase are of the first order. However, the transition between the two stripe phases is not of the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may also be important to model the material
YbMgGaO4. These findings will stimulate further experimental and theoretical works in understanding the quantum spin-liquid ground state in
YbMgGaO4.
Based on exact diagonalization and density matrix renormalization group method, we show that an anisotropic triangular lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an anisotropic spin structure factor with an exponential-decay spin correlator along the weaker coupling direction, consistent with the
Cs2CuCl4 compounds. In the obtained phase diagram, the spin-liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio ${J}^{\ensuremath{'}}∕J=0.78$, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime.
We study the spin-1 Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor
J1 and the next-nearest-neighbor
J2 couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and the density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the N\'eel magnetic state to the stripe magnetic state at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width
Ly=10, we find that around the same critical point the N\'eel and the stripe orders are strongly suppressed, which implies the absence of an intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$. Our results indicate that unlike the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square model, quantum fluctuations in the spin-1 model may not be strong enough to stabilize an intermediate nonmagnetic phase.
The nature of the quantum spin liquid (QSL) phase in the frustrated
J1-
J2 Heisenberg model on the triangular lattice remains an open and actively debated problem. In this work, we employ the infinite projected entangled-pair state (PEPS) to systematically investigate the model under different symmetry constraints. Our simulations reveal a direct transition from the
120∘ Néel state to a putative QSL at
J2/J1≈0.08, signaled by the collapse of magnetic order. We further show that, through either an appropriate unitary rotation or spontaneous spin long-range order, the stripe antiferromagnetic phase can also be accurately captured within the infinite PEPS framework. A central focus of our study is the role played by the PEPS symmetry in approximating the QSL ground-state sandwiched between the two magnetic phases. We first found that a fully-symmetric topological
Z2 Resonating Valence Bond state, which can be written as a simple PEPS with bond dimension
D=3, exhibits a reasonably good variational energy. Motivated by this finding, we have further constructed generic
Z2-symmetric PEPS of larger bond dimension (up to
D=7). We found that, under wavefunction optimization, spinons condense and, simultaneously, topological vison excitations get confined, hence precluding
Z2 topological order. This strongly indicates the gapless (or critical) nature of the QSL phase, which is most naturally consistent with a U(1) Dirac spin liquid scenario.
Making use of infinite projected entangled pair states, we investigate the ground-state phase diagram of the nearest-neighbor spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice. In agreement with previous studies, we find the ferromagnetic, ${120}^{\ensuremath{\circ}}$ magnetically ordered, ferroquadrupolar and antiferroquadrupolar phases, and confirm that all corresponding phase transitions are first order. Moreover, we provide an accurate estimate of the location of the ferroquadrupolar to ${120}^{\ensuremath{\circ}}$ magnetically ordered phase transition, thereby fully establishing the phase diagram. Also, we do not encounter any signs of the existence of a quantum paramagnetic phase. In particular, contrary to the equivalent square lattice model, we demonstrate that on the triangular lattice the one-dimensional Haldane phase does not reach all the way up to the two-dimensional limit. Finally, we investigate the possibility of an intermediate partially magnetic partially quadrupolar phase close to $\ensuremath{\theta}=\ensuremath{\pi}/2$, and we show that, also contrary to the square lattice case, this phase is not present on the triangular lattice.
A layered triangular lattice with spin-1/2 ions is an ideal platform to explore highly entangled exotic states like quantum spin liquid (QSL). Here, we report a systematic in-field neutron scattering study on a perfect two-dimensional triangular-lattice antiferromagnet, CsYbSe
2, a member of the large QSL candidate family rare-earth chalcogenides. The elastic neutron scattering measured down to 70 mK shows that there is a short-range 120
∘ magnetic order at zero field. In the field-induced ordered states, the spin-spin correlation lengths along the
c axis are relatively short, although the heat capacity results indicate long-range magnetic orders at 3 T
− 5 T. The inelastic neutron scattering spectra evolve from highly damped continuum-like excitations at zero field to relatively sharp spin wave modes at the plateau phase. Our extensive large-cluster density-matrix renormalization group calculations with a Heisenberg triangular-lattice nearest-neighbor antiferromagnetic model reproduce the essential features of the experimental spectra, including continuum-like excitations at zero field, series of sharp magnons at the plateau phase as well as two-magnon excitations at high energy. This work presents comprehensive experimental and theoretical overview of the unconventional field-induced spin dynamics in triangular-lattice Heisenberg antiferromagnet and thus provides valuable insight into quantum many-body phenomena.