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arXiv:1503.07570 · Physical Review B

Phase diagram of the spin−12 triangular J1−J2 Heisenberg model on a three-leg cylinder

S. N. Saadatmand, Benjamin James Powell, Ian P. McCulloch

Published Jun 9, 2015• 23 citations
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Abstract

We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest- and next-nearest-neighbor spin-exchange coupling, on three-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range ${120}^{\ensuremath{\circ}}$ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are nonchiral and planar. We also identify the nature of phase transitions.

DOI
10.1103/physrevb.91.245119

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We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest- and next-nearest-neighbor spin-exchange coupling, on three-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range 120\ensuremath∘{120}^{\ensuremath{\circ}}120\ensuremath∘ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are nonchiral and planar. We also identify the nature of phase transitions.
We study the S=1/2S=1/2S=1/2 Heisenberg model on the triangular lattice with nearest- and next-nearest-neighbor interactions J1{J}_{1}J1​ and J2{J}_{2}J2​ with the density matrix renormalization group, on long open cylinders with widths up to nine lattice spacings. In an intermediate J2{J}_{2}J2​ region $0.06\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.17$, we find evidence for a spin liquid (SL) state with short range spin-spin, bond-bond, and chiral correlation lengths, bordered by a classical ${120}^{\ensuremath{\circ}}$ N\'eel ordered state at small J2{J}_{2}J2​ and by a two sublattice collinear magnetically ordered state at larger J2{J}_{2}J2​. Focusing on J2/J1=0.1{J}_{2}/{J}_{1}=0.1J2​/J1​=0.1, we find a number of signatures of a gapped SL phase.
We study the spin-1 Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor J1{J}_{1}J1​ and the next-nearest-neighbor J2{J}_{2}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{L}_{y}=10Ly​=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.
We study an isotropic Heisenberg spin-12\frac{1}{2}21​ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling J3{J}_{3}J3​. J1{J}_{1}J1​ and J2{J}_{2}J2​ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small J2{J}_{2}J2​ limit, a short-range striped collinear phase is found in the presence of J3{J}_{3}J3​, whereas, in the large J2/J3{J}_{2}/{J}_{3}J2​/J3​ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large J3{J}_{3}J3​ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing J3{J}_{3}J3​. We apply this model to understand the magnetic properties of CaV2O5{\mathrm{CaV}}_{2}{\mathrm{O}}_{5}CaV2​O5​ and also fit the experimental data of susceptibility and magnetization. We note that J3{J}_{3}J3​ is a dominant interaction in this material, whereas J1{J}_{1}J1​ and J2{J}_{2}J2​ are approximately half of J3{J}_{3}J3​. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.
We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor (J1)({J}_{1})(J1​) and next-nearest-neighbor (J2)({J}_{2})(J2​) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1{J}_{2}/{J}_{1}J2​/J1​ and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin SSS, for J2/J1<1/8{J}_{2}/{J}_{1}<1/8J2​/J1​<1/8, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for J2=0{J}_{2}=0J2​=0, and for 1/8<J2/J1<11/8<{J}_{2}/{J}_{1}<11/8<J2​/J1​<1, they select the canted stripe state for all nonzero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary SSS, including S=1/2S=1/2S=1/2, near the saturation field by exploring the fact that near saturation the density of bosons is small for all SSS. We show that for S>1S>1S>1, the transition remains first order, with a finite hysteresis width, but for S=1/2S=1/2S=1/2 and, possibly, S=1S=1S=1, there appears a new intermediate phase without a quasiclassical long-range order.
Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J 2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J 2 = 0 is carefully analyzed.
Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.