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Register a new userEffect of further-neighbor interactions on the magnetization behaviors of the Ising model on a triangular lattice
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In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin states are identified to be stabilized in certain magnetic field regions, respectively, resulting in the magnetization plateaus at 2/3, 5/7, 7/9 and 5/6 of the saturation magnetization MS, in addition to the well known plateaus at 0, 1/3 and 1/2 of MS. The stabilization of these interesting orders can be understood as the consequence of the competition between Zeeman energy and exchange energy.
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To gain a better understanding of the interplay between frustrated long-range interactions and zero-temperature quantum fluctuations, we investigate the ground-state phase diagram of the transverse-field Ising model with algebraically-decaying long-range Ising interactions on quasi one-dimensional infinite-cylinder triangular lattices. Technically, we apply various approaches including low- and high-field series expansions. For the classical long-range Ising model, we investigate cylinders with an arbitrary even circumference. We show the occurrence of gapped stripe-ordered phases emerging out of the infinitely-degenerate nearest-neighbor Ising ground-state space on the two-dimensional triangular lattice. Further, while cylinders with circumferences $6$, $10$, $14$ et cetera are always in the same stripe phase for any decay exponent of the long-range Ising interaction, the family of cylinders with circumferences $4$, $8$, $12$ et cetera displays a phase transition between two different types of stripe structures. For the full long-range transverse-field Ising model, we concentrate on cylinders with circumference four and six. The ground-state phase diagram consists of several quantum phases in both cases including an $x$-polarized phase, stripe-ordered phases, and clock-ordered phases which emerge from an order-by-disorder scenario already present in the nearest-neighbor model. In addition, the generic presence of a potential intermediate gapless phase with algebraic correlations and associated Kosterlitz-Thouless transitions is discussed for both cylinders.
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on 6-leg infinite-length cylinders, and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.
In this work, we investigate the phase transitions and critical behaviors of the frustrated J1-J2-J3 Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second next nearest neighbor interaction J3 on the phase transition from a disordered state to the single stripe antiferromagnetic state. A continuous Ashkin-Teller-like transition behavior in a certain range of J3 is identified, while the 4-state Potts-critical end point [J3/J1]C is estimated based on the analytic method reported in earlier work [Jin et al., Phys. Rev. Lett. 108, 045702 (2012)]. It is suggested that the interaction J3 can tune the transition temperature and in turn modulate the critical behaviors of the frustrated model. Furthermore, it is revealed that an antiferromagnetic J3 can stabilize the staggered dimer state via a phase transition of strong first-order character.
We present a Quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction J and one diagonal second-neighbor interaction $J$, interpolating between square-lattice ($J=0$) and triangular-lattice ($J=J$) limits. At a transverse-field of $B_x=J$, the disorder-line first introduced by Stephenson, where the correlations go from Neel to incommensurate, meets the zero temperature axis at $Japprox 0.7 J$. Strong evidence is provided that the incommensurate phase at larger $J$, at finite temperatures, is a floating phase with power-law decaying correlations. We sketch a general phase-diagram for such a system and discuss how our work connects with the previous Quantum Monte Carlo work by Isakov and Moessner for the isotropic triangular lattice ($J=J$). For the isotropic triangular-lattice, we also obtain the entropy function and constant entropy contours using a mix of Quantum Monte Carlo, high-temperature series expansions and high-field expansion methods and show that phase transitions in the model in presence of a transverse field occur at very low entropy.
We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-$frac{1}{2}$ Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long range collinear and incommensurate spirals regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short range order counterparts, leaving an ample room for $0$-flux and nematic spin liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate $120^{circ}$ Neel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.
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