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arXiv:2304.06062 · Physical review. B./Physical review. B

Quantum phases in the honeycomb-lattice J1 – J3 ferro-antiferromagnetic model

Shengtao Jiang, Steven R. White, A. L. Chernyshev

Published Nov 14, 2023• 23 citations
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Abstract

Using large-scale density-matrix renormalzation group calculations and minimally augmented spin-wave theory, we demonstrate that the phase diagram of the quantum $S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}$--${J}_{3}$ ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-$z$ phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases replace the classical spiral state.

DOI
10.1103/physrevb.108.l180406

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Using large-scale density-matrix renormalzation group calculations and minimally augmented spin-wave theory, we demonstrate that the phase diagram of the quantum S=12J1S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}S=21​J1​--J3{J}_{3}J3​ ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-zzz phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases replace the classical spiral state.
We demonstrate the versatility, simplicity, and power of the minimally augmented spin-wave theory in studying phase diagrams of the quantum spin models in which unexpected magnetically ordered phases occur or the existing ones expand beyond their classical stability regions. We use this method to obtain approximate phase diagrams of the two paradigmatic spin-12\frac{1}{2}21​ models on the honeycomb lattice: the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ ferro-antiferromagnetic and ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic XXZXXZXXZ models. For the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ case, various combinations of the XXZXXZXXZ anisotropies are analyzed. In a dramatic deviation from their classical phase diagrams, which host significant regions of the noncollinear spiral phases, quantum fluctuations stabilize several unconventional collinear phases and significantly extend conventional ones to completely supersede spiral states. These results are in close agreement with the available density-matrix renormalization group calculations. The applicability of this approach to the other models and its potential extension to different types of orders are discussed.
We study the ground-state (GS) properties of the frustrated spin-12\frac{1}{2}21​ J1{J}_{1}J1​--J2{J}_{2}J2​--J3{J}_{3}J3​ Heisenberg model on the two-dimensional honeycomb lattice with ferromagnetic nearest-neighbor (${J}_{1}=\ensuremath{-}1$) exchange and frustrating antiferromagnetic next-nearest-neighbor (J2>0{J}_{2}>0J2​>0) and next-next-nearest-neighbor (J3>0{J}_{3}>0J3​>0) exchanges, for the case J3=J2{J}_{3}={J}_{2}J3​=J2​. We use the coupled-cluster method implemented to high orders of approximation, complemented by the Lanczos exact diagonalization of a large finite lattice with 32 sites, in order to calculate the GS energy, magnetic order parameter, and spin-spin correlation functions. In one scenario we find a quantum phase transition point between regions characterized by ferromagnetic order and a form of antiferromagnetic (``striped'') collinear order at ${J}_{2}^{c}\ensuremath{\approx}0.1095\ifmmode\pm\else\textpm\fi{}0.0005$, which is below the corresponding hypothetical transition point at J2cl=17{J}_{2}^{\mathrm{cl}}=\frac{1}{7}J2cl​=71​ ($\ensuremath{\approx}0.143$) for the classical version of the model, in which we momentarily ignore the intervening noncollinear spiral phase in the region 110<J2<15\frac{1}{10}<{J}_{2}<\frac{1}{5}101​<J2​<51​. Hence we see that quantum fluctuations appear to stabilize somewhat the collinear antiferromagnetic order in preference to the ferromagnetic order in this model. We compare results for the present ferromagnetic case (with ${J}_{1}=\ensuremath{-}1$) to previous results for the corresponding antiferromagnetic case (with J1=+1{J}_{1}=+1J1​=+1). The magnetic order parameter is found to behave similarly for the ferromagnetic and the antiferromagnetic models for large values of the frustration parameter J2{J}_{2}J2​. However, there are considerable differences in the behavior of the order parameters for the two models for ${J}_{2}/|{J}_{1}|\ensuremath{\lesssim}0.6$. For example, the quasiclassical collinear magnetic long-range order for the antiferromagnetic model (with J1=+1{J}_{1}=+1J1​=+1) breaks down at ${J}_{2}^{{c}_{2}}\ensuremath{\approx}0.60$, whereas the ``equivalent'' point for the ferromagnetic model (with ${J}_{1}=\ensuremath{-}1$) occurs at ${J}_{2}^{c}\ensuremath{\approx}0.11$. Unlike in the antiferromagnetic model (with J1=+1{J}_{1}=+1J1​=+1), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical antiferromagnetic phases (with N\'eel and striped order) for J2c1<J2<J2c2{J}_{2}^{{c}_{1}}<{J}_{2}<{J}_{2}^{{c}_{2}}J2c1​​<J2​<J2c2​​, with ${J}_{2}^{{c}_{1}}\ensuremath{\approx}0.47$, we find no clear indications at all in the ferromagnetic model for an intermediate magnetically disordered phase between the corresponding phases exhibiting ferromagnetic and striped order. Instead the evidence for the ferromagnetic model (with ${J}_{1}=\ensuremath{-}1$) points to one of two scenarios: either there is a direct first-order transition between the two magnetically ordered phases, as mentioned above; or there exists an intervening phase between them in the very narrow range $0.10\ensuremath{\lesssim}{J}_{2}\ensuremath{\lesssim}0.12$, which is probably a remnant of the spiral phase that exists in the classical counterpart of the model over the larger range 110<J2<15\frac{1}{10}<{J}_{2}<\frac{1}{5}101​<J2​<51​.
We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 J1{J}_{1}J1​-J2{J}_{2}J2​-J3{J}_{3}J3​ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength ${J}_{1}\ensuremath{\equiv}1$, we find four magnetically ordered phases in the parameter window ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, namely, the N\'eel, striped, and N\'eel-II collinear AFM phases, plus a spiral phase. The N\'eel-II phase appears as a stable GS phase in the classical version of the model only for values J3<0{J}_{3}<0J3​<0. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $({J}_{2}^{{c}_{1}},{J}_{3}^{{c}_{1}})=(0.51\ifmmode\pm\else\textpm\fi{}0.01,0.69\ifmmode\pm\else\textpm\fi{}0.01)$ between the N\'eel, striped, and QP phases; (b) $({J}_{2}^{{c}_{2}},{J}_{3}^{{c}_{2}})=(0.65\ifmmode\pm\else\textpm\fi{}0.02,0.55\ifmmode\pm\else\textpm\fi{}0.01)$ between the striped, spiral, and QP phases; and (c) $({J}_{2}^{{c}_{3}},{J}_{3}^{{c}_{3}})=(0.69\ifmmode\pm\else\textpm\fi{}0.01,0.12\ifmmode\pm\else\textpm\fi{}0.01)$ between the spiral, N\'eel-II, and QP phases.
Magnetic phases in the J1J_{1}J1​-J2J_{2}J2​ antiferromagnetic XY model on the honeycomb lattice
We study ground-state properties and phase diagram of the J1J_{1}J1​-J2J_{2}J2​ antiferromagnetic XY model on the honeycomb lattice by means of the developed corner transfer matrix renormalization group algorithm with the two-site unit cell and the infinite spiral projected entangled pair states ansatz. We identify the main phases: Néel, Ising, collinear, and incommensurate spiral phases, as well as the transitions between them, as functions of the ratio J2/J1J_{2}/J_{1}J2​/J1​. In the regime of competing types of ordering, we show that the energies of the dimerized states are systematically higher than the energies in the collinear phase. This collinear phase transforms to the incommensurate spiral phase through the second-order phase transition upon a further increase of J2/J1J_2/J_1J2​/J1​.
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1S=1S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first- (J1{J}_{1}J1​) and second-neighbor (J2{J}_{2}J2​) interactions ($0.0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$) by means of density-matrix renormalization group. In the parameter regime ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.27$, the system sustains a N\'eel antiferromagnetic phase. At the large J2{J}_{2}J2​ side ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.32$, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/21/21/2 system.
Searching for spin-liquid states has long been attracting both experimentalists and theorists. In this paper, we review recent density matrix renormalization group studies of the spin-½ XY model on the honeycomb lattice, with first-neighbor (J1 = 1) and frustrating second-neighbor (J2 > 0) interactions. For the intermediate frustration regime 0.22 ≲ J2 ≲ 0.36, there exists a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z-axis, despite the absence of any SzSz interactions in the Hamiltonian. Surrounding this phase as a function of J2 are antiferromagnetic phases with the moments pointing in the xy-plane for small J2 and a close competition between an xy-plane magnetic collinear phase and a dimer phase for large values of J2. No spin-liquid phases was found in the XY model even with the third-neighbor (J3 > 0) interactions.