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arXiv:1412.4263 · Modern Physics Letters B

Quantum phases of the frustrated XY models on the honeycomb lattice

Zhenyue Zhu, Steven R. White

Published Dec 12, 2014• 17 citations
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Abstract

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.

DOI
10.1142/s0217984914300166

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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.
Using the density matrix renormalization group on wide cylinders, we study the phase diagram of the spin-1/2 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, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any S(z)S(z) interactions in the Hamiltonian. Surrounding this phase as a function of J2 are antiferromagnetic phases with the moments pointing in the x-y plane for small J2 and a close competition between an x-y plane magnetic collinear phase and a dimer phase for large values of J2. We do not find any spin-liquid phases in this model.
We study the nearest-neighbor exchange (J1{J}_{1}J1​) and second-nearest-neighbor exchange (J2{J}_{2}J2​) XYXYXY antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice XYXYXY N\'eel order at small J2{J}_{2}J2​ vanishes at ${J}_{2}/{J}_{1}=0.22\ifmmode\pm\else\textpm\fi{}0.01$ in agreement with results from density matrix renormalization group (DMRG) studies. Near the transition, we find evidence for an approximate emergent symmetry between XYXYXY and Ising degrees of freedom, namely the nearest-neighbor Ising and XYXYXY spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating XYXYXY and Ising orders. At still larger J2/J1{J}_{2}/{J}_{1}J2​/J1​ the columnar and dimer energies are found to be nearly degenerate. At even larger J2{J}_{2}J2​ the columnar phase is obtained. The ground state energies in all three phases are in good agreement with the values found in the DMRG studies.
The frustrated XY model on the honeycomb lattice has drawn lots of attention because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this paper, we study the extended spin-12\frac{1}{2}21​ XY model with nearest-neighbor (J1)({J}_{1})(J1​), and next-nearest-neighbor (J2)({J}_{2})(J2​) interactions in the presence of a three-spins chiral $({J}_{\ensuremath{\chi}})$ term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small ${J}_{\ensuremath{\chi}}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a nonmagnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral SU(2)1SU{(2)}_{1}SU(2)1​ conformal field theory.
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.
Magnetic phases in the J1J_{1}J1​-J2J_{2}J2​ antiferromagnetic XY model on the honeycomb lattice
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