arXiv:1309.7913 · Physical Review Letters

Unexpected z -Direction Ising Antiferromagnetic Order in a Frustrated Spin- 1/2 J1−J2 XY Model on the Honeycomb Lattice

Zhenyue Zhu, David A. Huse, Steven R. White

Published Dec 16, 2013• 41 citations

Abstract

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.

DOI: 10.1103/physrevlett.111.257201

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arXiv:1309.7913 · Physical Review Letters

Unexpected z -Direction Ising Antiferromagnetic Order in a Frustrated Spin- 1/2 J1−J2 XY Model on the Honeycomb Lattice

Zhenyue Zhu, David A. Huse, Steven R. White

Published Dec 16, 2013• 41 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.111.257201

Related papers

Quantum phases of the frustrated XY models on the honeycomb lattice

Zhenyue Zhu, Steven R. White

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.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.

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Shou-Shu Gong, D. N. Sheng, Olexei I. Motrunich +1 more

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin- $\frac{1}{2}$ Heisenberg model on a honeycomb lattice with first ( ${J}_{1}$ ) and second ( ${J}_{2}$ ) neighbor antiferromagnetic interactions, where a ${Z}_{2}$ spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing ${J}_{2}$ , we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ${m}_{s}^{2}$ on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For $0.22<{J}_{2}/{J}_{1}<0.25$ , both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-$\frac{1}{2}$ Heisenberg model on a honeycomb lattice with first (${J}_{1}$) and second (${J}_{2}$) neighbor antiferromagnetic interactions, where a ${Z}_{2}$ spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing ${J}_{2}$, we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ${m}_{s}^{2}$ on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For $0.22<{J}_{2}/{J}_{1}<0.25$, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.

arXiv:1306.6067Physical Review BOct 29, 2013113 citations

Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin

S=1

Heisenberg model on the honeycomb lattice with the antiferromagnetic first- (

{J}_{1}

) and second-neighbor (

{J}_{2}

) 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

{J}_{2}

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-

1/2

system.

We study the nearest-neighbor exchange (

{J}_{1}

) and second-nearest-neighbor exchange (

{J}_{2}

)

XY

antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice

XY

N\'eel order at small

{J}_{2}

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

XY

and Ising degrees of freedom, namely the nearest-neighbor Ising and

XY

spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating

XY

and Ising orders. At still larger

{J}_{2}/{J}_{1}

the columnar and dimer energies are found to be nearly degenerate. At even larger

{J}_{2}

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.

Magnetic phases in the

J_{1}

J_{2}

antiferromagnetic XY model on the honeycomb lattice

We study ground-state properties and phase diagram of the

J_{1}

J_{2}

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

J_{2}/J_{1}

. 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

J_2/J_1

\frac{1}{2}

XY model with nearest-neighbor

({J}_{1})

, and next-nearest-neighbor

({J}_{2})

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)}_{1}

conformal field theory.

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-

\frac{1}{2}

Heisenberg model on a honeycomb lattice with first (

{J}_{1}

) and second (

{J}_{2}

) neighbor antiferromagnetic interactions, where a

{Z}_{2}

spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing

{J}_{2}

, we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment

{m}_{s}^{2}

on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For

0.22<{J}_{2}/{J}_{1}<0.25

, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.