Plaquette valence bond ordering in aJ1–J2Heisenberg antiferromagnet on a honeycomb lattice

Mosadeq, Hamid; Shahbazi, Farhad; Jafari, S. A.

doi:10.1088/0953-8984/23/22/226006

Cited by 90 publications

(158 citation statements)

References 58 publications

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“…On the full honeycomb lattice, previous studies have suggested a plaquette-ordered ground state for 0.2 J 2 0.4 [11][12][13]. In this parameter regime, the ground state of the single hexagon problem is the '-' singlet.…”

Section: The Single Hexagon Problemmentioning

confidence: 99%

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

2013

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We study the proposed plaquette-RVB (pRVB) state in the honeycomb lattice J1 − J2 model with frustration arising from next-nearest neighbour interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low energy excitations. Our calculation clarifies that the putative pRVB state necessarily has f-wave symmetry -the plaquette wavefunction is an antisymmetric combination of the Kekulé structures. We estimate the plaquette ordering amplitude, ground state energy and spin gap as a function of J2/J1. The pRVB state is most stable around J2/J1 ∼ 0.25. We identify the wavevectors of the lowest triplet excitations, which can be verified using exact diagonalization or DMRG studies. When J2 is reduced, we can have either a deconfined Quantum Phase Transition (QPT) or a first-order transition into a Néel state. When J2 is increased, we surmise that the system will undergo a first order phase transition into a state which breaks lattice rotational symmetry.

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Section: The Single Hexagon Problemmentioning

confidence: 99%

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

2013

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“…Exact diagonalization (ED) studies are very helpful, as arbitrary m-point correlation functions can be computed in principle. However, except of the valence bond crystal domain where the dimer Hilbert space projection [10] is justified [11], ED cannot reach sufficient system sizes to adequately determine all phase regimes [11][12][13]. Linear spin wave theory gives a qualitative tendency where the quantum corrections lead to, but is still strongly biased towards the classical limit [12][13][14].…”

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Magnetic order and paramagnetic phases in the quantumJ1-J2-J3honeycomb model

2011

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Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J1, J2, and J3 up to third nearest neighbors. We use an unbiased pseudofermion functional renormalization group method to compute the magnetic susceptibility and determine the ordered and disordered states of the model. Aside from antiferromagnetic, collinear, and spiral order domains, we find a large paramagnetic region at intermediate J2 coupling. For larger J2 within this domain, we find a strong tendency to staggered dimer ordering, while the remaining paramagnetic regime for low J2 shows only weak plaquet and staggered dimer response. We suggest this regime to be a promising region to look for quantum spin liquid states when charge fluctuations would be included. The search for a quantum spin liquid phase in nature ever since has been a complicated task not only from experiment, but also from theory [1,2]. This stems from the fact that the properties of a quantum spin liquid are very peculiar: quantum fluctuations have to form a many-body singlet state without long-range correlations of any kind of operator. Since the notion of frustration in quantum spin systems which is the main resource of fluctuations to accomplish a magnetically disordered quantum state at zero temperature, studies of a plethora of spin Hamiltonians on different lattices tell us that even most frustrated quantum systems tend to establish some sort of long-range correlations such as seen in a valence bond solid phase: while local spin operator correlations rapidly fall off there, long-range dimer-dimer correlations spoil the phenomenology of a quantum spin liquid.The remarkable numerical studies by Meng et al.[3] are a fortunate exception. In their work, they report on the first unambiguous discovery of a genuine spin liquid phase from a generic microscopic model. They consider the Hubbard model on the honeycomb lattice by Monte Carlo methods and find a spin-gapped phase at U/t = 4.3 which shows no long-range correlations of any kind, neither charge density wave, superconductivity or even spin solid-type correlations such as that of a valencebond crystal formation. Moreover, the study finds a clear excitation gap and no symmetry breaking of any lattice symmetry or parity P and time-reversal T , which already excludes chiral spin liquids and algebraic spin liquids.One path of further understanding the magnetic quantum phases on the honeycomb lattice is the development of effective descriptions for the Hubbard model itself such as gauge theory [4] and slave boson mean field theory methods [5,6]. Another direction, however, which we pursue in this Letter is to analyze the Gutzwiller-projected Hubbard model on the honeycomb lattice. Specifically, we consider Heisenberg spin couplings up to third nearest neighbors labeled as the J 1 -J 2 -J 3 model. The motivation for this is two-fold. First, the J 1 -J 2 -J 3 model projects onto the square root fraction o...

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“…A remarkable example where the existence of such a state has been inferred is the spin-1/2 kagome-lattice Heisenberg antiferromagnet, which has been extensively studied both theoretically and experimentally [1][2][3], even though the precise nature of the spin-liquid state (gapped vs gapless) is still under debate [3][4][5][6]. Another model that has recently received considerable attention for its potential to realize spin-liquid states is the spin-1/2 Heisenberg model on the honeycomb lattice, with nearest-neighbor (NN) J 1 and next-to-nearest neighbor (NNN) J 2 exchange interactions [7][8][9][10][11][12][13][14][15][16]. This is in part motivated by its close relation to the Hubbard model, for which the possibility of having a spin-liquid ground state has been under close scrutiny [17][18][19].…”

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Nature of the phases in the frustratedXYmodel on the honeycomb lattice

et al. 2013

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We study the phase diagram of the frustrated XY model on the honeycomb lattice by using accurate correlated wave functions and variational Monte Carlo simulations. Our results suggest that a spin-liquid state is energetically favorable in the region of intermediate frustration, intervening between two magnetically ordered phases. The latter ones are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the model. The construction of the spin-liquid state is based on a decomposition of the underlying bosonic particles in terms of spin-1/2 fermions (partons), with a Gutzwiller projection enforcing no single occupancy, as well as a long-range Jastrow factor.PACS numbers: 75.10. Kt, 67.85.Jk, 21.60.Fw, 75.10.Jm A quantum spin liquid is an exotic state in which strong quantum fluctuations (usually generated by frustration) preclude ordering or freezing, even at zero temperature [1]. Despite intensive theoretical and experimental research, finding quantum spin liquids in materials and in realistic spin models continues to be a challenge. A remarkable example where the existence of such a state has been inferred is the spin-1/2 kagome-lattice Heisenberg antiferromagnet, which has been extensively studied both theoretically and experimentally [1][2][3], even though the precise nature of the spin-liquid state (gapped vs gapless) is still under debate [3][4][5][6]. Another model that has recently received considerable attention for its potential to realize spin-liquid states is the spin-1/2 Heisenberg model on the honeycomb lattice, with nearest-neighbor (NN) J 1 and next-to-nearest neighbor (NNN) J 2 exchange interactions [7][8][9][10][11][12][13][14][15][16]. This is in part motivated by its close relation to the Hubbard model, for which the possibility of having a spin-liquid ground state has been under close scrutiny [17][18][19].A closely related spin model with a rich phase diagram and the promise to support a gapless spin liquid phase is the J 1 − J 2 spin-1/2 XY model on the honeycomb lattice [20,21], which is the main subject of this Rapid Communication. Its Hamiltonian can be written aswhere S α i is the αth component of the spin-1/2 operator at site i. This model can be thought of as a Haldane-Bose-Hubbard model [20,[22][23][24], i.e., the Haldane model [25] on the honeycomb lattice with NN hopping J 1 and complex NNN hopping |J 2 |e ıφ , where spinless fermions are replaced by hard-core bosons and φ = 0. Hard-core boson creation and annihilation operators can then be mapped onto spin operators ((1). The total number of bosons (N ) is related to the total magnetization in the spin language, since n i = S z i + 1/2. Here, we focus on the half-filled case, where N equals one half the number of sites (V ).This model was studied in Ref.[20] by means of exact diagonalization on small clusters. There, evidence was found supporting the existence of a spin liq...

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Plaquette valence bond ordering in aJ₁–J₂Heisenberg antiferromagnet on a honeycomb lattice

Cited by 90 publications

References 58 publications

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

Magnetic order and paramagnetic phases in the quantumJ1-J2-J3honeycomb model

Nature of the phases in the frustratedXYmodel on the honeycomb lattice

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