2013
DOI: 10.1103/physrevb.88.165138
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Phase diagram of the spin-12J1-J2Heisenberg model on a honeycomb lattice

Abstract: We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-1 2Heisenberg 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 × 6 × 6. With increasing J 2 , we find a Néel phase wi… Show more

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Cited by 115 publications
(171 citation statements)
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References 82 publications
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“…For the geometry induced nematic order such as the order in the neighboring Néel phase without a C 4 symmetry breaking, one can see that the order decays very fast to vanish with growing cylinder width, in contrast to the scaling behavior in the intermediate phase. As a numerical method, we would like to point out that for detecting lattice symmetry breaking, edge bond pinning has been shown effective in quantum Monte Carlo 60 and DMRG simulations 58,59,61 . In the recent DMRG calculations for the spin-1/2 J 1 − J 2 triangular Heisenberg model [62][63][64] , a strong nematic order is also found, which is considered as an evidence of a spontaneous rotational symmetry breaking of the identified spin liquid phase.…”
Section: Nematic Ordermentioning
confidence: 99%
See 1 more Smart Citation
“…For the geometry induced nematic order such as the order in the neighboring Néel phase without a C 4 symmetry breaking, one can see that the order decays very fast to vanish with growing cylinder width, in contrast to the scaling behavior in the intermediate phase. As a numerical method, we would like to point out that for detecting lattice symmetry breaking, edge bond pinning has been shown effective in quantum Monte Carlo 60 and DMRG simulations 58,59,61 . In the recent DMRG calculations for the spin-1/2 J 1 − J 2 triangular Heisenberg model [62][63][64] , a strong nematic order is also found, which is considered as an evidence of a spontaneous rotational symmetry breaking of the identified spin liquid phase.…”
Section: Nematic Ordermentioning
confidence: 99%
“…To further study magnetic order, we calculate spin struc- i,j S i · S j e i q·( ri− rj ) (N is the total numer of sites) from the spin correlations S i · S j of the L × L sites in the middle of the RCL-2L cylinder, which efficiently reduces edge effects of open cylinder [57][58][59] . In the stripe and Néel AFM states, m 2 ( q) has the characteristic peak at q = (0, π)/(π, 0) and (π, π), respectively; these are shown in Figs.…”
Section: Magnetic and Quadrupolar Ordersmentioning
confidence: 99%
“…Theoretically, QSLs have been sought in spin-1/2 antiferromagnets with frustrated and/or competing interactions on triangular [28][29][30][31] , honeycomb [32][33][34][35][36] , square [37][38][39] , and kagomé [40][41][42][43][44] lattices. Amongst all these, the kagomé Heisenberg model (KHM) appears to possess the most robust QSL phase, and the only one consistently found in unbiased density matrix renormalization group (DMRG) calculations.…”
Section: Introductionmentioning
confidence: 99%
“…A solid proof for a system which shows a spin liquid ground state has long been elusive, due to inherent numerical and analytical problems in frustrated systems. Nonetheless, some good evidence for possible spin liquid states has recently been presented for the Hubbard model on the honeycomb [7] and the anisotropic triangular lattice [8], as well as for for the Heisenberg model on a Kagome lattice [1, 9-11], and on the J 1 -J 2 frustrated square lattice [12][13][14].…”
mentioning
confidence: 99%
“…A solid proof for a system which shows a spin liquid ground state has long been elusive, due to inherent numerical and analytical problems in frustrated systems. Nonetheless, some good evidence for possible spin liquid states has recently been presented for the Hubbard model on the honeycomb [7] and the anisotropic triangular lattice [8], as well as for for the Heisenberg model on a Kagome lattice [1, 9-11], and on the J 1 -J 2 frustrated square lattice [12][13][14].In particular, the J 1 -J 2 Heisenberg model has been treated with a vast array of theoretical methods , which is also the model originally considered by Anderson [6]. Early numerical works have shown an intermediate phase between ordinary Néel order for J 2 0.4J 1 and collinear Néel order for J 2 0.6J 1 [15], but the underlying correlations in this phase remain hotly debated.…”
mentioning
confidence: 99%