On Next-Nearest-Neighbor Interaction in Linear Chain. I

Majumdar, Chanchal K.; Ghosh, D.

doi:10.1063/1.1664978

Cited by 818 publications

(542 citation statements)

References 13 publications

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“…For θ = 90 • (J 1 = 0), the model has only NNN interactions. This state is composed of three uncoupled spin ladders, one in each tripartite sublattice, forming a perfect MajumdarGhosh state of alternating singlet dimers [3,5]. The formation of this phase is a direct consequence of the three-leg form of the lattice, Fig.…”

Section: A Limiting Casesmentioning

confidence: 99%

“…In one-dimensional (1D) systems, powerful analytical and numerical methods have allowed a deep understanding of phenomena such as fractionalization [4], dimerization [5], and symmetry protected topological order [6,7]. In two-dimensional (2D) systems, there remain many more open problems such as understanding spin liquids [8,9], intrinsic topological order [10,11], and the connection between exotic magnetic phases and unconventional superconductivity [9,12].…”

Section: Introductionmentioning

confidence: 99%

“…However, studies of this model have failed to find an RVB state and the evidence [17,18] is now very strong that for the pure isotropic model with nearest-neighbor interactions the ground state is a 120 • magnetically ordered state [1]. Variants of the THM describe some properties of organic materials [8,9] such as κ-(BEDT-TTF) 2 Cu 2 (CN) 3 3 [20,21] and also some quasi-two-dimensional inorganic materials [8,9,[22][23][24][25] In one dimension the prototypical frustrated system is the zig-zag chain, which has an exact solution at the MajumdarGhosh point [3,5] where the NN coupling is twice the next-nearest-neighbor (NNN) coupling. The ground state * s.saadatmand@uq.edu.au is characterized by long-range dimer order and is twofold degenerate.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder

2015

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We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest-and next-nearest-neighbor spin-exchange coupling, on three-leg ladders. Using the density-matrix renormalizationgroup method, we obtain the complete phase diagram of the model, which includes quasi-long-range 120 • and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are nonchiral and planar. We also identify the nature of phase transitions.

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Section: A Limiting Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder

2015

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“…Proposed ground states here include various types of QSL states [32][33][34] as well as valence-bond solid (VBS) states [35][36][37][38] . The literature on VBS states has a long history going back to the well known Ghosh-Majumdar model 39 . The common theme in works on VBS is the frustration-driven transition from the AFM state to a total spin S = 0 singlet state.…”

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confidence: 99%

Paired electron crystal: Order from frustration in the quarter-filled band

et al. 2011

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We present a study of the effects of simultaneous charge-and spin-frustration on the twodimensional strongly correlated quarter-filled band on an anisotropic triangular lattice. Our conclusions are based on exact diagonalization studies that include electron-electron interactions as well as adiabatic electron-phonon coupling terms treated self-consistently. The broken-symmetry states that dominate in the weakly frustrated region near the rectangular lattice limit are the well known antiferromagnetic state with in-phase lattice dimerization along one direction, and the Wigner crystal state with the checkerboard charge order. For moderate to strong frustration, however, the dominant phase is a novel spin-singlet paired-electron crystal (PEC), consisting of pairs of charge-rich sites separated by pairs of charge-poor sites. The PEC, with coexisting charge-order and spin-gap in two dimension, is the quarter-filled band equivalent of the valence bond solid (VBS) that can appear in the frustrated half-filled band within antiferromagnetic spin Hamiltonians. We discuss the phase diagram as a function of on-site and intersite Coulomb interactions as well as electronphonon coupling strength. We speculate that the spin-bonded pairs of the PEC can become mobile for even stronger frustration, giving rise to a paired-electron liquid. We discuss the implications of the PEC concept for understanding several classes of quarter-filled band materials that display unconventional superconductivity, focusing in particular on organic charge transfer solids. Our work points out the need to go beyond quantum spin liquid (QSL) concepts for highly frustrated organic charge-transfer solids such as κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, which we believe show frustration-induced charge disproportionation at low temperatures. We discuss possible application to layered cobaltates and 1 4 -filled band spinels.

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“…As is clear from the figure, there is a finite gap to the lowest triplet state, but not to the singlets. If we had a system with broken symmetry, as in the Majumdar-Ghosh model, we would expect two singlet states to become degenerate in the thermodynamic limit, but a gap to all other states [12,13]. This is not the case here.…”

mentioning

confidence: 81%

Gapless singlet modes in thekagoméstrips: A study through density-matrix-renormalization group and strong-coupling analysis

Pati

Singh

1999

Phys. Rev. B

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Recently Azaria et al have studied strips of the Kagomé-lattice in the weak-coupling limit, where they consist of two spin-half chains on the outside weakly coupled to an array of half-integer spins in the middle. Using a number of mappings they have arrived at the interesting result that in this system all spin excitations are gapped but there are gapless spinless modes. Here we study these Kagomé strips in the limit where the interchain couplings are comparable to the coupling to the middle spins by density matrix renormalization group and by a strong coupling analysis. In the limit when the coupling to the middle-spin dominates, the 5-spins of the unit-cell reduce to a single S=3/2 spin, and the overall system has well known gapless spin excitations. We study the phase transition from this phase to the weak-coupling phase. We also carry out a strong coupling analysis away from the S=3/2 limit, where the five-spin blocks have four degenerate ground states with S=1/2, which can be thought of as two spin and two pseudospin degrees of freedom. A numerical study of this strong coupling model also suggests a finite spin-gap.The spin-half Kagomé-lattice antiferromagnet has proven to be a very fascinating system. Studies based on exact diagonalization of finite systems [1,2]and series expansions [3,4] strongly suggest that the system has a quantum disordered ground state. Finite size studies show a gap to spin excitations, but the most fascinating aspect of these numerical studies is the existence of a large number of spin-zero excitations below the lowest triplet state. Their number appears to grow exponentially with the size of the system [5][6][7]. The question of whether these spin-zero excitations are gapped or gapless and whether they form a well defined excitation mode of the system has not been resolved.In this respect an interesting system was recently studied by Azaria et al [8]. They considered a 3-chain strip of the Kagomé-lattice shown in Fig 1. This is a onedimensional system with half-integral spin per unit cell, and is thus subject to the Lieb-Schultz-Mattis (LSM) theorem [9]. Most interestingly, Azaria et al find that the system has no broken symmetries, a spin-gap but gapless spin-zero excitations. This is a rather unusual possibility, but permitted by the LSM theorem. Azaria et al study the system perturbatively in the weak coupling limit, where the Kagomé strip reduces to two spin-half chains on the outside with couplings J on the chains, coupled weakly with the array of middle spins, with couplings J ⊥ . Using a Majorana fermion representation for the low energy degrees of freedom on the spin-chains and employing a number of mappings, they conclude that these Kagomé strips have a spin-gap, which is exponentially small in J ⊥ /J , and there are gapless spin-zero modes. The importance of these studies to the Kagomé-strip limit J ⊥ = J , and furthermore to the Kagomé-lattice antiferromagnets remains unclear. Given the large number of approximate mappings, an independent numerical study of the model ...

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On Next-Nearest-Neighbor Interaction in Linear Chain. I

Cited by 818 publications

References 13 publications

Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder

Phase diagram of thespin−12triangularJ1−J2Heisenberg model on a three-leg cylinder

Paired electron crystal: Order from frustration in the quarter-filled band

Gapless singlet modes in thekagoméstrips: A study through density-matrix-renormalization group and strong-coupling analysis

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