Quantum solitons in the sawtooth lattice

Sen, Diptiman; Shastry, B. Sriram; Walstedt, R. E.; Cava, R. J.

doi:10.1103/physrevb.53.6401

Cited by 112 publications

(192 citation statements)

References 18 publications

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“…In fact, utilizing the Raleigh-Ritz variational principle 11,19,20,21 , we can exactly prove the state given by Eq. (4) is the ground state of Hamiltonian (2) as long as J ⊥ ≥ 2J.…”

Section: Spin-1/2 Latticementioning

confidence: 99%

“…Because there exists no intrinsic mechanics responsible for binding the dimer and monomer together to form a bound state in a spontaneously trimerized system, it is reasonable to assume that the dimer and monomer are well separated and they could be treated separately. Similar schemes have been used to evaluate the excitation spectrum in the spin-sawtooth system 19,20 . Under such an approximation, the excitation spectrum can be represented as a sum of monomer part and dimer part, i.e.,…”

Section: Spin-1 Lattice With Su(3) Symmetrymentioning

confidence: 99%

“…For a mixed spin △ chain with size of 8 + 8, we get its ground state energy given by E g 1/2,1 (8, 8) /16 = −0.646773. We note that the ground state of a spin △ chain or a spin sawtooth model with S i = 1/2 is exactly known 19,20,27 .…”

Section: Spin-1/2 Latticementioning

confidence: 99%

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Exact ground state and elementary excitations of the spin tetrahedron chain

et al. 2006

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We study the antiferromagnetic spin exchange models with S = 1/2 and S = 1 on a onedimensional tetrahedron chain by both analytical and numerical approaches. The system is shown to be effectively mapped to a decoupled spin chain in the regime of strong rung coupling, and a spin sawtooth lattice in the regime of weak rung coupling with spin 2S on the top row and spin S on the lower row. The ground state for the homogeneous tetrahedron chain is found to fall into in the regime of strong rung coupling. As a result, the elementary excitation for the spin-1/2 system is gapless whereas the excitation for the spin-1 system has a finite spin gap. With the aid of the exact diagonalization method, we determine the phase diagram numerically and find the existence of an additional phase in the intermediate regime. This phase is doubly degenerate and is characterized by an alternating distribution of rung singlet and rung spin 2S. We also show that the SU (3) exchange model on the same lattice has completely different kind of ground state from that of its SU (2) correspondence and calculate its ground state and elementary excitation analytically.

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“…In fact, utilizing the Raleigh-Ritz variational principle 11,19,20,21 , we can exactly prove the state given by Eq. (4) is the ground state of Hamiltonian (2) as long as J ⊥ ≥ 2J.…”

Section: Spin-1/2 Latticementioning

confidence: 99%

Section: Spin-1 Lattice With Su(3) Symmetrymentioning

confidence: 99%

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Exact ground state and elementary excitations of the spin tetrahedron chain

et al. 2006

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“…The excitations of the sawtooth chain are gapped and are of topological origin. They are found to be "kink"-"antikink"-type domain wall structures [5,6]. Anisotropic variants of sawtooth chain have also been investigated revealing additional features [7,8].…”

Section: Introductionmentioning

confidence: 99%

Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds

Ohanyan¹

2009

Condens. Matter Phys.

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The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground state properties are also investigated, the corresponding ground state phase diagram is presented.

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“…They often give rise to many body ground states in which many constituents become entangled, from which new collective degrees of freedom emerge. Examples include Valence Bond Solid (VBS) phases [1], decoupled chains [2] and spin liquids. At each level of entanglement, a new effective theory is needed to describe the low energy properties of the system.…”

Section: Introductionmentioning

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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Quantum solitons in the sawtooth lattice

Cited by 112 publications

References 18 publications

Exact ground state and elementary excitations of the spin tetrahedron chain

Exact ground state and elementary excitations of the spin tetrahedron chain

Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

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