Resonating Valence Bond Theory of Coupled Heisenberg Chains

White, Steven R.; Noack, R. M.; Scalapino, D. J.

doi:10.1103/physrevlett.73.886

Cited by 416 publications

(456 citation statements)

References 20 publications

Supporting

Mentioning

409

Contrasting

Unclassified

Order By: Relevance

“…This reflects the well-known even-odd effect in the ground state of uniform (i.e. non-dimerized) spin ladders [18,4] that is expected to hold also to the spin tubes without frustration. In this effect, the even- legged uniform systems have an excitation gap while the odd-legged ones do not.…”

Section: Discussionsupporting

confidence: 52%

Quantum phase transitions of spin chiral nanotubes

Matsumoto

Sakai

Sato

et al. 2005

Physica E: Low-dimensional Systems and Nanostructures

View full text Add to dashboard Cite

Recently many interesting magnetic nanostructures have been fabricated and much attention is arising on the rich magnetic properties that originate in the quantum effects eminent in the nanoscale world. One of the peculiar aspects of the quantum effects is the spin excitation gap. In the spin-1/2 low-dimensional systems, the spin gap often appears when the lattice dimerization or the frustration in the spin-spin interaction are introduced. In the present study, we investigate the ground-state property of the spin-1/2 antiferromagnetic spin chiral nanotubes with the spatial modulation in the spin-spin interaction. The ground-state phase diagrams of them are determined by observing the behavior of the expectation value of the Lieb-SchultzMattis slow-twist operator calculated by the quantum Monte Carlo method with the continuous-time loop algorithm. We discuss the relation between the characteristic of the topology of the phase diagram and the chiral vector of the nanotubes.Key words: chiral nanotubes; spin gap; quantum Monte Carlo method PACS: 75.10. Jm, 75.40.Mg, 75.50.Ee, 75.75.+a MotivationThese days the experimental techniques have made a lot of progress and good experimentalists have synthesized the nanoscale magnets which realize the models that had been discussed only theoretically before. Among them are the BIP-TENO as the spin-1 twoleg ladder [1], the compound [(CuCl2tachH)3Cl]Cl2 (tach=cis,trans-1,3,5-triamino-cyclohexane) as the triangular spin nanotube [2], and the oxygen molecules adsorbed on the inner surface of the porous material as a many-leg spin tube [3]. The spin ladders [4] and tubes [5] have attracted attention in the course of the extensive studies on the low-dimensional magnets, part of which started from the discussions on the Haldane gap [6] of the one-dimensional spin chains. The appearance of the spin excitation gap is one of the interesting macroscopic quantum phenomena. In spin-1/2 systems, it occurs when the frustration in the spin-spin interaction or the lattice dimerization is introduced. A good example of the former case is the triangular spin nanotube [7] whose spontanous dimerized and gapped ground state had been theoretically investigated [8] and now got a strong possibility of an experimental realization in the near future [2]. During the course of studies on the low-dimensional systems, the huge amount of studies on the carbon nanotubes

show abstract

Section: Discussionsupporting

confidence: 52%

Quantum phase transitions of spin chiral nanotubes

Matsumoto

Sakai

Sato

et al. 2005

Physica E: Low-dimensional Systems and Nanostructures

View full text Add to dashboard Cite

show abstract

“…This model exhibits some similarities, but also marked differences from the standard two-chain spin-ladder [3][4][5][6][7], shown in Figure 2. While inter-chain coupling is relevant in the ladder model, producing a gap which scales linearly (up to logarithmic corrections) for either sign of the coupling, it is marginal for the zigzag chain, producing a gap only for antiferromagnetic sign, which scales exponentially with coupling, ∆ ∝ exp(− constant J 1 /J 2 ).…”

Section: Fig 2 the Spin Laddermentioning

confidence: 83%

Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: Analogies to the Kondo lattice

1996

View full text Add to dashboard Cite

Using the density matrix renormalization group and a bosonization approach, we study a spin-1/2 antiferromagnetic Heisenberg chain with near-neighbor coupling J 1 and frustrating second-neighbor coupling J 2 , particularly in the limit J 2 >> J 1 . This system exhibits both dimerization and incommensurate spiral spin correlations. We argue that this system is closely related to a doped, spin-gapped phase of the one-dimensional Kondo lattice.

show abstract

“…Both, antiferromagnetic Heisenberg ladders 30 and decorated chains 31,32,33 , have quantum-disordered ground states with a finite correlation length ξ 0 . In antiferromagnetic ladders the ground state has a RVB nature 34 , and for the necklace it has a dimer-singlet nature 31,32 . When segments of such structures become part of a larger cluster, as it is the case in the inhomogeneous percolation model, they locally retain ground state properties similar to the thermodynamic limit if their length l is large compared to the correlation length ξ 0 .…”

Section: Inhomogeneous Bond Dilution Of the Qhaf On The Square Lamentioning

confidence: 99%

Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets

Roscilde

Haas

2006

Phys. Rev. B

View full text Add to dashboard Cite

We investigate quantum phase transitions in the spin-1/2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a novel quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating cluster with short ranged antiferromagnetic order. In this phase, the low-temperature uniform susceptibility diverges algebraically with non-universal exponents. This is a signature that the novel quantum-disordered phase is a quantum Griffiths phase, as also directly confirmed by the statistical distribution of local gaps. This study thus presents evidence of a genuine quantum Griffiths phenomenon in a two-dimensional Heisenberg antiferromagnet.

show abstract

Resonating Valence Bond Theory of Coupled Heisenberg Chains

Cited by 416 publications

References 20 publications

Quantum phase transitions of spin chiral nanotubes

Quantum phase transitions of spin chiral nanotubes

Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: Analogies to the Kondo lattice

Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets

Contact Info

Product

Resources

About