Observation of<i>S</i>=1/2 degrees of freedom in an<i>S</i>=1 linear-chain Heisenberg antiferromagnet

Hagiwara, Masayuki; Katsumata, Kenji; Affleck, Ian; Halperin, Bertrand I.; Renard, Jean‐Pierre

doi:10.1103/physrevlett.65.3181

Cited by 392 publications

(250 citation statements)

References 18 publications

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“…This picture was supported by EPR measurements of [Ni(C 2 H 8 N 2 ) 2 (NO 2 )]ClO 4 (NENP) doped with nonmagnetic ions [7], where resonances corresponding to the fractional spin S = 1/2 states at the "open" ends of the S = 1 Ni chains were observed. Similar measurements for doping with magnetic ions are also consistent with S = 1/2 end states [8]. This effect, if robust, would correspond to the only instance in magnetism where a low energy collective excitation has no classical analog.…”

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confidence: 69%

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Electron spin resonance of defects in the Haldane systemY2BaNiO5

1999

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We calculate the electron paramagnetic resonance (EPR) spectra of the antiferromagnetic spin-1 chain compound Y2BaNi1−xMgxO5 for different values of x and temperature T much lower than the Haldane gap (∼ 100K). The low-energy spectrum of an anisotropic Heisenberg Hamiltonian, with all parameters determined from experiment, has been solved using DMRG. The observed EPR spectra are quantitatively reproduced by this model. The presence of end-chain S = 1/2 states is clearly observed as the main peak in the spectrum and the remaining structure is completely understood. This picture was supported by EPR measurements of [Ni(C 2 H 8 N 2 ) 2 (NO 2 )]ClO 4 (NENP) doped with nonmagnetic ions [7], where resonances corresponding to the fractional spin S = 1/2 states at the "open" ends of the S = 1 Ni chains were observed. Similar measurements for doping with magnetic ions are also consistent with S = 1/2 end states [8]. This effect, if robust, would correspond to the only instance in magnetism where a low energy collective excitation has no classical analog.However, Ramirez et al.[9] also tested the presence of free S = 1/2 states by studying the specific heat of non-magnetic defects in Y 2 BaNiO 5 , with magnetic fields up to 9T and temperatures down to 0.2K. They found that the shape and magnitude of the Schottky anomaly associated with the defects in Y 2 BaNi 1−x Zn x O 5 are better described by a simple model involving spin-1 excitations, instead of the S = 1/2 excitations of the VBS. In order to eliminate the apparent discrepancy with the EPR measurements in NENP, Ramirez et al. [9] pointed out the possibility that a small fraction of ethylene diamine complexes in NENP acquire charge at structural defects induced by Zn doping. As it is not uncommon that structural defects induce a paramagnetic behavior in organic compounds, they propose that similar EPR measurements should be performed on Y 2 BaNi 1−x A x O 5 (A a nonmagmetic ion) where x is more easily calibrated [9]. EPR is an appropriate technique to determine the existence of S=1/2 end states because it allows to distinguish between S=1/2 and S=1 spins in the presence of spatial anisotropy.In a recent paper [6], a precise fit of the above mentioned specific heat measurements was done, solving the low-energy spectrum of an anisotropic Heisenberg Hamiltonian for Y 2 BaNi 1−x Zn x O 5 . It was shown that there is no contradiction between EPR in NENP [7] and specific heat measurements in Y 2 BaNi 1−x Zn x O 5 [9]. The results supported the existence of S = 1/2 excitations for sufficiently long chains and clearly indicated that the anisotropy plays a very important role in the low temperature properties. However, EPR experiments would unambiguously detect the presence of such excitations and definitely confirm the validity of the theory.Recently, Saylor et al [13] have measured the EPR spectra of Y 2 BaNi 1−x Mg x O 5 at temperature T = 2K for different values of Mg concentration. The spectra show a prominent main peak, which can be associated with free S=1/2 spins, surr...

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supporting

confidence: 69%

“…Similar measurements for doping with magnetic ions are also consistent with S = 1/2 end states [8]. This effect, if robust, would correspond to the only instance in magnetism where a low energy collective excitation has no classical analog.…”

supporting

confidence: 69%

Electron spin resonance of defects in the Haldane systemY2BaNiO5

1999

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“…(8) with s = 1 2 . So, the Haldane phase of spin-1 chain has a spin- 1 2 boundary spin at each chain end [63,65,66]! We see that the Haldane phase is described by a fixed-point action which is a topological nonlinear σ model containing only the 2π -quantized topological term.…”

Section: B Path Integral Approach To a Spin-1 Chainmentioning

confidence: 99%

Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinearσmodels and a special group supercohomology theory

2014

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Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G, which can all be smoothly connected to the trivial product states if we break the symmetry. It has been shown that a large class of interacting bosonic SPT phases can be systematically described by group cohomology theory. In this paper, we introduce a (special) group supercohomology theory which is a generalization of the standard group cohomology theory. We show that a large class of short-range interacting fermionic SPT phases can be described by the group supercohomology theory. Using the data of supercocycles, we can obtain the ideal ground state wave function for the corresponding fermionic SPT phase. We can also obtain the bulk Hamiltonian that realizes the SPT phase, as well as the anomalous (i.e., non-onsite) symmetry for the boundary effective Hamiltonian. The anomalous symmetry on the boundary implies that the symmetric boundary must be gapless for (1+1)-dimensional [(1+1)D] boundary, and must be gapless or topologically ordered beyond (1+1)D. As an application of this general result, we construct a new SPT phase in three dimensions, for interacting fermionic superconductors with coplanar spin order (which have T 2 = 1 time-reversal Z T 2 and fermion-number-parity Z f 2 symmetries described by a full symmetry group Z T 2 × Z f 2 ). Such a fermionic SPT state can neither be realized by free fermions nor by interacting bosons (formed by fermion pairs), and thus are not included in the K-theory classification for free fermions or group cohomology description for interacting bosons. We also construct three interacting fermionic SPT phases in two dimensions (2D) with a full symmetry group Z 2 × Z f 2 . Those 2D fermionic SPT phases all have central-charge c = 1 gapless edge excitations, if the symmetry is not broken.

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“…This edge state has been studied in detail by numerical method [12,13], where the singlet and triplet (Kennedy triplet) states become degenerate in the thermodynamic limit (the four-fold degeneracy). Furthermore a doping of an impurity of S = 1/2 brings a local magnetic structure which causes an interesting energy structures [14][15][16]. The effects of bond impurity has been also studied [17].…”

Section: Introductionmentioning

confidence: 99%

Local magnetic structure due to inhomogeneity of interaction inS=12antiferromagnetic chains

et al. 2000

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We study the magnetic properties of S = 1/2 antiferromagnetic Heisenberg chains with inhomogeneity of interaction. Using a quantum Monte Carlo method and an exact diagonalization method, we study bond-impurity effect in the uniform S = 1/2 chain and also in the bond-alternating chain. Here 'bond impurity' means a bond with strength different from those in the bulk or a defect in the alternating order. Local magnetic structures induced by bond impurities are investigated both in the ground state and at finite temperatures, calculating the local magnetization, the local susceptibility and the local field susceptibility. We also investigate the force acting between bond impurities and find the force generally attractive.

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Observation ofS=1/2 degrees of freedom in anS=1 linear-chain Heisenberg antiferromagnet

Cited by 392 publications

References 18 publications

Electron spin resonance of defects in the Haldane systemY2BaNiO5

Electron spin resonance of defects in the Haldane systemY2BaNiO5

Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinearσmodels and a special group supercohomology theory

Local magnetic structure due to inhomogeneity of interaction inS=12antiferromagnetic chains

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