Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets

Abstract

We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean field universality of the critical coupling times the coordination number of the lattice. Inspired by the recent development of characterization of symmetry protected topological states, of which the Haldane phase of spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we provide direct evidence that the quasi-one-dimensional Haldane phase is indeed a non-trivial symmetry protected topological state.

Combining microscopic and macroscopic probes to untangle the single-ion anisotropy and exchange energies in an S=1 quantum antiferromagnet

“…12. The phase boundaries, as deduced from QMC calculations, separate regions of XY −AFM order from the disordered quantum paramagnetic and Haldane phases; the three phases converge 12 at the quantum critical point D/J = 0.97. The relative position of [Ni(HF 2 )(pyz) 2 ]SbF 6 is indicated on the phase diagram using both the precise J /J and D/J ratios from INS and those estimated from a mean-field analysis of the critical fields observed in pulsed-field magnetization.…”

“…This includes the observation of field-induced Bose-Einstein condensation in NiCl 2 -4SC(NH 2 ) 2 [6][7][8], as well as the development of a Haldane phase in both [Ni(C 2 H 8 N 2 ) 2 NO 2 ]ClO 4 [9] and [Ni(HF 2 )(3-Clpy) 4 ]BF 4 (Clpy = C 5 H 4 NCl = chloropyridine) [10][11][12]. Groundstate diversity is attributable to the interplay between the single-ion anisotropy (D) and Heisenberg spin-exchange interactions in these materials, which are determined (in part) by the lattice geometry 12 . The flexibility offered by the crystal structures of quasi-one dimensional (Q1D) coordination polymers renders them ideal systems to advance our understanding of the quantum-critical phenomena associated with S = 1 systems.…”

“…The three magnetic phases are expected to converge at a quantum critical point (QCP) [13], located at D/J = 0.97 for purely 1D chains (Fig. 12) [12]. Therefore, the ability to measure J, J and D precisely, in addition to obtaining an unambiguous experimental determination of the magnetic ground state in real systems, is a crucial step towards testing the theoretical predictions of quantum phenomena in Q1D S = 1 chains.…”

Dynamics of a bond-disorderedS=1quantum magnet nearz=1criticality

“…Fortunately, the phase diagram of Hamiltonian (1) is well known numerically, 36,49,50 and shown in Fig. 5.…”

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrxDupont1, Capponi2, Laflorencie3 2017Phys. Rev. Lett.145280View full textAdd to dashboardCite

“…1]. Note that the S = 1 chains are not of Haldane type, due to the large anisotropy D [29]. In the absence of chemical disorder (x = 0), NiCl 2 -4SC(NH 2 ) 2 (DTN) provides a very good realization of magnetic field-induced Bose-Einstein condensation (BEC) in a quantum spin system [30][31][32][33] Fig.…”