Unusual excitations and double-peak specific heat in a bond-alternating spin-1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">Γ</mml:mi></mml:math> chain
Qiang Luo, Shijie Hu, Hae-Young Kee
Abstract
One-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this paper, we study such phases in a bond-alternating spin-1 $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ chain built of a Kitaev ($K$) interaction and an off-diagonal $\mathrm{\ensuremath{\Gamma}}$ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spin-1 Heisenberg chain, is identified in a wide region. A gapped Kitaev phase situated at dominant ferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaev phase has extremely short range spin correlations and is characterized by finite ${\mathbb{Z}}_{2}$-valued quantities on bonds. Its lowest entanglement spectrum is unique, in contrast to the Haldane phase, whose entanglement spectrum is doubly degenerate. In addition, the Kitaev phase shows a double-peak structure in the specific heat at two different temperatures. In the pure Kitaev limit, the two peaks are representative of the development of short-range spin correlation at ${T}_{h}\ensuremath{\simeq}0.5680$ and the freezing of ${\mathbb{Z}}_{2}$ quantities at ${T}_{l}\ensuremath{\simeq}0.0562$, respectively. By considering bond anisotropy, regions of Haldane phase and Kitaev phase are enlarged, accompanied by the emergence of dimerized phases and three distinct magnetically ordered states.