Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$\Gamma$ chain

TL;DR

This paper investigates bond-alternating spin-1 K-Gamma chains, revealing a Haldane phase, a Kitaev phase with unique entanglement properties, and double-peak specific heat features linked to short-range correlations and Z2 quantity freezing.

Contribution

It identifies and characterizes novel gapped phases in a spin-1 K-Gamma chain, including a Kitaev phase with distinctive entanglement and thermodynamic signatures, expanding understanding of one-dimensional quantum spin systems.

Findings

Discovery of a Haldane phase in the chain.

Identification of a Kitaev phase with unique entanglement spectrum.

Observation of double-peak specific heat related to spin correlations.

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 $K$-$\Gamma$ chain built of a Kitaev ($K$) interaction and an off-diagonal $\Gamma$ 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 $T_h \simeq 0.5680$ and the freezing of $\mathbb{Z}_2$ quantities at $T_l \simeq 0.0562$, 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.