Field-Induced Transitions and Spin Gaps in Low-Dimensional Quantum Antiferromagnets

Anders W. Sandvik, Elbio R. Dagotto, Douglas J. Scalapino

Kazuo Hida

The multiple reentrant quantum phase transitions in the $S=1/2$ antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with the interchain mean field approximation. It is assumed that the odd-th bond is antiferromagnetic with strength $J$ and even-th bond can take the values ${\JS}$ and ${\JW}$ $ ({\JS} > J > {\JW} > 0)$ randomly with probability $p$ and $1-p$, respectively. The pure version ($p=0$ and $p=1$) of this model has a spin gap but exhibits a field induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For $0 < p < 1$, the antiferromagnetism is induced by randomness at small field region where the ground state is disordered due to the spin gap in the pure case. At the same time, this model exhibits randomness induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between the transverse antiferromagnetic phases and disordered plateau phases with the increase of the magnetic field for moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and the jumps between them, It is also found that the antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.

Patrick Pilch, Kirill Amelin, Gary Schmiedinghoff +13 more

We report on terahertz spectroscopic measurements of quantum spin dynamics on single crystals of a spin-1/2 frustrated spin-ladder antiferromagnet ${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$ as a function of temperature, polarization, and applied external magnetic fields. Spin triplon excitations are observed at zero field and split in applied magnetic fields. For magnetic fields applied along the crystallographic $a$ axis, a quantum phase transition at ${B}_{c1}=21.4$ T is featured by a low-energy excitation mode emerging above ${B}_{c1}$, which indicates a gap reopening. For fields along the $b$ axis and the $c$ axis, different field dependencies are observed for the spin triplon excitations, whereas no low-lying modes could be resolved at field-induced phase transitions. We perform a theoretical analysis of the magnetic field dependence of the spin triplon modes by using continuous unitary transformations to determine an effective low-energy Hamiltonian. Through an exhaustive parameter search we find numerically optimized parameters to very well describe the experimentally observed modes, which corroborate the importance of significant magnetic anisotropy in the system.

Subir Sachdev A

Akira Matsuo, Kohei Hosokawa, Yasuo Narumi +7 more

Subir Sachdev A, Kwon Park