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arXiv:2308.15372 · Physical review. B./Physical review. B

Theory of fractionally magnetized quantum ferromagnet

Isao Maruyama, Shin Miyahara

Published Oct 6, 2023• 5 citations
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Abstract

We present a theory to realize entangled quantum spin states with fractional magnetization. The origin of magnetization reduction is partly emergent antiferromagnetism, that is, the spin liquefaction of ferromagnetism. We study a ferromagnetic bilinear coupling region of the spin-$S$ ($\ensuremath{\geqq}1$) bilinear-biquadratic spin chain based on (i) a rigorous eigenstate correspondence between the spin-$S$ model and spin-$\frac{1}{2}$ model and (ii) a numerical exact-diagonalization calculation up to $S=3$. As a result, we obtain a fractional magnetized $M=1\ensuremath{-}1/(2S)$ phase, where ground states have quantum entanglement-reflecting corresponding spin-$\frac{1}{2}$ antiferromagnetic ground states in a ferromagnetic background. This spin-liquefaction theory of ferromagnets can be generalized to any-dimensional lattices even under a magnetic field. This fractional ferromagnetism opens another research field of quantum ferromagnets.

DOI
10.1103/physrevb.108.l140404

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We present a theory to realize entangled quantum spin states with fractional magnetization. The origin of magnetization reduction is partly emergent antiferromagnetism, that is, the spin liquefaction of ferromagnetism. We study a ferromagnetic bilinear coupling region of the spin-SSS (\ensuremath≧1\ensuremath{\geqq}1\ensuremath≧1) bilinear-biquadratic spin chain based on (i) a rigorous eigenstate correspondence between the spin-SSS model and spin-12\frac{1}{2}21​ model and (ii) a numerical exact-diagonalization calculation up to S=3S=3S=3. As a result, we obtain a fractional magnetized M=1\ensuremath−1/(2S)M=1\ensuremath{-}1/(2S)M=1\ensuremath−1/(2S) phase, where ground states have quantum entanglement-reflecting corresponding spin-12\frac{1}{2}21​ antiferromagnetic ground states in a ferromagnetic background. This spin-liquefaction theory of ferromagnets can be generalized to any-dimensional lattices even under a magnetic field. This fractional ferromagnetism opens another research field of quantum ferromagnets.
We present a theory to realize fractionally magnetized quantum ferromagnet in aspin−S≧2\mathbf{spin}-S \geqq 2spin−S≧2bilinear-biquadratic spin systems. The origin of the fractionally magnetized state is spin-liquefaction of ferromagnetism which means partly emergent antiferromagnetism. The realization of the spin-liquefaction of ferromagnetism is guaranteed due to a rigorous eigenstate correspondence between theSpin−S\mathbf{Spin}-SSpin−Smodel andspin−12\mathbf{spin} - \frac{1}{2}spin−21​model, i. e., “eigensystem embedding”. This spin-liquefaction theory of ferromagnets can be generalized to any-dimensional lattices. As a typical case, we discuss the two-dimensional models on a square lattice with a numerical exact-diagonalization.
We present a theory of the realization of a ferromagnetic Haldane state in a spin-2 bilinear-biquadratic spin system on an orthogonal-dimer chain. The coexistence of a ferromagnetic state and a Haldane state is due to the rigorous correspondence between the eigenstates of a spin-2 model and a spin-12\frac{1}{2}21​ Heisenberg model, i.e., ``eigensystem embedding.'' Numerical exact-diagonalization calculations indicate that the ground state in the model is a fractionally magnetized M=3/4M=3/4M=3/4 Haldane state. Moreover, a ferromagnetic-dimer multiplet state is an exact ground state on a lattice, where the direct product of dimer singlet states is the ground state in a spin-12\frac{1}{2}21​ Heisenberg model that includes one-, two-, and three-dimensional orthogonal-dimer lattices. Eigensystem embedding demonstrates that a quantum ferromagnet can be obtained for an arbitrary spin $S\ensuremath{\geqq}2$ in any dimension and for any lattice in which anomalous ground states are realized in a spin-12\frac{1}{2}21​ Heisenberg model.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic Heisenberg model are studied. The biquadratic interaction for spin-1/2 chains is eliminated and transformed to the quadratic interaction. Doing a numerical experiment, new insight as to how the classical phases get modified on the inclusion of quantum fluctuations is provided. Observed results suggest the existence of an intermediate region in the ground state phase diagram of the frustrated ferromagnetic spin-1/2 chains with combination of dimer and chiral orders. In addition, from the quantum entanglement view point, differences between quantum phases are also obtained. The nearest neighbor spins never be entangled in the frustrated ferromagnetic chains but are entangled up to the Majumdar-Ghosh point in the frustrated antiferromagnetic chains. On the other hand, the next nearest neighbor spins in the mentioned intermediate region are entangled.
We study a spin-SSS ferromagnetic model with exactly-written ground states, known as the partially-magnetized valence bond solid (VBS) states with magnetization m=(S−1)/Sm=(S-1)/Sm=(S−1)/S, which is a ferromagnetic generalization of the Affleck-Kennedy-Lieb-Tasaki model. We find that the VBS state and an antiferromagnetic ground state with magnetization m=0m=0m=0 are degenerate for S=3/2S=3/2S=3/2 and S=2S=2S=2 by using the Lanczos method and the density matrix renormalization group method (DMRG). However, increasing SSS, the magnetization of the ground states is uniquely determined as the fraction m=(S−1)/Sm=(S-1)/Sm=(S−1)/S. This is not just a ferromagnet, but a quantum ferromagnet due to quantum entanglement inherent in VBS states. In the low-energy excitation spectrum, we find the coexistence of the Haldane gap and Goldstone-like ferromagnetic magnon excitation. This ``magnetic chimera'' clearly appears under a finite magnetic field. Finally, we discuss an application to the measurement-based quantum computation and an extension of the Haldane's conjecture.
The spin phase diagram of interacting electrons in a quantum wire under a high magnetic field is investigated by finite-system exact diagonalization. Various phases emerge as a function of interaction strength and aspect ratio. Stable spin-polarized states correspond to two-dimensional fractional quantum Hall states of filling fractions 1/q,1/q,1/q, with qqq odd. Spin-singlet ground states for six electrons with filling fractions around 25−−12\frac{2}{5}--\frac{1}{2}52​−−21​ are inspected in detail, and a real-space singlet pairing state peculiar to wire systems is found for a larger aspect ratio.