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arXiv:1607.03617 · Acta Physica Polonica A

Breakdown of a Magnetization Plateau in Ferrimagnetic Mixed Spin-(1/2,S) Heisenberg Chains due to a Quantum Phase Transition towards the Luttinger Spin Liquid

Jozef Strečka

Published Apr 1, 2017• 13 citations
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Abstract

Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.

DOI
10.12693/aphyspola.131.624

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Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
At zero temperature, thermal fluctuation is eliminated and phase transitions will occur due to quantum fluctuations that arise from the Heisenberg uncertainty principle. Magnetic insulators, described by the Heisenberg model Hamiltonian, are a known class of physical systems that can undergo quantum phase transitions when submitted to a magnetic field. The magnetic field induces the transition by closing energy gaps through the Zeeman effect. Examples of systems that undergo these transitions are the antiferromagnetic spin-1 chain, the antiferromagnetic spin- 1/2 ladder, the ferrimagnetic mixed spin-1 and spin- 1/2 chains and ladders. The presence of a gap in the energy spectrum with zero magnetic field leads to a magnetization plateau in the magnetization curve. We use the density matrix renormalization group to investigate the magnetization curves of the mixed spin-1 and spin- 1/2 ladder, for antiferromagnetic and ferro- magnetic couplings between the ladder legs J⊥. For J⊥ > 0, the ground-state is ferrimagnetic with the total spin equal to 1/3 of the saturation value, in accord with the Lieb-Mattis theorem. The magnetization curve presents a plateau at total magnetization 1/3 of the saturation value, the 1/3-plateau since the ground state has a gap to excitations that increase the total spin by 1 unit. Decreasing J⊥ below zero, the ground state becomes a singlet, but the 1/3-plateau survives down to a critical value J⊥ = Jc. Given that the gap closes with the magnetization fixed, it is a Kosterlitz-Thouless transition type. To determine Jc, we have made a finite-size scale analysis of the plateau width.
Bipartite Lieb-Mattis ferrimagnetism and the symmetry-protected Haldane phase are paradigmatic mechanisms in quasi-one-dimensional quantum magnets. Both emerge, in distinct regimes, in a mixed-spin 111-12\tfrac{1}{2}21​-12\tfrac{1}{2}21​ Heisenberg trimer chain with antiferromagnetic backbone exchange JJJ and a side spin-12\tfrac{1}{2}21​ coupled to each backbone spin by an exchange JtJ_tJt​ of either sign. Using the density matrix renormalization group, we compute magnetization curves and the entanglement spectrum and entropy. ForJt>0J_t>0Jt​>0 a robust ferrimagnetic plateau forms at magnetization per unit cell m=1m=1m=1, whose multiplet entropy reflects how the conserved magnetization splits between the halves. For Jt<0J_t<0Jt​<0 an m=0m=0m=0 plateau opens and grows with ∣Jt∣|J_t|∣Jt​∣, while the m=1m=1m=1 plateau closes. AsJt→−∞J_t\to-\inftyJt​→−∞ the chain maps onto a spin-111 Heisenberg chain with coupling J/2J/2J/2: the m=0m=0m=0 width Δh≃0.196\Delta h\simeq 0.196Δh≃0.196 matches half the Haldane gap. Exponentially localized spin-12\tfrac{1}{2}21​ edge states and the even-fold degeneracy of the entanglement spectrum confirm the Haldane character of the m=0m=0m=0 phase.
Ferrimagnetic and Haldane-type phases in a mixed-spin 111-12\tfrac{1}{2}21​-12\tfrac{1}{2}21​ quantum trimer chain
Bipartite Lieb-Mattis ferrimagnetism and the symmetry-protected Haldane phase are paradigmatic mechanisms in quasi-one-dimensional quantum magnets. Both emerge, in distinct regimes, in a mixed-spin 111-12\tfrac{1}{2}21​-12\tfrac{1}{2}21​ Heisenberg trimer chain with antiferromagnetic backbone exchange JJJ and a side spin-12\tfrac{1}{2}21​ coupled to each backbone spin by an exchange JtJ_tJt​ of either sign. Using the density matrix renormalization group, we compute magnetization curves and the entanglement spectrum and entropy. For Jt>0J_t>0Jt​>0 a robust ferrimagnetic plateau forms at magnetization per unit cell m=1m=1m=1, whose multiplet entropy reflects how the conserved magnetization splits between the halves. For Jt<0J_t<0Jt​<0 an m=0m=0m=0 plateau opens and grows with ∣Jt∣|J_t|∣Jt​∣, while the m=1m=1m=1 plateau closes. As Jt→−∞J_t\to-\inftyJt​→−∞ the chain maps onto a spin-111 Heisenberg chain with coupling J/2J/2J/2: the m=0m=0m=0 width Δh≃0.196Δh\simeq 0.196Δh≃0.196 matches half the Haldane gap. Exponentially localized spin-12\tfrac{1}{2}21​ edge states and the even-fold degeneracy of the entanglement spectrum confirm the Haldane character of the m=0m=0m=0 phase.
Quantum phase transitions in alternating spin-(12\frac{1}{2}21​, 52\frac{5}{2}25​) Heisenberg chains
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.
Quantum many-body edge and extended magnon excitations from the 1/3 plateau of the anisotropic Heisenberg model on an open AB2{AB}_{2}AB2​ chain in a magnetic field hhh are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and hhh in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge state degeneracy, and a topological change of the excitations from gapped magnons with quadratic long-wavelength dispersion to a linear spinon dispersion in the Luttinger liquid gapless phase as the anisotropy $\ensuremath{\lambda}$ approaches the critical point from the $\ensuremath{\lambda}>0$ side of the phase diagram.