Quantum vs Classical Magnetization Plateaus of <i>S</i>=1/2 Frustrated Heisenberg Chains

Hida, Kazuo; Affleck, Ian

doi:10.1143/jpsj.74.1849

Cited by 49 publications

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“…This model has a magnetization plateau at 1/3 of the saturation magnetization M s as investigated in [5].…”

Section: Hamiltonianmentioning

confidence: 99%

“…In the magnetic field, another type of translational symmetry breakdown is recently found by Okunishi and Tonegawa [2,3] and Tonegawa et al [4] resulting in a nontrivial magnetization plateau at one third of full magnetization M s . The present author and Affleck [5] have investigated the effect of period three exchange modulation on this plateau state. It turned out that the transition between the classical plateau state and the quantum plateau state takes place within the 1/3 plateau state Another remarkable effect of frustration is the stabilization of ferrimagnetic ground state.…”

Section: Introductionmentioning

confidence: 99%

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Ferrimagnetic states inS= 1/2 frustrated Heisenberg chains with period 3 exchange modulation

Hida

2007

J. Phys.: Condens. Matter

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Abstract. Ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and DMRG method. It is known that this model has a magnetization plateau at 1/3 of the saturation magnetization M s . On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if frustration is strong. This state further continues to the above mentioned 1/3-plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M s /3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.

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“…This model has a magnetization plateau at 1/3 of the saturation magnetization M s as investigated in [5].…”

Section: Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ferrimagnetic states inS= 1/2 frustrated Heisenberg chains with period 3 exchange modulation

Hida

2007

J. Phys.: Condens. Matter

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“…For parameters for which the matrix M k is not positive definite we add to the Hamiltonian the term V defined in Eq. (2). From the expression ofV in terms of HP bosons it is clear that it leaves H (0) and H (1) unchanged while its effect on the bosonic Hamiltonian is to increase ∆ k and all diagonal elements of M k by δ/2.…”

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confidence: 98%

“…Of all these remarkable features, magnetization plateaus at rational value of the magnetization are probably the best documented ones experimentally, and their theory is likewise quite advanced. Following the terminology of Hida and Affleck [2], two kinds of plateaus have been identified [3]: 'classical' plateaus [4][5][6], whose structure has a simple classical analog with spins up or down along the external field, and 'quantum' plateaus [7][8][9][10][11], which have no classical analog and correspond to a Wigner crystal of triplets in a sea of singlets. In the case of quantum plateaus, the mechanism is clear: frustration reduces the kinetic energy of triplets, resulting in a crystallization at commensurate densities.…”

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confidence: 99%

Quantum stabilization of classically unstable plateau structures

2013

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Motivated by the intriguing report, in some frustrated quantum antiferromagnets, of magnetization plateaus whose simple collinear structure is not stabilized by an external magnetic field in the classical limit, we develop a semiclassical method to estimate the zero-point energy of collinear configurations even when they do not correspond to a local minimum of the classical energy. For the spin-1/2 frustrated square-lattice antiferromagnet, this approach leads to the stabilization of a large 1/2 plateau with "up-up-up-down" structure for J 2 /J 1 > 1/2, in agreement with exact diagonalization results, while for the spin-1/2 anisotropic triangular antiferromagnet, it predicts that the 1/3 plateau with "up-up-down" structure is stable far from the isotropic point, in agreement with the properties of Cs 2 CuBr 4 .Introduction.-Frustration is responsible for the emergence of several remarkable properties in quantum magnets, ranging from rather exotic types of order such as quadrupolar or nematic order to resonating valence bond or algebraic spin liquids [1]. In the presence of an external field, frustration is also known to be at the origin of several types of accidents in the magnetization curve, including kinks, jumps and plateaus. Of all these remarkable features, magnetization plateaus at rational value of the magnetization are probably the best documented ones experimentally, and their theory is likewise quite advanced. Following the terminology of Hida and Affleck [2], two kinds of plateaus have been identified [3]: 'classical' plateaus [4][5][6], whose structure has a simple classical analog with spins up or down along the external field, and 'quantum' plateaus [7][8][9][10][11], which have no classical analog and correspond to a Wigner crystal of triplets in a sea of singlets. In the case of quantum plateaus, the mechanism is clear: frustration reduces the kinetic energy of triplets, resulting in a crystallization at commensurate densities. The main open problem is to be predictive for high commensurability plateaus since it requires a precise knowledge of the long-range part of the triplet-triplet interaction.By contrast, and somehow surprisingly, the theory of classical plateaus is not complete yet. The paradigmatic example of a classical plateau is the 1/3 magnetization plateau of the Heisenberg antiferromagnet on a triangular lattice, studied by Chubukov and Golosov [5] in the context of a 1/S expansion. In this system the three sublattice up-up-down (uud) structure appears classically at H = H sat /3, and quantum fluctuations stabilize this uud state in a finite field range around H sat /3, leading to the 1/3 plateau. The basic qualitative idea in the spirit of the order by disorder is that collinear configurations often have a softer spectrum and, hence, a smaller zeropoint energy [12,13]. The prediction of the 1/3 plateau has been confirmed by exact diagonalization of finite clusters for S = 1/2 and 1 [14], and the theory of Chubukov and Golosov can be extended to all cases where a collinear state is ...

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“…For a uniform F-AF chain, the exact ground states for arbitrary S tot and S z tot is written down explicitly in the closed form (13). In each state, p singlet pairs are distributed uniformly among the remaining N − 2p unpaired spins.…”

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Exact Degenerate Ground States for the F–AF Spin Chain with Bond Alternation

Suzuki

Takano

2008

J. Phys. Soc. Jpn.

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We investigate the J1-J2 spin chain consisting of spins with magnitude 1 2. The nearestneighbor and the next-nearest-neighbor exchange interactions are ferromagnetic and antiferromagnetic, respectively, and induce strong frustration. Both these interactions involve the bond alternation. We find exact solutions for all the degenerate ground states on the phase boundary of the ferromagnetic phase. The degeneracy remains irrespective of two parameters representing the bond alternation. The exact solutions are of closed forms for no bond alternation and of recursion formulae in general. The exact solutions are applicable to the ∆ chain as a special case.KEYWORDS: quantum spin chain, frustration, ferromagnetic interaction, exact ground stateThe low-dimensional quantum spin system has been an interesting subject of numerous studies from long years ago. In particular, the interplay of quantum fluctuation and geometrical frustration is of current interest. In onedimensional spin systems, various exotic phases and phenomena are reported such as quantum chiral phases, 1-9 1 3 -plateau 10-13 and singlet cluster solid. 14The J 1 -J 2 spin chain is a well-known one-dimensional spin model, which has the nearest-neighbor (NN) and the next-nearest-neighbor (NNN) interactions with exchange parameters J 1 and J 2 , respectively. We restrict ourselves to the case that the spin magnitude s is 1 2 . For J 1 > 0 and J 2 > 0, because of the frustration, the spin chain is known to exhibit a quantum phase transition from a gapless Tomonaga-Luttinger-liquid phase to a gapped dimerized phase at J 1 /J 2 ≃ 4.15.15, 16 At the MajumdarGhosh point of J 1 /J 2 = 2, the ground states are of exact tensor product forms of singlet NN dimers. 17Another type of frustration is induced in the J 1 -J 2 spin chain, if the NN interaction is ferromagnetic (J 1 < 0) and the NNN interaction is antiferromagnetic (J 2 > 0). We call this J 1 -J 2 spin chain the F-AF chain. The F-AF chain is realized in, e.g., Rb 2 Cu 2 Mo 3 O 12 with J 1 /J 2 ≃ −318 and LiCuVO 4 with J 1 /J 2 ≃ −0.3. 19 Relatively less attention has been paid to the F-AF chain until such materials are discovered. We are interested in the difference between frustration effects of the F-AF chain and of the J 1 -J 2 chain with both J 1 > 0 and J 2 > 0. Further, the uniform F-AF chain is extended to a model including bond alternation, if the NN and/or the NNN interactions have alternative strengths. The competition between frustration and bond alternation is of another physical interest.In the uniform F-AF chain, the ground state is fully ferromagnetic for J 1 < −4J 2 .20-22 For −4J 2 < J 1 < 0, numerical studies suggest a gapless singlet ground state, 16, 23 while a detailed analysis based on the field theory predicts a tiny but non-zero spin-gap for small |J 1 |.24 At the phase boundary of J 1 = −4J 2 , Hamada et al.25 found the exact singlet ground state under the periodic boundary condition (PBC). The exact solution is of a resonating-valence-bond (RVB) form.At the phase boundary for the F-AF ...

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Quantum vs Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains

Cited by 49 publications

References 18 publications

Ferrimagnetic states inS= 1/2 frustrated Heisenberg chains with period 3 exchange modulation

Ferrimagnetic states inS= 1/2 frustrated Heisenberg chains with period 3 exchange modulation

Quantum stabilization of classically unstable plateau structures

Exact Degenerate Ground States for the F–AF Spin Chain with Bond Alternation

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