<i>S</i>=1/2 Quantum Heisenberg Ladder and<i>S</i>=1 Haldane Phase

Watanabe, Hiroshi; Nomura, K.; Takada, Satoshi

doi:10.1143/jpsj.62.2845

Cited by 58 publications

(49 citation statements)

References 36 publications

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“…The gap opens at α = 0 and increases monotonously with increasing α, and saturates at a certain value scaled by |J 1 |. This means that ∆ is finite for all α at β = 0, which is consistent with the prediction by the bozonization method [24] and the conformal field theory [27]. In the limit of α = 0 the system is exactly reduced to a S = 1 AFM Heisenberg chain…”

supporting

confidence: 82%

“…We can find a direct jump from S = 0 to S = L/2 at α ∼ 0. Haldane gapped state.-So far, the spin gapped state has been verified in the limit of β = 0 [23,24]. This can be interpreted as a realization of the AKLT VBS state.…”

mentioning

confidence: 91%

“…In the limit of β = 0, the system (1) is equivalent to spin ladder with AFM legs and FM rung couplings. Since this system can be effectively reduced to an S = 1 AFM Heisenberg chain with regarding two S = 1/2 spins on each rung as a S = 1 spin [23,24], the ground state is gapped as predicted by Haldane conjecture [22]. Therefore, the ground state can be well described by a valence-bond-solid (VBS) picture, proposed in the Affleck-Lieb-Kennedy-Tasaki (AKLT) model [25].…”

mentioning

confidence: 99%

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Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

et al. 2017

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Motivated by the magnetic properties of the spin-chain compounds LiCuSbO4≡LiSbCuO4 and Rb2Cu2Mo3O12, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM) (J1, J 1 < 0) and next-nearest-neighbor antiferromagnetic (J2 > 0) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at 2α = β/(1 + β), where α is the frustration ratio J2/|J1| and β the degree of dimerization J 1 /J1. In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO4. For larger α, corresponding to Rb2Cu2Mo3O12, and smaller β there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps. Introduction.-The exotic phenomena emerged by magnetic frustration have long been fascinating subjects of research in condensed matter physics [1]. Nowadays, quasi one-dimensional (1D) frustrated systems, despite their simple structure, are at the center of attention as a playground for novel ground states that can emerge from frustration and strong quantum fluctuations due to low dimensionality. So far, various unconventional magnetic states such as quantum spin liquids [2,3], spin-Peierls states [4], and Tomonaga-Luttinger (TL) liquid phases [5] have been investigated. Currently, among the hottest topics are magnetic multipolar and in particular spin-nematic states [6][7][8][9][10][11] in which magnon bound states are formed from a subtle competition between geometrical balance of ferromagnetic (FM) and antiferromagnetic (AFM) correlations among spins.

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supporting

confidence: 82%

mentioning

confidence: 91%

mentioning

confidence: 99%

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Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

et al. 2017

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“…Most studies on quantum spin ladders [24][25][26][27][28] consider antiferromagnetic coupling along the legs due to an interest in understanding exotic quantum phenomena, such as the experimentally observed high-T c transitions in antiferromagnetic ladder models for strontium-based superconducting cuprates [22,29]. Quantum spin-1/2 ladders with ferromagnetic interaction along the legs have also received attention [30][31][32][33], particularly in the study of synthetic ferromagnetic chains built from Cu 2+ compounds [30].…”

Section: The Modelmentioning

confidence: 99%

“…Also, multi-leg spin-1/2 ladders have been extensively used to investigate Haldane's conjecture [23] with respect to the dichotomy between quantum chains with integer and half-odd integer spins, and their gapped and gapless energy spectra, respectively [24]. However, though significant efforts have been made towards understanding the complex phase diagram of spin ladder systems, successful characterization of the different quantum phases have only been achieved in some limiting cases or through approximate models [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Detecting phase boundaries of quantum spin-1/2 XXZ ladder via bipartite and multipartite entanglement transitions

Roy

Dhar

Rakshit

et al. 2017

Journal of Magnetism and Magnetic Materials

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Phase transition in quantum many-body systems inevitably causes changes in certain physical properties which then serve as potential indicators of critical phenomena. Besides the traditional order parameters, characterization of quantum entanglement has proven to be a computationally efficient and successful method for detection of phase boundaries, especially in one-dimensional models. Here we determine the rich phase diagram of the ground states of a quantum spin-1/2 XXZ ladder by analyzing the variation of bipartite and multipartite entanglements. Our study characterizes the different ground state phases and notes the correspondence with known results, while highlighting the finer details that emerge from the behavior of ground state entanglement. Analysis of entanglement in the ground state provides a clearer picture of the complex ground state phase diagram of the system using only a moderate-size model.

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Ladder ising spin configurations. I. Heat capacity

Mejdani

Lambros

1996

Physica Status Solidi (b)

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We consider a ladder Ising spin model (with two coupled Ising spin chains), characterized by two couplings (interchain and intrachain couplings), to study in detail, in an analytical way, its thermal behaviour and particularly the variation of the specific heat versus temperature, the ratio of interaction constants, and the magnetic field. It is interesting that when the competition betwecn interchain and intrachain interactions is strong the specific heat exhibits a double peak and when the compctition is not, so strong the specific heat has a single peak. Further, without entering into details, we give, in a numerical way, some similar results for more complicated ladder configurations (with more than two linear king chains). The spin-; ladders or systems of spin chains may be realized in nature by vanadyl pyrophosphate ((VO),PzO7) or similar materials. All these intermediate systems are today important to gain further insight into the physics of one-dimensional spin chains and two-dimensional high-TL spin systems, both of which have shown interesting and unusual magnetic and superconducting properties. It is plausible that experimental and theoretical studies of ladders may lead to other interesting physical phenomena.

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S=1/2 Quantum Heisenberg Ladder andS=1 Haldane Phase

Cited by 58 publications

References 36 publications

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Detecting phase boundaries of quantum spin-1/2 XXZ ladder via bipartite and multipartite entanglement transitions

Ladder ising spin configurations. I. Heat capacity

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