Onset of incommensurability at the valence-bond-solid point in the<i>S</i>=1 quantum spin chain

Schollwöck, Ulrich; Jolicœur, Thierry; Garel, Thomas

doi:10.1103/physrevb.53.3304

Cited by 156 publications

(204 citation statements)

References 48 publications

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“…This is a topological phase, containing for θ = arctan(1/3) the AKLT point 28 whose ground state can be written in terms of matrix product states. The entire phase is characterized by free edge spins and a non vanishing string order parameter 22,29 :…”

Section: The Spin-1 Chain In a Uniaxial Field: Previous Resultsmentioning

confidence: 99%

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

2011

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The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry breaking field as well as the emergence of novel phases. Previous studies have analyzed the effect of such uniaxial anysotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anysotropy. To this aim, we employ the density matrix renormalization group (DMRG) together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect.

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Section: The Spin-1 Chain In a Uniaxial Field: Previous Resultsmentioning

confidence: 99%

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

2011

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“…Finally, Eq. (7) can be used to realize the most general spin-1 bilinear-biquadratic model 75 with the Y 2,0 angular dependence 69 . It would be particularly interesting to follow Refs.…”

Section: Applications To Exotic Quantum Magnetismmentioning

confidence: 99%

Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

et al. 2013

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Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHoxY1−xF4.Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases.

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“…16) θ AKLT = arctan 1/3, the ground state is exactly known to be a valence bond solid, and for θ > θ AKLT the spin correlation functions become incommensurate. 22,27 Between the ULS point and θ = π/2, the system is gapless and shows antiferroquadrupolar spin-nematic quasi long range order (QLRO). 24 For negative values of θ, between θ = −3/4π and θ = −π/4 the system is dimerized and has a finite gap.…”

Section: Introductionmentioning

confidence: 99%

“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24] For our considerations, it is helpful to keep in mind the following aspects of its phase diagram. Between the two integrable points θ TB = −π/4 (the TakhtajanBabujian point, 14,15 TB) and θ ULS = π/4 (the Uimin-LaiSutherland point, [11][12][13] ULS) the chain possesses a finite Haldane gap.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadraticS=1Heisenberg chain in a magnetic field

et al. 2011

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We investigate the properties of the Heisenberg S = 1 chain with bilinear and biquadratic interactions in a magnetic field using the Density Matrix Renormalization Group, Bethe ansatz and field theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This liquid undergoes a continuous pair unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector chiral phase.

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Onset of incommensurability at the valence-bond-solid point in theS=1 quantum spin chain

Cited by 156 publications

References 48 publications

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadraticS=1Heisenberg chain in a magnetic field

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