Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions

Rakov, Mykhailo V.; Weyrauch, M.

doi:10.1088/2399-6528/aa7470

Cited by 10 publications

(12 citation statements)

References 65 publications

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“…8 (similar result was obtained in Ref. [32]). At criticality, θ/π = −1/4, the ground state energy is known 24,25 The boundary term, b, is found by subtracting the total bulk energy from the ground state energy for some large system size.…”

Section: Details Of the Simulationssupporting

confidence: 90%

Finite Size Scaling at the Topological Transition: Bilinear-Biquadratic Spin-1 Chain

Wang,

Zhang,

Kamenev

2019

Preprint

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We consider a finite size scaling across a topological phase transition between dimerized and Haldane phases in bilinear-biquadratic spin-1 chain. To this end we perform high-accuracy variational matrix product state simulations. We show that the scaling function, expressed in terms of L/ξ, where L is the chain length and ξ is the correlation length, coincides with that of three species of non-interacting massive Majorana fermions. This is in agreement with the fact that the critical theory of the model has central charge c = 3/2. On the other hand, the correlation length ξ exhibits a non-trivial dependence on parameters of the model.

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Section: Details Of the Simulationssupporting

confidence: 90%

Finite Size Scaling at the Topological Transition: Bilinear-Biquadratic Spin-1 Chain

Wang,

Zhang,

Kamenev

2019

Preprint

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“…3. They are compared to Bethe Ansatz results (N < 84) [12,13], exact diagonalization data [1] for small systems (N = 10 and N = 12) as well as DMRG data (N = 16,N = 32 and N = 64) we calculated with a code [23] explicitly implementing SU(2) symmetry. Two different fits to the HOTRG data based on Eq.…”

Section: The Critical Pointmentioning

confidence: 99%

Bilinear-biquadratic spin-1 model in the Haldane and dimerized phases

Rakov,

Weyrauch

2021

Preprint

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We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model in the dimerized and Haldane phases using a tensor renormalization method. At the critical point θ = −π/4 the finitesize spectrum predicted by the Wess-Zumino-Witten (WZW) model can only partly be confirmed. We find a singlet-singlet gap which does not fit into the WZW systematics. The results obtained are compared to Bethe Ansatz, exact diagonalization, and DMRG calculations for specific parameters.

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“…Theirin, the trajectory and phase plots of the system with bilinear and also biquadratic interactions. An algorithm for SU(2) symmetric matrix product states with periodic boundary conditions was implemented, where, it was applied to a study of the spectrum and correlation properties of the spin-1 bilinear-biquadratic Heisenberg model (Rakov and Weyrauch 2017).Very recently, it was shown that for a NLSE, whatever its formulation, is integrable (or completely integrable) when the real and imaginary parts are linearly dependent ). In the absence of biquadratic interactions, the (2 + 1) dimensional HFSC was currently studied in the Literature.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal-transverse soliton chains analog to heisenberg ferromagnetic spin chains in (2+1) dimensional with biquadrant interactions

Abdel‐Gawad

2022

Opt Quant Electron

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In quantum spin systems, lower energy state for a nuclear spin in an external field is spin ($$+1/2$$ + 1 / 2 ) while the higher energy state is spin ($$-1/2$$ - 1 / 2 ). A continuum analog to the discrete model led to nonlinear Schrodinger equation (NLSE) with higher order dispersion. Recently, a model equation with bilinear and biquadratic interactions in the (2 + 1) dimensional Heisenberg ferromagnetic spin chain (HFSC), was derived in the literature. This model equation is a NLSE with quartic dispersion and fifth degree nonlinearity, and it was rarely considered in the literature. The, only, work done has shown solitons solutions. This motivated us to consider this problem for inspecting the multiple characteristics of the HFSC in space-time. Here, the exact solutions of the HFSC biquadratic model equation are obtained by using the unified method (UM). In applications, it is found the UM is of low time cost in symbolic computations. So, we think that it prevails the known methods. The solutions obtained are evaluated numerically and shown in figures.These figures reveal that the solutions exhibit longitudinal-transverse (L-T) solitons chains (SCs) with presence (or absence) of tunneling, depending on the values of the parameters of high dispersivity and high nonlinearity. Also, L-T zig-zag SCs are observed, where pulses with higher amplitudes (or gaps) occur along a characteristic line. Furthermore, L-TSCs modulation along the space axes is shown. It is remarked that the contour plots show complex lattice waves, which is relevant to the spin chain system. So, the present work reveals new solitons structures induced by bilinear-biquadratic interactions of HFSC.

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Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions

Cited by 10 publications

References 65 publications

Finite Size Scaling at the Topological Transition: Bilinear-Biquadratic Spin-1 Chain

Finite Size Scaling at the Topological Transition: Bilinear-Biquadratic Spin-1 Chain

Bilinear-biquadratic spin-1 model in the Haldane and dimerized phases

Longitudinal-transverse soliton chains analog to heisenberg ferromagnetic spin chains in (2+1) dimensional with biquadrant interactions

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