Learning the Effective Spin Hamiltonian of a Quantum Magnet

Yu, Sizhuo; Gao, Yuan; Chen, Binbin; Li, Wei

doi:10.1088/0256-307x/38/9/097502

Cited by 13 publications

(15 citation statements)

References 70 publications

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“…For each trial parameter set, we compute the same thermodynamic quantities from the model by using the XTRG solver [33,40]. We search for the parameter set that minimizes the total loss function through an unbiased and efficient Bayesian optimization process [31]. See Methods for more details.…”

Section: Resultsmentioning

confidence: 99%

“…The index α labels different physical quantities, e.g., magnetic specific heat and susceptibilities, and N α counts the number of data points in O α . The optimization of L over the parameter space spanned by {J xy , J z , J PD , J Γ } is conducted via the Bayesian optimization [31]. The Landé factor g ab,c and the Van Vleck paramagnetic susceptibilities χ vv ab,c are optimized via the Nelder-Mead algorithm for each fixing {J xy , J z , J PD , J Γ }.…”

Section: Methodsmentioning

confidence: 99%

“…In practice, we perform the automatic parameter searching using the package QMagen developed by some of the authors [31,57], and the results shown in the main text are obtained via over 450 Bayesian iterations. After that, we introduce an additional parameter, the next-nearest-neighbor Heisenberg term J 2 , and perform another 400 searching iterations.…”

Section: Methodsmentioning

confidence: 99%

“…We establish the microscopic description of NBCP with realistic model parameters by fitting the model to intermediate-and high-temperature experimental thermal data. We expedite the fitting process by using the Bayesian optimization [31] equipped with an efficient quantum manybody thermodynamic solver -exponential tensor renormalization group (XTRG) [32,33]. Our model is corroborated by reproducing quantitatively the experimental low-temperature magnetization curves by density matrix renormalization group (DMRG) [34] calculations.…”

Section: Introductionmentioning

confidence: 91%

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Spin Supersolidity in Nearly Ideal Easy-axis Triangular Quantum Antiferromagnet Na$_2$BaCo(PO$_4$)$_2$

Gao¹,

Fan²,

Li³

et al. 2022

Preprint

Self Cite

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Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na2BaCo(PO4)2 (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular lattice antiferromagnet with significant easyaxis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network quantum many-body simulations, we establish a microscopic model description of this material with realistic model parameters. The resulted model can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. As a consequence, the NBCP hosts a spin supersolid state that breaks both the lattice translational and spin U(1) symmetries. The NBCP therefore represents an ideal material platform to explore the field-tunable quantum phase transitions and Berezinskii-Kosterlitz-Thouless melting of the spin supersolidity.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

See 2 more Smart Citations

Spin Supersolidity in Nearly Ideal Easy-axis Triangular Quantum Antiferromagnet Na$_2$BaCo(PO$_4$)$_2$

Gao¹,

Fan²,

Li³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A difficult step in the quantification of models has been inversion from measured data to a model-the so-called inverse scattering problem, which is usually ill-posed due to loss of phase information. In this regard, machine learning (ML) [74,75] has shown promising results [76][77][78][79][80]. Here we combine ML approaches with large-scale semi-classical simulations (SCSs) [80].…”

mentioning

confidence: 99%

Extraction of the interaction parameters for $α-$RuCl$_3$ from neutron data using machine learning

Samarakoon,

Laurell,

Balz

et al. 2022

Preprint

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FIG. 2. (a) Machine-learned phase map varying Γ/|K| and J 3 /|K| through the optimal solution for α-RuCl 3 at fixed J 1 /|K| = −0.1 and J 2 /|K| = 0, with K < 0. Labeled phases include ferromagnetic [FM], zigzag [Z.Z.] and planar zigzag [Z.Z. (2D)] orders. The ellipsoidal approximation to the optimal solution is marked in panel (a) in dark-red. Due to uneven sampling of the IMA process from which the data was taken, the prediction accuracy varies in parameter space resulting in a blotchy appearance. The different colors, which represent different structure factors S (Q), are predicted by a trained neural network as explained in the main text. Panel (b) shows the surrogate predicted neutron structure factor, S Sur (Q), at numbered locations indicated in (a) and Fig. 1(c). Corresponding spin structures for the long-range ordered phases labeled 1, 3-7 are given in the SM [21]. Note that Z.Z. and Z.Z. (2D) have similar long-range order, but along different spin-orientation directions. This occurs because, as discussed in Ref. [22], when K < 0 the spin orientation in zigzag ground states depends on the sign of Γ. Due to the neutron spin polarization factor, the two S (Q) are different in the shown plane, despite yielding the same trace over spin correlations, α S αα (Q). Some of the diffuse S (Q), taken at either phase boundaries or critical points, are also shown. The S (Q) labeled 11 and 12 are for the pure AFM and FM Kitaev models.

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Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2

Gao

Fan

et al. 2022

npj Quantum Mater.

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Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na2BaCo(PO4)2 (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. According to the established model, the NBCP hosts a spin supersolid state that breaks both the lattice translation symmetry and the spin rotational symmetry. Such a state is a spin analog of the long-sought supersolid state, thought to exist in solid Helium and optical lattice systems, and share similar traits. The NBCP therefore represents an ideal material-based platform to explore the physics of supersolidity as well as its quantum and thermal melting.

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Learning the Effective Spin Hamiltonian of a Quantum Magnet

Cited by 13 publications

References 70 publications

Spin Supersolidity in Nearly Ideal Easy-axis Triangular Quantum Antiferromagnet Na$_2$BaCo(PO$_4$)$_2$

Spin Supersolidity in Nearly Ideal Easy-axis Triangular Quantum Antiferromagnet Na$_2$BaCo(PO$_4$)$_2$

Extraction of the interaction parameters for $α-$RuCl$_3$ from neutron data using machine learning

Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2

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