Tensor Network Calculation of the Logarithmic Correction Exponent in the <i>XY</i> Model

Hong, Seongpyo; Kim, D.-H.

doi:10.7566/jpsj.91.084003

Cited by 6 publications

(3 citation statements)

References 57 publications

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“…In ref. [16], where the classical XY model is analyzed, the octagonal tensor ring is prepared by the full SVDs without any approximation, and the bond dimensions are truncated by entanglement filtering projectors after that; it has numerically shown that this choice improves the speed of convergence significantly. In the numerical works in our current paper, we adopt their choice for the initial condition of the loop optimization step.…”

Section: Loop-tnr (Entanglement Filtering and Loop Optimization)mentioning

confidence: 99%

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Improved coarse-graining methods for two dimensional tensor networks including fermions

Asaduzzaman

Catterall

Meurice

et al. 2023

J. High Energ. Phys.

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We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson-Majorana fermions and for the two flavor Gross-Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher’s zeros.

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Section: Loop-tnr (Entanglement Filtering and Loop Optimization)mentioning

confidence: 99%

“…and will show more complicated fixed point structure. Indeed, precise investigations on the classical XY model have been reported with the use of the loop-TNR [16,34]. Thus applying the improved methods to the staggered Thirring model would be a legitimate direction to gain some new insights.…”

Section: Jhep01(2023)024mentioning

confidence: 99%

Improved coarse-graining methods for two dimensional tensor networks including fermions

Asaduzzaman

Catterall

Meurice

et al. 2023

J. High Energ. Phys.

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show abstract

“…and will show more complicated fixed point structure. Indeed, precise investigations on the classical XY model have been reported with the use of the loop-TNR [18,19]. Thus applying the improved methods to the staggered Thirring model would be a legitimate direction to gain some new insights.…”

Section: Ryo Sakaimentioning

confidence: 99%

Entanglement filtering and improved coarse-graining on two dimensional tensor networks including fermions

Sakai¹,

Asaduzzaman²,

Catterall³

et al. 2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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Tensor renormalization group (TRG) has attractive features like the absence of sign problems and the accessibility to the thermodynamic limit, and many applications to lattice field theories have been reported so far. However it is known that the TRG has a fictitious fixed point that is called the CDL tensor and that causes less accurate numerical results. There are improved coarse-graining methods that attempt to remove the CDL structure from tensor networks. Such approaches have been shown to be beneficial on two dimensional spin systems. We discuss how to adapt the removal of the CDL structure to tensor networks including fermions, and numerical results that contain some comparisons to the plain TRG, where significant differences are found, will be shown. The detailed discussion of this work is given in ref. [1].

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Tensor network based finite-size scaling for two-dimensional Ising model

et al. 2023

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Tensor Network Calculation of the Logarithmic Correction Exponent in the XY Model

Cited by 6 publications

References 57 publications

Improved coarse-graining methods for two dimensional tensor networks including fermions

Improved coarse-graining methods for two dimensional tensor networks including fermions

Entanglement filtering and improved coarse-graining on two dimensional tensor networks including fermions

Tensor network based finite-size scaling for two-dimensional Ising model

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