Tensor renormalization group study of the three-dimensional 
<i>O</i>
(2) model

Bloch, Jacques; Jha, Raghav G.; Lohmayer, Robert; Meister, Maximilian

doi:10.1103/physrevd.104.094517

Cited by 19 publications

(20 citation statements)

References 39 publications

(59 reference statements)

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“…In this talk we present first tensor-network results for the three-dimensional 𝑂 (2) model in thermal equilibrium at non-zero chemical potential and temperature [1]. We validate our results using benchmark data obtained with the worm algorithm [2][3][4].…”

Section: Introductionmentioning

confidence: 59%

“…𝑇 (1) → 𝑇 (2) 𝑇 (2) → 𝑇 (3) 𝑇 (3) → 𝑇 (4) 𝑇 (4) Figure 1: Typical blocking procedure in 2d HOTRG using alternating contraction directions. After each blocking a new local tensor is constructed.…”

Section: Higher Order Tensor Renormalization Groupmentioning

confidence: 99%

“…[16] for a review. Herein we present the first tensor-network study of the three-dimensional 𝑂 (2) model [1].…”

Section: Introductionmentioning

confidence: 99%

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Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature

Bloch¹,

Lohmayer²,

Meister³

2021

Preprint

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We present results of tensor-network simulations of the three-dimensional 𝑂 (2) model at nonzero chemical potential and temperature, which were computed using the higher-order tensorrenormalization-group method (HOTRG). This necessitated enhancements to the HOTRG blocking procedure to reduce the truncation error in the case of anisotropic tensors. Moreover, the construction of the truncated vector spaces was adapted to strongly reduce the effect of systematic errors in the computation of observables using the finite-difference method. Our (improved) HOTRG results for the evolution of the number density with the chemical potential are in agreement with results obtained with the worm algorithm, and both the Silver Blaze phenomenon at zero temperature and the temperature dependence of the number density can be adequately reproduced.

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Section: Introductionmentioning

confidence: 59%

Section: Higher Order Tensor Renormalization Groupmentioning

confidence: 99%

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Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature

Bloch¹,

Lohmayer²,

Meister³

2021

Preprint

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“…In practice we use an improved blocking strategy, which we call improved contraction order (ICO), where, at each blocking step, the contraction direction which yields the smallest (approximate) HOSVD truncation error is chosen [5,6].…”

Section: Tensor Methodsmentioning

confidence: 99%

Tensor-network simulation of the strong-coupling $U(N)$ model

Milde¹,

Bloch²,

Lohmayer³

2021

Preprint

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We apply tensor network methods to study the strong-coupling 𝑈 (𝑁) model in its dimer formulation. In three and four dimensions, we investigate the chiral condensate as a function of the quark mass and the degree of the symmetry group, and find good agreement with Monte Carlo simulations. Particularly interesting is the study of chiral symmetry breaking as a function of the mass and the volume, which clearly shows that this symmetry is spontaneously broken in the limit of infinite volume and zero mass.

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“…In this paper, we will focus on the triad method applied to the three-dimensional spin system especially the q-state Potts model and see how far we can go. This is a continuation of a long program of research where tensor networks have been applied extensively to spin systems and gauge theories in two and three dimensions [8][9][10][11][12][13]. Most of the tensor network studies of three-dimensional spin models are restricted to Ising model, however, there was a study of q = 3 Potts model in Ref.…”

Section: Introductionmentioning

confidence: 99%

Tensor renormalization of three-dimensional Potts model

Jha¹

2022

Preprint

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We study the q-state Potts models on a cubic lattice in the thermodynamic limit using tensor renormalization group transformations with the triad approximation. By computing the thermodynamic potentials, we locate the first-order phase transitions for 10 < q ≤ 20 which has not been explored using any method. We also examine the efficiency of the triad approximation method in obtaining the fixed-point tensor and comment on how this can be improved.

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Tensor renormalization group study of the three-dimensional O (2) model

Cited by 19 publications

References 39 publications

Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature

Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature

Tensor-network simulation of the strong-coupling $U(N)$ model

Tensor renormalization of three-dimensional Potts model

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