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Scaling hypothesis for matrix product states

Bram Vanhecke (UGent) , Jutho Haegeman (UGent) , Karel Van Acoleyen (UGent) , Laurens Vanderstraeten (UGent) and Frank Verstraete (UGent)
Author
Organization
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  • QUTE (Quantum tensor networks and entanglement)
Abstract
We study critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theories. The critical point, exponents, and central charge are determined by optimizing them to obtain a data collapse. We benchmark this method by studying critical Ising and Potts models, where we also obtain a scaling Ansatz for the correlation length and entanglement entropy. The formulation of those scaling functions turns out to be crucial for studying critical quantum field theories on the lattice. For the case of lambda phi(4) with mass parameter mu(2) and lattice spacing a, we demonstrate a double data collapse for the correlation length delta xi(mu, lambda, D) = (xi) over tilde((alpha - alpha(c))(delta/a)(-1/nu)) with D the bond dimension, delta the gap between eigenvalues of the transfer matrix, and alpha(c) = mu(2)(R)/lambda the parameter which fixes the critical quantum field theory.
Keywords
RENORMALIZATION-GROUP

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Please use this url to cite or link to this publication:

MLA
Vanhecke, Bram, et al. “Scaling Hypothesis for Matrix Product States.” PHYSICAL REVIEW LETTERS, vol. 123, no. 25, 2019, doi:10.1103/physrevlett.123.250604.
APA
Vanhecke, B., Haegeman, J., Van Acoleyen, K., Vanderstraeten, L., & Verstraete, F. (2019). Scaling hypothesis for matrix product states. PHYSICAL REVIEW LETTERS, 123(25). https://doi.org/10.1103/physrevlett.123.250604
Chicago author-date
Vanhecke, Bram, Jutho Haegeman, Karel Van Acoleyen, Laurens Vanderstraeten, and Frank Verstraete. 2019. “Scaling Hypothesis for Matrix Product States.” PHYSICAL REVIEW LETTERS 123 (25). https://doi.org/10.1103/physrevlett.123.250604.
Chicago author-date (all authors)
Vanhecke, Bram, Jutho Haegeman, Karel Van Acoleyen, Laurens Vanderstraeten, and Frank Verstraete. 2019. “Scaling Hypothesis for Matrix Product States.” PHYSICAL REVIEW LETTERS 123 (25). doi:10.1103/physrevlett.123.250604.
Vancouver
1.
Vanhecke B, Haegeman J, Van Acoleyen K, Vanderstraeten L, Verstraete F. Scaling hypothesis for matrix product states. PHYSICAL REVIEW LETTERS. 2019;123(25).
IEEE
[1]
B. Vanhecke, J. Haegeman, K. Van Acoleyen, L. Vanderstraeten, and F. Verstraete, “Scaling hypothesis for matrix product states,” PHYSICAL REVIEW LETTERS, vol. 123, no. 25, 2019.
@article{8647425,
  abstract     = {We study critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theories. The critical point, exponents, and central charge are determined by optimizing them to obtain a data collapse. We benchmark this method by studying critical Ising and Potts models, where we also obtain a scaling Ansatz for the correlation length and entanglement entropy. The formulation of those scaling functions turns out to be crucial for studying critical quantum field theories on the lattice. For the case of lambda phi(4) with mass parameter mu(2) and lattice spacing a, we demonstrate a double data collapse for the correlation length delta xi(mu, lambda, D) = (xi) over tilde((alpha - alpha(c))(delta/a)(-1/nu)) with D the bond dimension, delta the gap between eigenvalues of the transfer matrix, and alpha(c) = mu(2)(R)/lambda the parameter which fixes the critical quantum field theory.},
  articleno    = {250604},
  author       = {Vanhecke, Bram and Haegeman, Jutho and Van Acoleyen, Karel and Vanderstraeten, Laurens and Verstraete, Frank},
  issn         = {0031-9007},
  journal      = {PHYSICAL REVIEW LETTERS},
  keywords     = {RENORMALIZATION-GROUP},
  language     = {eng},
  number       = {25},
  pages        = {6},
  title        = {Scaling hypothesis for matrix product states},
  url          = {http://dx.doi.org/10.1103/physrevlett.123.250604},
  volume       = {123},
  year         = {2019},
}

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