Visualizing the renormalization group flows with tensor network
DIPC Seminars
- Speaker
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Atsushi Ueda, University of Tokyo
- When
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2022/06/22
14:00 - Place
- Hybrid Seminar, Donostia International Physics Center
- Add to calendar
-
iCal
In recent years, tensor networks have become popular as a numerical means to
investigate quantum/classical systems. Especially in one-dimensional quantum
systems, they have contributed widely to classifying critical phenomena and
topological phases due to their compatibility with conformal field theory.
[1-2] Similarly, in the two-dimensional classical critical model, it has been
shown that the scaling dimension and central charge can be calculated using
the fixed point tensor obtained by tensor network renormalization, and has
attracted attention as a "new way to solve old problems." [3]
In this presentation, we will show that the renormalization group flow (RG
flow), the phase diagram around a critical point, can also be computed
quantitatively using tensor network renormalization.[4] As a practical
example, we will calculate the coupling constants in field theory at each
scale from the classical XY model and show that they are consistent with the
Kosterlitz RG flow. If time permits, we will introduce applications to the
RP^2 model, a more complex classical two-dimensional system. [5]
[1] P. Calabrese and J. Cardy, J. Phys. A: Math. Theor. 42, 504005 (2009).
[2] F. Pollmann et al, Phys. Rev. B 81, 064439 (2010).
[3] ZC. Gu and XG. Wen, Phys. Rev. B 80, 155131 (2009).
[4] A. Ueda and M. Oshikawa, Phys. Rev. B 104, 165132 (2021).
[5] A. Ueda and M. Oshikawa, arXiv:2202.07042 (2022).
Host: Roman Orus
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