Snapshot Spectrum and Critical Phenomenon for Two-Dimensional Classical Spin Systems

Imura, Yukinari; Okubo, Tsuyoshi; Morita, Satoshi; Okunishi, Kouichi

doi:10.7566/jpsj.83.114002

Cited by 11 publications

(29 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, ensemble averaged snapshot spectra (EASS) are inevitably complicated by the ensemble disorder. For instance, the EASS at both critical temperature T C and very high temperature T T C look superficially similar to the spectra of random matrices, despite the former having a much higher (conformal) symmetry 27,28 . Ensemble disorder has also resulted in marked deviations from the snapshot entropy scaling law S χ ∼ aχ η log χ b derived in Refs.…”

Section: Introductionmentioning

confidence: 86%

See 1 more Smart Citation

Random-fractalAnsatzfor the configurations of two-dimensional critical systems

Lee¹,

Ozaki²,

Matsueda³

2016

Phys. Rev. E

View full text Add to dashboard Cite

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

show abstract

Section: Introductionmentioning

confidence: 86%

“…4,26, the onset of criticality in Ising and Potts models were unambiguously identified from the scaling behavior of their snapshot entropies. Subsequently, this scaling behavior was also rigorously shown 27,28 to yield the scaling exponent of the system.…”

Section: Introductionmentioning

confidence: 95%

Random-fractalAnsatzfor the configurations of two-dimensional critical systems

Lee¹,

Ozaki²,

Matsueda³

2016

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…If Γ/J is large enough in the disordered phase, WL configurations are eventually random in the spatial direction, so that a universal curve of the eigenvalue distribution can be expected, as in the case of the high-temperature limit of the 2D classical Ising model. 14) Another parameter is the effective aspect ratio of the WL snapshot defined as…”

Section: Disordered Phasementioning

confidence: 99%

“…For two-dimensional (2D) classical spin systems, very recently, a similar but different idea of the quantum entanglement was proposed for classical MC; a snapshot spectrum and snapshot entropy were defined for the singular value spectrum of a snapshot generated by a MC simulation. [13][14][15] It was shown that the snapshot spectrum gave hierarchical decomposition of snapshot images in Ref. [13], and a characteristic behavior of a snapshot entropy was also observed.…”

Section: Introductionmentioning

confidence: 99%

Snapshot Spectra in the World-Line Quantum Monte Carlo for One-Dimensional Quantum Spin Systems

Seki

Okunishi

2019

J. Phys. Soc. Jpn.

Self Cite

View full text Add to dashboard Cite

We introduce a snapshot density matrix and snapshot spectrum for world-line (WL) quantum Monte Carlo simulations, by integrating out the continuous-imaginary-time index of WL snapshots. For the transverse-field Ising chain, we reveal fundamental properties of the snapshot spectrum as follows. (i) In the ordered phase, the isolated peak corresponding to the maximum eigenvalue appears, indicating the classical nature of WL configurations. (ii) In the disordered phase, the spectrum converges to the dome-like distribution characterized by an effective aspect ratio of the snapshots. (iii) At the critical point, the power-law distribution is observed with an appropriate scaling analysis of the fixed aspect ratio. For the XXZ chain, we also obtain numerical results consistent with the above properties. In addition, the representation-basis dependence of the snapshot spectrum is also discussed.

show abstract

“…Recently, Matsueda et al proposed a new idea of the way to image analysis based on the singular value decomposition [21][22][23][24][25]. These previous studies suggested that the singular values λ j decay in a power law or exponentially reflecting the correlation scales shown in the image [21][22][23]. In the present section, we try to perform the singular value decomposition of an image by quantum annealing.…”

Section: A Singular Value Decomposition Of Two-dimensional Datamentioning

confidence: 99%

Singular-value decomposition using quantum annealing

et al. 2015

View full text Add to dashboard Cite

In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value decomposition requires the maximum eigenstate. The key idea is to transform the sign of the final Hamiltonian, and the maximum eigenstate is obtained by quantum annealing. Furthermore, the adiabatic time scale is obtained by the approximation focusing on the maximum eigenvalue.

show abstract

Snapshot Spectrum and Critical Phenomenon for Two-Dimensional Classical Spin Systems

Cited by 11 publications

References 21 publications

Random-fractalAnsatzfor the configurations of two-dimensional critical systems

Random-fractalAnsatzfor the configurations of two-dimensional critical systems

Snapshot Spectra in the World-Line Quantum Monte Carlo for One-Dimensional Quantum Spin Systems

Singular-value decomposition using quantum annealing

Contact Info

Product

Resources

About