Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B./Physical review. B

Principal component analysis of quantum phase transitions and crossovers using dynamical functional data

Anonymous

Published Sep 21, 2026• 0 citations
Publisher
DOI
10.1103/4hrw-196g

Related papers

Quantum data compression by principal component analysis

Chao‐Hua Yu, Fei Gao, Song Lin +1 more

arXiv:1810.10710•Quantum Information Processing•Jul 1, 2019•86 citations

Principal Component Analysis of quantum correlation

Renzo Mosetti

arXiv:1603.00872•The European Physical Journal Plus•Dec 1, 2016•3 citations

Machine learning of frustrated classical spin models (II): Kernel principal component analysis

Ce Wang, Hui Zhai

In this work, we apply a principal component analysis (PCA) method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previous work with the linear PCA method, the kernel PCA can capture nonlinear functions. In this case, the Z 2 chiral order of the classical spins in these lattices is indeed a nonlinear function of the input spin configurations. In addition to the principal component revealed by the linear PCA, the kernel PCA can find two more principal components using the data generated by Monte Carlo simulation for various temperatures as the input. One of them is related to the strength of the U (1) order parameter, and the other directly manifests the chiral order parameter that characterizes the Z 2 symmetry breaking. For a temperature-resolved study, the temperature dependence of the principal eigenvalue associated with the Z 2 symmetry breaking clearly shows second-order phase transition behavior.

arXiv:1803.01205•Frontiers of Physics•Jun 13, 2018•50 citations

A Detailed View of Quantum Phase Transitions

Science•Jan 28, 2000•0 citations

Principal component analysis of absorbing state phase transitions

Cristiano Muzzi, Ronald Santiago Cortes, Devendra Singh Bhakuni +4 more

We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes-directed bond percolation and branching and annihilating random walks with an even number of offspring. We find that the uncentered PCA of data sets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation, we are furthermore able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of data sets.

arXiv:2405.12863•Physical review. E•Dec 12, 2024•8 citations

Phase transition extracted by principal component analysis in the disordered Moore–Read state

Na 娜 Jiang 江, Shuaixin 帅鑫 Fu 付, Zhengzhi 正直 Ma 马 +1 more

Abstract We study the influence of disorder on the Moore–Read state by principal component analysis (PCA), which is one of the ground state candidates for the 5/2 fractional Hall state. By using PCA, the topological features of the ground state wave functions with different disorder strengths can be distilled. As the disorder strength increases, the Moore–Read state will be destroyed. We explore the phase transition by analyzing the overlaps between the random sample wave functions and the topologically distilled state. The cross-point between the amplitudes of the principal component and its counterpart is the phase transition point. Additionally, the origin of the second component comes from the excited states, which is different from the Laughlin state.

Chinese Physics B•Feb 5, 2025•1 citation
In this work, we apply a principal component analysis (PCA) method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previous work with the linear PCA method, the kernel PCA can capture nonlinear functions. In this case, the Z 2 chiral order of the classical spins in these lattices is indeed a nonlinear function of the input spin configurations. In addition to the principal component revealed by the linear PCA, the kernel PCA can find two more principal components using the data generated by Monte Carlo simulation for various temperatures as the input. One of them is related to the strength of the U (1) order parameter, and the other directly manifests the chiral order parameter that characterizes the Z 2 symmetry breaking. For a temperature-resolved study, the temperature dependence of the principal eigenvalue associated with the Z 2 symmetry breaking clearly shows second-order phase transition behavior.
We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes-directed bond percolation and branching and annihilating random walks with an even number of offspring. We find that the uncentered PCA of data sets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation, we are furthermore able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of data sets.
Abstract We study the influence of disorder on the Moore–Read state by principal component analysis (PCA), which is one of the ground state candidates for the 5/2 fractional Hall state. By using PCA, the topological features of the ground state wave functions with different disorder strengths can be distilled. As the disorder strength increases, the Moore–Read state will be destroyed. We explore the phase transition by analyzing the overlaps between the random sample wave functions and the topologically distilled state. The cross-point between the amplitudes of the principal component and its counterpart is the phase transition point. Additionally, the origin of the second component comes from the excited states, which is different from the Laughlin state.