arXiv subjects

Wen-Yu Su

Publications and source records attributed to Wen-Yu Su.

3 recordsLinked to original sources

arXiv2025

On the criticality of the configuration-space statistical geometry

While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the statistics of pairwise distances $r_H$ between configurations. Focusing on the concrete example of Ising spins, we establish crucial analytical links between this geometry and fundamental real-space observables, i.e., the magnetization and two-point spin correlation functions. This link unveils the universal scaling law in the configuration space: the standard deviation of the normalized distances exhibits universal criticality as $\sqrt{\mathrm{Var}(r_H)}\sim L^{-2\beta/\nu}$, provided that the system possesses zero magnetization and satisfies $4\beta/\nu < d$. We validate this scaling with stochastic series expansion quantum Monte Carlo simulations of the transverse-field Ising model(TFIM). Furthermore, we propose configuration-space diagnostics that go beyond local real-space observables. First, the distribution probability $P(r_H)$ parameterized by the transverse field $h$ forms a one-dimensional manifold. Information-geometric analyses, particularly the Fisher information defined on this manifold, successfully pinpoint the TFIM phase transition, regardless of the measurement basis. Second, for the Su-Schrieffer-Heeger Heisenberg model, a parity index derived from $P(r_H)$ successfully characterizes the symmetry-protected topological phase and its transition. Our work establishes configuration space geometry as a novel perspective on quantum criticality, revealing how macroscopic universal phenomena are encoded within its global statistical features.

cond-mat.stat-mech↗

arXiv2024

Probing phase transitions with correlations in configuration space

In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we show that the generic correlation of distances between configurations, with a degree of freedom proportional to the lattice size, can probe phase transitions using importance sampling procedures like Monte Carlo simulations. The distribution of sampled distances varies significantly across different phases, suggesting universal critical behavior for uncertainty and participation entropy. For various classical spin models with different phases and transitions, finite-size analysis based on these quantities accurately identifies phase transitions and critical points. Notably, in all cases, the critical exponent derived from the uncertainty of distances equals the anomalous dimension governing real-space correlation decay. Thus, configuration space correlations, defined by distance uncertainties, share the same decay ratio as real-space correlations, determining the universality class of phase transitions. This work applies to diverse lattice models with different local degrees of freedom, e.g., two levels for Ising-like models, discrete multi-levels for q-state clock models, and continuous local levels for the XY model, offering a robust, alternative method for understanding complex phases and transitions.

cond-mat.stat-mech↗

arXiv2023

Investigating Berezinskii-Kosterlitz-Thouless phase transitions in Kagome spin ice by quantifying Monte Carlo process: Distribution of Hamming distances

We reinvestigate the phase transitions of the Ising model on the Kagome lattice with antiferromagnetic nearest-neighbor and ferromagnetic next-nearest-neighbor interactions, which has a six-state-clock spin ice ground state and two consecutive Berezinskii-Kosterlitz-Thouless (BKT) phase transitions. Employing the classical Monte Carlo (MC) simulations, the phases are characterized by the magnetic order parameter, and the critical temperatures are obtained by the finite-size scaling of related physical quantities. Moreover, we attempt to gain general information on the phase transitions from the MC process instead of MC results and successfully extract the correct transition points with surprisingly high accuracy. Specifically, we focus on the selected data set of uncorrelated MC configurations and quantify the MC process using the distribution of two-configuration Hamming distances in this small data collection. This distribution is more than a quantity that features different behaviors in different phases but also nicely supports the same BKT scaling form as the order parameter, from which we successfully determine the two BKT transition points with surprisingly high accuracy. We also discuss the connection between the phase transitions and the intrinsic dimension extracted from the Hamming distances, which is widely used in the growing field of machine learning and is reported to be able to detect critical points. Our findings provide a new understanding of the spin ice transitions in the Kagome lattice and can hopefully be used similarly to identify transitions in the quantum system on the same lattice with strong frustrations.

cond-mat.stat-mech↗