BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg--Landau Model
Abstract
We study a one-dimensional fractional U(1) Ginzburg--Landau model whose quadratic part has Fourier multiplier |k|σ, focusing on the marginal case σ=1. This dispersion yields logarithmic spin-wave fluctuations, suggesting BKT-like behavior despite the one-dimensional setting. We sample the equilibrium Gibbs measure using stochastic Gross--Pitaevskii dynamics and analyze correlation functions, dimensionless ratios, effective exponents, and twist responses. The correlation function shows a low-temperature algebraic branch with a temperature-dependent exponent, while the high-temperature regime exhibits a nonlocal-kernel-induced tail consistent with C(r)∼ r−2. The correlation and Binder ratios are nearly size independent at low temperature and collapse with the BKT-type variable (T−TBKT)(log L)2; finite-size effects set in around T≃0.35−−0.4, consistent with TBKT≃0.35. Unlike the two-dimensional XY model, twist responses do not yield a finite helicity modulus: the ordinary linear-response quantity grows with system size, whereas the cusp twist response scales as L−η(T), like the squared zero-mode order parameter. Thus, the transition is BKT-like in correlation scaling, but lacks a universal helicity-modulus jump.
Versions
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BibTeX
@misc{endo2026bktlike,
title = {{BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional $U(1)$ Ginzburg--Landau Model}},
author = {Hitomi Endo and Michikazu Kobayashi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.00721},
eprint = {2609.00721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg--Landau Model
AU - Hitomi Endo
AU - Michikazu Kobayashi
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.00721
UR - https://arxiv.org/abs/2609.00721
AB - We study a one-dimensional fractional U(1) Ginzburg--Landau model whose quadratic part has Fourier multiplier |k|^σ, focusing on the marginal case σ=1. This dispersion yields logarithmic spin-wave fluctuations, suggesting BKT-like behavior despite the one-dimensional setting. We sample the equilibrium Gibbs measure using stochastic Gross--Pitaevskii dynamics and analyze correlation functions, dimensionless ratios, effective exponents, and twist responses. The correlation function shows a low-temperature algebraic branch with a temperature-dependent exponent, while the high-temperature regime exhibits a nonlocal-kernel-induced tail consistent with C(r)∼ r^−2. The correlation and Binder ratios are nearly size independent at low temperature and collapse with the BKT-type variable (T−T_BKT)(log L)^2; finite-size effects set in around T≃0.35−−0.4, consistent with T_BKT≃0.35. Unlike the two-dimensional XY model, twist responses do not yield a finite helicity modulus: the ordinary linear-response quantity grows with system size, whereas the cusp twist response scales as L^−η(T), like the squared zero-mode order parameter. Thus, the transition is BKT-like in correlation scaling, but lacks a universal helicity-modulus jump.
ER -