Crossover duality for the quantum long-range Ising chain: perturbation theory around the short-range endpoint and a DMRG test
Abstract
We propose a weakly coupled description of the long-range transverse-field Ising chain near its short-range crossover at s*=7/4, where the couplings decay as r−1−s. The Ising conformal field theory is coupled to an instantaneous Gaussian field through σχ, extending the classical long-range Ising duality to quantum chains. The equal-time interaction generates a stress-tensor deformation that causes the velocity to run and renormalizes the dynamical critical exponent z. Conformal perturbation theory gives z=1−0.720 δ+O(δ2), 1/ν=(1+z)/2+O(δ2), and ω=δ+O(δ2), with δ=s*−s. DMRG calculations on periodic chains of up to $128$ sites provide a consistency test using theoretical inputs for 1/ν and ω. After accounting for slow finite-size corrections, static and dynamical estimates of z agree, supporting the crossover expansion at s=1.5 and a two-sided Padé interpolation at s=1, $1.25$, and $1.5$.
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BibTeX
@misc{rong2026crossover,
title = {{Crossover duality for the quantum long-range Ising chain: perturbation theory around the short-range endpoint and a DMRG test}},
author = {Junchen Rong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05284},
eprint = {2611.05284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05284},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Crossover duality for the quantum long-range Ising chain: perturbation theory around the short-range endpoint and a DMRG test
AU - Junchen Rong
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05284
UR - https://arxiv.org/abs/2611.05284
AB - We propose a weakly coupled description of the long-range transverse-field Ising chain near its short-range crossover at s_*=7/4, where the couplings decay as r^−1−s. The Ising conformal field theory is coupled to an instantaneous Gaussian field through σχ, extending the classical long-range Ising duality to quantum chains. The equal-time interaction generates a stress-tensor deformation that causes the velocity to run and renormalizes the dynamical critical exponent z. Conformal perturbation theory gives z=1−0.720 δ+O(δ^2), 1/ν=(1+z)/2+O(δ^2), and ω=δ+O(δ^2), with δ=s_*−s. DMRG calculations on periodic chains of up to $128$ sites provide a consistency test using theoretical inputs for 1/ν and ω. After accounting for slow finite-size corrections, static and dynamical estimates of z agree, supporting the crossover expansion at s=1.5 and a two-sided Padé interpolation at s=1, $1.25$, and $1.5$.
ER -