Theory of criticality-enabled U(1) symmetry breaking in a class of 1+1D systems
Abstract
We develop an analytic theory of the recently proposed U(1) symmetry breaking at interacting 1+1D Lifshitz quantum critical points. The low-energy theory contains two compact fields, θ and ϕ, coupled by a Berry term that makes θ canonically conjugate to the conserved density ∂xϕ. Within a controlled large-N limit, we establish long-range order (LRO) of eiβθ and stretched-exponential decay of the conjugate vertex, log⟨ eiβϕ(x)e−iβϕ(0)⟩∝−|β|4/3|x|2/3. Beyond large N, we argue that U(1) LRO follows if the dynamical exponent satisfies z≠1, consistent with existing calculations. Using finite-size and infinite-system DMRG, we study an itinerant-electron chain with U(1)rtimesℤ2 symmetry, whose spin sector realizes this theory at a ferromagnetic quantum critical point. We find spin-nematic LRO in Si+Si+1+ and stretched-exponential electron Green's functions, revealing distinctive non-Gaussian signatures of criticality-enabled order.
Related
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BibTeX
@misc{andriyakhina2026theory,
title = {{Theory of criticality-enabled $U(1)$ symmetry breaking in a class of 1+1D systems}},
author = {E. S. Andriyakhina and A. S. Shankar and T. Senthil and Z. D. Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38581},
eprint = {2609.38581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38581},
}
RIS
TY - UNPB
TI - Theory of criticality-enabled U(1) symmetry breaking in a class of 1+1D systems
AU - E. S. Andriyakhina
AU - A. S. Shankar
AU - T. Senthil
AU - Z. D. Shi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2609.38581
UR - https://arxiv.org/abs/2609.38581
AB - We develop an analytic theory of the recently proposed U(1) symmetry breaking at interacting 1+1D Lifshitz quantum critical points. The low-energy theory contains two compact fields, θ and ϕ, coupled by a Berry term that makes θ canonically conjugate to the conserved density ∂_xϕ. Within a controlled large-N limit, we establish long-range order (LRO) of e^iβθ and stretched-exponential decay of the conjugate vertex, log⟨ e^iβϕ(x)e^−iβϕ(0)⟩∝−|β|^4/3|x|^2/3. Beyond large N, we argue that U(1) LRO follows if the dynamical exponent satisfies z≠1, consistent with existing calculations. Using finite-size and infinite-system DMRG, we study an itinerant-electron chain with U(1)rtimesℤ_2 symmetry, whose spin sector realizes this theory at a ferromagnetic quantum critical point. We find spin-nematic LRO in S_i^+S_i+1^+ and stretched-exponential electron Green's functions, revealing distinctive non-Gaussian signatures of criticality-enabled order.
ER -