Jordan-Wigner mapping between quantum-spin and fermionic Casimir effects

Katsumasa Nakayama; Kei Suzuki

Home/Archive/arXiv

arXiv · 2601.18867

Jordan-Wigner mapping between quantum-spin and fermionic Casimir effects

Katsumasa Nakayama·Kei Suzuki

View original source ↗Read source document ↗Export metadata ↓

Abstract

The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.

Explore related subjects

cond-mat.stat-mech cond-mat.mes-hall cond-mat.str-el hep-th quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Katsumasa Nakayama, Kei Suzuki. 2026-01-26. Jordan-Wigner mapping between quantum-spin and fermionic Casimir effects. https://arxiv.org/abs/2601.18867

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗