Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.13782

Scalene Yang-Baxter triples realize all nearest-neighbour Hamiltonians with global additive symmetries

Pramod Padmanabhan·Somnath Maity·Akash Sinha·Vladimir Korepin
View original source ↗Read source document ↗Export metadata ↓

Abstract

We establish that bond Hamiltonian densities, up to local difference terms whose sum vanishes under periodic boundary conditions, lying in the commutant of bond operators, $w_j\pm w_{j+1}$, is a necessary and sufficient condition for a one-dimensional nearest-neighbour Hamiltonian to conserve a uniform or staggered sum of the one-site operators $w_j$. Starting from these local commutants, we show that every such Hamiltonian and its conserved charge can be obtained from monodromy matrices constructed using regular and non-regular members of scalene Yang-Baxter triples. The results hold on periodic chains of length $L\geq3$, with even length required in the staggered case. The results do not require translation invariance, and hence the interaction on each bond can be chosen independently from the full corresponding commutant. Our representation-independent construction applies in arbitrary finite local dimension and exhausts the Hamiltonians with either prescribed additive symmetry, without requiring ordinary Yang-Baxter integrability. We illustrate the construction with spin-$\tfrac12$ and spin-1 systems and discuss its relation to the double-commutant theorem. Classifying the one-site generators $w$ and their associated bond commutants provides a route to classifying such Hamiltonians with additive conserved charges.

Explore related subjects

cond-mat.stat-mechhep-thmath-phmath.MPnlin.SI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pramod Padmanabhan, Somnath Maity, Akash Sinha, Vladimir Korepin. 2026-10-09. Scalene Yang-Baxter triples realize all nearest-neighbour Hamiltonians with global additive symmetries. https://arxiv.org/abs/2610.13782

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

KEEP EXPLORING

Related papers

arXiv2026

Topologically quantized macroscopic attractor states in hydrated DNA

Driven dissipative systems at ambient conditions typically exhibit continuous responses shaped by fluctuations and relaxation, with discrete macroscopic states arising only under specific dynamical constraints. Here, we report the emergence of discrete attractor states in a quasi-two-dimensional hydrated DNA sample under magnetic excitation. The transverse polarization voltage $V_{xy}$ displays telegraph switching between well-defined levels, indicating stochastic transitions between metastable macroscopic states. Statistical analysis of the voltage time series reveals bimodal distributions and strong Bayesian model selection in favor of multiple coexisting states. A phenomenological phase-field framework describes the observed metastability and switching in terms of a proposed collective $U(1)$ polarization phase. Within this interpretation, phase-slip dynamics and integer-labeled winding sectors provide a possible organizing principle for the discrete macroscopic response. The results suggest that macroscopic quantization can emerge in a classical system at ambient conditions as a consequence of dissipative dynamics constrained by phase topology.

cond-mat.stat-mech↗
arXiv2026

Classification of topological phases of matter in stochastic systems

Topological phases of matter support edge states protected from random perturbations, and the identification of the discrete non-spatial symmetries and dimensions that support such phases was systematically developed for quantum systems and analogous platforms. While topological phases were also discovered in stochastic systems and posited as mechanisms for key biochemical processes, a classification consistent with their Markovian constraints remains lacking, impeding generalization to new scenarios. To address this, we develop new methods including a new homotopy approach, real-space invariants and a redefinition of the point gap to classify both transient and steady states. We find robust transient states in two symmetry classes, no symmetry and pseudo-Hermiticity respectively, while topological steady states are expected only in systems without symmetry. We identify the dimensions with non-trivial phases and their group structure, creating a rigorous framework for predicting robust behavior in active and living matter.

cond-mat.stat-mech↗
arXiv2026

Closed analytical form of many-body free volume and thermodynamics of monodisperse hard disks

The hard disk model is a fundamental reference system for excluded volume physics, liquid structure, and 2D ordering. Yet, despite its apparent simplicity, an analytical formulation of its thermodynamics has remained difficult because the free volume available to disks centers has a highly nontrivial many-body geometry. Here we show that this geometry admits a closed and exact representation: for any given hard disk configuration, the free volume can be analytically expressed through intersection areas of up to five exclusion disks. This provides a direct geometrical route from particle coordinates to the configurational partition function and entropy. We prove that the N disk partition function factorizes into a product of conditional free volumes and identify its two limiting asymptotic forms: the low density fluid regime controlled by extensive cavities and the high density fluid regime controlled by intensive private cells. Using the geometric measures computed from representative equilibrium particle configurations, the resulting theory reproduces the established hard disk equation of state over almost the entire density range up to close packing. At intermediate densities, the analysis reveals a mixed fluid regime in which localized caged defects provide an additional configurational entropy within the density interval preceding liquid hexatic coexistence. Finally, the five disk intersection area is shown to be a sensitive local scalar measure of hexagonal ordering, complementing the orientational order parameter and emphasizing the central role of many-body correlations.

cond-mat.stat-mech↗