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arXiv:2605.19421

Fractonic Constraints and Magnetic Order in a Dipole-Conserving Spin Chain

Prabhakar, Giuseppe De Tomasi, Soumya Bera

Published May 19, 2026• 0 citations
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Abstract

This work investigates the competition between dipole conservation, which imposes strong dynamical constraints and prevents the propagation of isolated spin excitations, and Ising-type interactions that favor ordering. Specifically, we explore the ground state phase diagram of a one-dimensional spin chain in the presence of both fractonic constraints and interactions. Despite the kinetic constraints, the system stabilizes an antiferromagnetic dipole-ordered ground state, where the ordering occurs at the level of spin pairs rather than individual spins. At a large Ising interaction strength, the model undergoes a phase transition from a dipole-ordered phase to a spin antiferromagnetic phase. In contrast, for ferromagnetic Ising interactions, the model exhibits both antiferromagnetic and ferromagnetic dipole ordered phases. At sufficiently large negative interaction strength, the dipole ordered phase transitions to a ferromagnetic phase with conventional spin ferromagnetic order. To characterize these distinct phases, we employ density matrix renormalization group (DMRG) simulations alongside large-scale diagonalization. We analyze appropriate order parameters, along with features of the entanglement spectrum and dynamical spectral functions. In limiting cases, the observed transitions can be understood by mapping the dipole conserving model onto effective XXZ models in a restricted Hilbert space of composite spins.

DOI
10.48550/arxiv.2605.19421

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This work investigates the competition between dipole conservation, which imposes strong dynamical constraints and prevents the propagation of isolated spin excitations, and Ising-type interactions that favor ordering. Specifically, we explore the ground state phase diagram of a one-dimensional spin chain in the presence of both fractonic constraints and interactions. Despite the kinetic constraints, the system stabilizes an antiferromagnetic dipole-ordered ground state, where the ordering occurs at the level of spin pairs rather than individual spins. At a large Ising interaction strength, the model undergoes a phase transition from a dipole-ordered phase to a spin antiferromagnetic phase. In contrast, for ferromagnetic Ising interactions, the model exhibits both antiferromagnetic and ferromagnetic dipole ordered phases. At sufficiently large negative interaction strength, the dipole ordered phase transitions to a ferromagnetic phase with conventional spin ferromagnetic order. To characterize these distinct phases, we employ density matrix renormalization group (DMRG) simulations alongside large-scale diagonalization. We analyze appropriate order parameters, along with features of the entanglement spectrum and dynamical spectral functions. In limiting cases, the observed transitions can be understood by mapping the dipole conserving model onto effective XXZ models in a restricted Hilbert space of composite spins.
We investigate the zero-temperature phase diagram of a one-dimensional constrained quantum spin chain realized in coherently driven Rydberg-atom arrays with competing local Rabi driving and dipole-dipole exchange interactions. Projecting onto the blockade-constrained Hilbert space yields an effective model in which local and nonlocal quantum fluctuations compete on equal footing. Combining exact diagonalization, the density-matrix renormalization group, and variational uniform matrix-product-state calculations, we establish a complete phase diagram comprising a Luttinger liquid, an antiferromagnetic ordered phase, and a polarized paramagnet. We identify two distinct mechanisms for the destruction of antiferromagnetic order: a conventional Ising transition at strong driving and a continuous quantum melting into the Luttinger liquid at weak driving, characterized using entanglement-based diagnostics and finite-entanglement scaling. In addition, we uncover an exact ground-state factorization line embedded within the ordered phase, providing an analytically tractable zero-entanglement reference point for experiments with programmable Rydberg quantum simulators.
The ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain is studied with Ising-type anisotropy on the ferromagnetic bond. This model tends to the spin-1 antiferromagnetic Heisenberg chain with on-site anisotropy in the limit of strong ferromagnetic bond. It is found that the Haldane-gap phase, the large-D phase, and the two types of N\'eel phases appear as the ground state of this model. The duality relations between these four phases are proved for several limiting cases. The string order parameter characterizing the large-D phase is introduced based on these duality relations. The ground-state phase diagram is determined by the numerical diagonalization of the finite-size system.
We investigate the ground-state phase diagram of the spin-1 Kitaev–Heisenberg (KH) chain in the presence of uniaxial single-ion anisotropy D z using the density-matrix renormalization-group method. The relative strength of the Heisenberg and Kitaev interactions is parametrized by a coupling angle ϕ , defined by J = cos ϕ and K = sin ϕ . By combining energy-based diagnostics with finite-size extrapolations of order parameters and correlation functions, we obtain a comprehensive phase diagram as a function of ϕ and D z . The phase diagram contains ferromagnetic and Néel ordered phases, collinear states with four-site spin modulation, magnetically disordered or critical regimes, two Kitaev-dominated spin-liquid-like regions, and a topological Haldane phase near the Heisenberg limit. We find that the Kitaev-dominated disordered regions acquire finite parameter widths in the spin-1 model, whereas the Haldane phase is fragile against Kitaev-type anisotropy, especially for D z < 0 . Positive D z generally suppresses magnetic order and expands nonmagnetic regimes, while negative D z enhances Ising-like magnetic order. At D z = 0 , we also identify an exactly solvable point at tan ϕ = − 2 ( ϕ / π ≃ 1.6476 ) , which gives rise to a first-order transition between the Néel- z state and a four-site collinear state. We further contrast these findings with the spin- 1 / 2 KH chain and with the spin-1 honeycomb KH model, highlighting the distinct roles of single-ion anisotropy and dimensionality in Kitaev-type magnets.
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We study the behavior of a model of two XXZ spin chains coupled by an isotropic exchange interaction JK{\mathit{J}}_{\mathit{K}}JK​ as the anisotropies and spin velocities in the individual chains are varied. In the limit of large antiferromagnetic JK{\mathit{J}}_{\mathit{K}}JK​ we map the model's low-energy sector onto an Ising model in a transverse field; in the limit of large ferromagnetic JK{\mathit{J}}_{\mathit{K}}JK​ we map the model's low-energy sector onto that of a single spin-one chain. For small JK{\mathit{J}}_{\mathit{K}}JK​, we study the model perturbatively via Abelian and non-Abelian bosonization. We determine the possible phases, approximate locations of the phase boundaries, universality classes of the transitions, and asymptotic behavior of correlation functions. We believe our model captures the essential physics of the interplay between the compensation of local moments and magnetic ordering, which may be important for the heavy-fermion materials.
We study the role of long-range dipolar interactions on antiferromagnetic spin chains, from the classical $S\ensuremath{\rightarrow}\ensuremath{\infty}$ limit to the deep quantum case S=1/2S=1/2S=1/2, including a transverse magnetic field. To this end, we combine different techniques such as classical energy minima, classical Monte Carlo, linear spin waves, bosonization, and density matrix renormalization group (DMRG). We find a phase transition from the already reported dipolar ferromagnetic region to an antiferromagnetic region for high enough antiferromagnetic exchange. Thermal and quantum fluctuations destabilize the classical order before reaching magnetic saturation in both phases, and also close to zero field in the antiferromagnetic phase. In the extreme quantum limit S=1/2S=1/2S=1/2, extensive DMRG computations show that the main phases remain present with transition lines to saturation significatively shifted to lower fields, in agreement with the bosonization analysis. The overall picture maintains a close analogy with the phase diagram of the anisotropic XXZ spin chain in a transverse field.