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arXiv:2607.25806

Kinetically induced order from mobility-constrained excitations

Aprem P. Joy, Urban F. P. Seifert

Published Jul 28, 2026• 0 citations
arXivHTMLPDF

Abstract

A fascinating feature of strongly correlated systems is that excitations may carry nontrivial quantum numbers under emergent symmetries which, in some cases, may strongly constrain their motion. We show that such constrained excitations can play a central role in driving symmetry-breaking long-range order through a kinetic mechanism: coupling to a local order-parameter field activates the mobility of otherwise constrained excitations, and condensation of the order parameter then enables a large gain in kinetic energy, thereby stabilizing a phase with long-range order. We illustrate this mechanism in two settings: (i) a dimerization instability in a spin chain with a magnetization dipole conservation law, and (ii) itinerant magnetism of electrons in the Kitaev-Kondo model, where charge carriers couple to local moments that form a spin liquid. This mechanism becomes operative whenever a finite density of mobility-constrained excitations is present, either through non-equilibrium preparation or thermal activation. In the latter case, we argue that increasing temperature can, counterintuitively, promote order by enhancing the kinetic-energy gain of thermally activated excitations.

DOI
10.48550/arxiv.2607.25806

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A fascinating feature of strongly correlated systems is that excitations may carry nontrivial quantum numbers under emergent symmetries which, in some cases, may strongly constrain their motion. We show that such constrained excitations can play a central role in driving symmetry-breaking long-range order through a kinetic mechanism: coupling to a local order-parameter field activates the mobility of otherwise constrained excitations, and condensation of the order parameter then enables a large gain in kinetic energy, thereby stabilizing a phase with long-range order. We illustrate this mechanism in two settings: (i) a dimerization instability in a spin chain with a magnetization dipole conservation law, and (ii) itinerant magnetism of electrons in the Kitaev-Kondo model, where charge carriers couple to local moments that form a spin liquid. This mechanism becomes operative whenever a finite density of mobility-constrained excitations is present, either through non-equilibrium preparation or thermal activation. In the latter case, we argue that increasing temperature can, counterintuitively, promote order by enhancing the kinetic-energy gain of thermally activated excitations.
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.
We study the emergence of magnetic order in localized spins that interact solely through their coupling to a Kitaev-type spin liquid. Using three toy models – the Kitaev model, the Yao–Lee model, and a square-lattice generalization of the Kitaev model – we calculate the effective exchange Hamiltonians mediated by the fractionalized excitations of these spin liquids. This setup is analogous to a Kondo lattice model, where conduction electrons are replaced by itinerant Majorana fermions. In the Kitaev model, our results show that the lowest-order perturbation theory generates short-range interactions with modified couplings and extending to sixth order introduces longer-range interactions while preserving the quantum spin-liquid ground state . Models involving more Majorana flavors on honeycomb and square lattices exhibit more complex behavior. The honeycomb Yao–Lee model with three flavors of itinerant Majorana fermions generates long-range RKKY-type interactions, leading to antiferromagnetic order and partial gapping of the Majorana fermion spectrum. In contrast, the square-lattice model produces a combination of anisotropic short- and long-range interactions, which can give rise to either a dimerized quantum paramagnetic state or an Ising antiferromagnet, depending on the parameters. These results illustrate the rich variety of magnetic orders that can be mediated by Kitaev-type spin liquids.
Understanding mechanisms of quantum ordering in strongly correlated systems remains a central challenge in condensed matter physics, with implications for designing novel quantum materials. Here, we investigate kinetic antiferromagnetism on a triangular lattice under an applied magnetic field, where spin polarons emerge as charge-magnon bound states with mutual attraction. Using large-scale diagrammatic Monte Carlo simulations, we show that this interaction drives high-temperature phase separation into charge- and magnon-rich regions, bordered by polarized Mott insulating voids. Spectral function analysis reveals a substantial energy correction from magnon interactions, indicating that these carrier-rich regions form a strongly bound charge-magnon liquid. These findings shed new light on recent experiments on MoTe_{2}/WSe_{2} moiré bilayers, underscoring kinetic magnetism as a unique pathway for strong intercarrier attraction and high-temperature quantum ordering, with potential applications in quantum materials.
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Abstract These lecture notes deal with aspects of out-of-equilibrium behaviour in topologically ordered systems, broadly interpreted as systems that do not develop a local order parameter at low temperature (e.g. symmetry breaking) and yet exhibit non-trivial global properties. The specific cases of classical spin ice and the quantum toric code are discussed. Within classical systems, it is found that substantial progress can be made in understanding the dynamics through effective modelling of the vacuum and its emergent excitations. However, at the quantum level, modelling is limited to that of leading energy barriers and asymptotic behavior, although it turns out that an intriguing parallel can be drawn between the toric code Hamiltonian and a class of lattice systems known as kinetically constrained models.