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arXiv:2509.17332

Quantum coherence induced by magnons

Vítor Vieira, F. M. de Paula

Published Sep 22, 2025• 0 citations
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Abstract

We analyze quantum coherence generated by non-interacting magnons in a ferromagnetic spin chain described by the isotropic Heisenberg model. The exact expression derived for the reduced density operator of an arbitrary subsystem reveals that single-site coherence vanishes, while maximal coherence arises in a pure single-mode magnon state. Remarkably, this maximum depends solely on the number of coherently superposed microstates. Based on this property, we introduce coherence-based definitions of entropy, temperature, and heat capacity, establishing a formal analogy with standard thermodynamic quantities.

DOI
10.48550/arxiv.2509.17332

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We analyze quantum coherence generated by non-interacting magnons in a ferromagnetic spin chain described by the isotropic Heisenberg model. The exact expression derived for the reduced density operator of an arbitrary subsystem reveals that single-site coherence vanishes, while maximal coherence arises in a pure single-mode magnon state. Remarkably, this maximum depends solely on the number of coherently superposed microstates. Based on this property, we introduce coherence-based definitions of entropy, temperature, and heat capacity, establishing a formal analogy with standard thermodynamic quantities.
A general property of quantum coherence is its non-increasing behavior during any incoherent quantum operation, such as an incoherent quantum channel in a noisy environment. We address that thermal coherence can mitigate these losses by offering relative improvements for different quantum models considering the ferromagnetic and antiferromagnetic properties. It is possible to obtain the thermal coherence of density operators obtained by the actions of the Hamiltonians, even for higher temperatures and certain values of the other parameters compared to other models. By adjusting the parameters, it is maximized such that the state of the output is maximally coherent. These make it possible to create maximal coherence in realizing any quantum information task in a noisy environment.
We investigate the spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate. The degree of this degeneration is found analytically. It is shown that the residual entropy per spin is s0=12ln2{s}_{0}=\frac{1}{2}ln\phantom{\rule{0.16em}{0ex}}2s0​=21​ln2. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The corresponding thermodynamic quantities are calculated using full exact diagonalization of finite chains up to N=22N=22N=22. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.
Quasiparticles are physically motivated mathematical constructs for simplifying the seemingly complicated many-body description of solids. A complete understanding of their dynamics and the nature of the effective interactions between them provides rich information on real material properties at the microscopic level. In this paper, we explore the dynamics and interactions of magnon quasiparticles in a ferromagnetic spin-1 Heisenberg chain with easy-axis on-site anisotropy, a model relevant for the explanation of recent terahertz optics experiments on NiNb2O6{\mathrm{NiNb}}_{2}{\mathrm{O}}_{6}NiNb2​O6​ [P. Chauhan et al., Phys. Rev. Lett. 124, 037203 (2020)], and nonequilibrium dynamics in ultracold-atomic settings [W. C. Chung et al., Phys. Rev. Lett. 126, 163203 (2021)]. We build a picture for the properties of clouds of a few magnons with the help of exact diagonalization and density matrix renormalization group calculations supported by physically motivated Jastrow wave functions. We show how the binding energy of magnons effectively reduces with their number and explain how this energy scale is of direct relevance for dynamical magnetic susceptibility measurements. This understanding is used to make predictions for ultracold-atomic platforms, which are ideally suited to study the thermalization of multimagnon states. We simulate the nonequilibrium dynamics of these chains using the matrix product state based time-evolution block decimation algorithm and explore the dependence of revivals and thermalization on magnon density and easy-axis on-site anisotropy (which controls the strength of effective magnon interactions). We observe behaviors akin to those reported for many-body quantum scars, which we explain with an analytic approximation that is accurate in the limit of small anisotropy.
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and of the equilibrium reduced density matrix of a subsystem for the two different statistics introduced in Part I. In order to analyze their consistency with thermodynamics, these quantities of interest are evaluated in the limit of large number of components of the isolated system. The main results can be summarized as follows: typical values of the entropy and of the equilibrium reduced density matrix as functions of the internal energy in the fixed expectation energy ensemble do not satisfy the requirement of thermodynamics. On the contrary, the thermodynamical description is recovered from the random pure state ensemble (RPSE), provided that one considers systems large enough. The thermodynamic limit of the considered properties for the spin system reveals a number of important features. First canonical statistics (and thus, canonical typicality as long as the fluctuations around the average value are small) emerges without the need of assuming the microcanonical space for the global pure state. Moreover, we rigorously prove (i) the equivalence of the "global temperature," derived from the entropy equation of state, with the "local temperature" determining the canonical state of the subsystems; and (ii) the equivalence between the RPSE typical entropy and the canonical entropy for the overall system.
We investigate the entanglement properties of the excited states of the spin- Heisenberg ( XXX ) chain with isotropic antiferromagnetic interactions, by exploiting the Bethe ansatz solution of the model. We consider eigenstates obtained from both real and complex solutions ('strings') of the Bethe equations. Physically, the former are states of interacting magnons, whereas the latter contain bound states of groups of particles. We first focus on the situation with few particles in the chain. Using exact results and semiclassical arguments, we derive an upper bound S MAX for the entanglement entropy. This exhibits an intermediate behaviour between logarithmic and extensive, and it is saturated for highly-entangled states. As a function of the eigenstate energy, the entanglement entropy is organized in bands. Their number depends on the number of blocks of contiguous Bethe–Takahashi quantum numbers. In the presence of bound states a significant reduction in the entanglement entropy occurs, reflecting that a group of bound particles behaves effectively as a single particle. Interestingly, the associated entanglement spectrum shows edge-related levels. At a finite particle density, the semiclassical bound S MAX becomes inaccurate. For highly-entangled states S A ∝ L c , with L c the chord length, signalling the crossover to extensive entanglement. Finally, we consider eigenstates containing a single pair of bound particles. No significant entanglement reduction occurs, in contrast with the few-particle case.
By numerically exact calculations of spin-1/2 antiferromagnetic Heisenberg models on small clusters up to 24 sites, we demonstrate that quantum entanglement between subsystems A and B in a pure ground state of a whole system A + B can induce thermal equilibrium in subsystem A. Here, the whole system is bipartitoned with the entanglement cut that covers the entire volume of subsystem A. An effective temperature T A of subsystem A induced by quantum entanglement is not a parameter but can be determined from the entanglement von Neumann entropy S A and the total energy E A of subsystem A calculated for the ground state of the whole system.We show that temperature T A can be derived by minimizing the relative entropy for the reduced density matrix operator of subsystem A and the Gibbs state (i.e., thermodynamic density matrix operator) of subsystem A with respect to the coupling strength between subsystems A and B. Temperature T A is essentially identical to the thermodynamic temperature, for which the entropy and the internal energy evaluated using the canonical ensemble in statistical mechanics for the isolated subsystem A agree numerically with the entanglement entropy S A and the total energy E A of subsystem A. Fidelity calculations ascertain that the reduced density matrix operator of subsystem A for the pure but entangled ground state of the whole system A + B matches, within a maximally 1.5% error in the finite size clusters studied, the thermodynamic density matrix operator of subsystem A at temperature T A , despite that these density-matrix operators are different in general.We also find that temperature T A evaluated from the ground state of the whole system depends insignificantly on the system sizes, which is consistent with the fact that the thermodynamic temperature is an intensive quantity.We argue that quantum fluctuation in an entangled pure state can mimic thermal fluctuation in a subsystem.We also provide two simple but nontrivial analytical examples of free bosons and free fermions for which the two density-matrix operators are exactly the same if the effective temperature T A is adopted.We furthermore discuss implications and possible applications of our finding.