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Frédéric Mila

Publications and source records attributed to Frédéric Mila.

At least 19 recordsLinked to original sources
arXiv2026

Magnetic excitations of the strongly-anisotropic triangular XXZ model: a projected spin-product state approach

Recent experiments have sparked interest on the ground-state properties and on the excitation spectrum of the spin-$1/2$ triangular XXZ model with strong Ising-like anisotropy. In this work, we introduce and analyze a ``projected'' coherent-state approximation to the model, constructed by projecting spin-product states onto the low-energy configurations of the triangular Ising antiferromagnet. Within this approximation, we discuss the structure of the ground-state ordering and the magnetization curve under a longitudinal field. We then discuss the excitation spectrum by linearizing equations of motion deriving from a time-dependent variational principle. This leads to a natural description of spin-wave-like excitations within the strongly constrained Hilbert space. At zero field, the variational approximation leads to a very flat landscape of quasi-degenerate states, which results in a low-energy pseudo-Goldstone mode in the excitation spectrum. We compare our results to experimental measurements on the cobaltite K$_{2}$Co(SeO$_{3}$)$_{2}$ (KCSO). Our approximation leads to a dramatic improvement as compared to linear spin-wave theory. However, there remain deviations in the value of the pseudo-Goldstone gap and in the dispersion near $M$ points at low field.

cond-mat.str-el↗
arXiv2026

Pinwheel-shaped bound triplet pairs in the magnetization plateaus of SrCu$_2$(BO$_3$)$_2$

The sequence of magnetization plateaus at 1/8, 2/15, 1/6, 1/4, 1/3, 2/5, and 1/2 of the saturation observed in SrCu$_2$(BO$_3$)$_2$ remained a puzzle until tensor-networks-based numerical simulations suggested that the low-magnetization plateaus are stabilized as Wigner crystals of spin-2 bound states, and not as one of the standard configurations (semiclassical up-down, or crystals of triplets). We report on $^{63,65}$Cu nuclear magnetic resonance spectra up to 41.9 T: Based on constraints deduced from the 1/3 plateau, we show that the spectra in the 1/8 and 2/15 plateaus indeed agree with the prediction for the spin-2 bound states, while being incompatible with a crystal of triplets. This adds the formation of Wigner crystals of bound states as an alternative fundamental paradigm in the theory of magnetization plateaus.

cond-mat.str-el↗
arXiv2026

Topological Triplons in the Pinwheel Valence Bond Solid on the Kagome Lattice

We investigate the triplon excitations of the pinwheel valence-bond-solid phase on the deformed kagome lattice compound Rb2Cu3SnF12. Using bond-operator mean-field theory, we compute the triplon band structure, dynamical structure factor, Berry curvatures and the associated thermal Hall response. We show that the presence of Dzyaloshinskii-Moriya interactions and an external magnetic field are key for endowing triplon bands with nontrivial Chern numbers. We find good qualitative agreement of the low-energy dynamical structure factor with neutron-scattering experiments. An applied magnetic field can isolate the lowest triplon Chern band leading to a tunable thermal Hall conductivity for accessible temperature and field regimes. Our results establish the deformed kagome pinwheel valence-bond solid as a promising platform for topological triplon physics and for observing the associated thermal Hall effect.

cond-mat.str-el↗
arXiv2026

Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model

Motivated by recent experimental studies, we investigate the spectrum of the nearest-neighbour triangular XXZ model within the $1/S$ expansion, in the limit in which the exchange couplings present a strong easy-axis anisotropy $J_{xy}/J_{zz} \ll 1$. We show that in the limit in which $1/S \to 0$ and $J_{xy} \to 0$ at fixed $V = J_{zz}/(S J_{xy})$, the triangular spin model can be reduced to an effective boson model with quartic interactions on the honeycomb lattice. This effective model interpolates between a spin-wave ($V \to 0$) and a strong-coupling limit ($V \to \infty$) and encodes in a simple framework the regimes discussed by Kleine~\emph{et al.}~[Z. Phys. B Condens. Matter~{\bf 86}, 405 (1992);~{\bf 87}, 103 (1992)]. For zero field, the classical ground state of the model presents an accidental degeneracy, which can be traced to a simple symmetry of the classical energy. The model thus offers a transparent realization of a theory with quantum order-by-disorder and a pseudo-Goldstone mode. We analyze the spectrum at zero magnetic field by calculating the self-energy at one-loop order. In the calculation, we introduce a self-consistent renormalization of the energy scale and of the pseudo-Goldstone energy gap; the latter renormalization is essential to remove infrared divergences in the on-shell corrections to the energy dispersion. Finally, we discuss qualitatively the structure of the one-loop corrections in comparison with the spectrum observed experimentally in K$_{2}$Co(SeO$_{3}$)$_{2}$.

cond-mat.str-el↗
arXiv2026

Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states

The Shastry-Sutherland model is an effective model of the layered material SrCu$_2$(BO$_3$)$_2$, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states (iPEPS), a two-dimensional tensor network ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range $0.785(5) \le J'/J \le 0.82(1)$.

cond-mat.str-el↗
arXiv2026

Topological Devil's staircase in a constrained kagome Ising antiferromagnet

We show that the constrained Ising model on the kagome lattice with infinite first and third neighbor couplings undergoes an infinite series of thermal first-order transitions at which, as in the Kasteleyn transition, linear defects of infinite length condense. However, their density undergoes abrupt jumps because of the peculiar structure of the low temperature phase, which is only partially ordered and hosts a finite density of zero-energy domain walls. The number of linear defects between consecutive zero-energy domain walls is quantized to integer values, leading to a devil's staircase of topological origin. By contrast to the devil's staircase of the ANNNI and related models, the wave-vector is not fixed to commensurate values inside each phase.

cond-mat.str-el↗
arXiv2025

Tensor-network study of the ground state of maple-leaf Heisenberg antiferromagnet

We study the quantum phase diagram of the spin-$1/2$ nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to $C_3$-symmetric lattices. Focusing on the fully antiferromagnetic $J$-$J_d$ model with $J_h = J_t := J$, we map out the ground-state phase diagram as a function of the dimer coupling $J_d$. Our results show that the system hosts only two phases: a magnetically ordered canted-$120^\circ$ phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at $J_d/J \approx 1.45$. Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.

cond-mat.str-el↗
arXiv2025

Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice

We investigate the spin-$1/2$ Heisenberg antiferromagnet on the ruby lattice with uniform first- and second-neighbor interactions, which forms a two-dimensional network of corner-sharing tetrahedra. Using infinite projected entangled pair states (iPEPS), we study the ground state of the system to find that it assumes a gapped threefold-degenerate simplex crystal ground state, with strong singlets formed on pairs of neighboring triangles. We argue that the formation of the simplex singlet ground state at the isotropic point relates to the weak inter-triangle coupling limit where an effective spin-chirality Hamiltonian on the honeycomb lattice exhibits an extensively degenerate ground state manifold of singlet coverings at the mean-field level. Under an applied Zeeman field, the iPEPS simulations uncover magnetization plateaus at $m/m_s = 0, 1/3, 1/2,$ and $2/3$, separated by intermediate supersolid phases, all breaking the sixfold rotational symmetry of the lattice. Unlike the checkerboard lattice, these plateaus cannot be described by strongly localized magnons.

cond-mat.str-el↗
arXiv2025

Observation of Unprecedented Fractional Magnetization Plateaus in a New Shastry-Sutherland Ising Compound

Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice (SSL), offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these systems leads to the emergence of novel phases. We present the characterization of Er2Be2GeO7, an SSL compound with Er3+ ions forming orthogonal dimers separated by non-magnetic layers whose structure is invariant under the P-421m space group. Neutron scattering reveals an antiferromagnetic dimer structure at zero field, typical of Ising spins on that lattice and consistent with the anisotropic magnetization observed. However, magnetization measurements exhibit fractional plateaus at 1/4 and 1/2 of saturation, in contrast to the expected 1/3 plateau of the SSL Ising model. By comparing the energy of candidate states with ground-state lower bounds we show that this behavior requires spatially anisotropic interactions, leading to an anisotropic Shastry-Sutherland Ising Model (ASSLIM) symmetric under the Cmm2 space group. This anisotropy is consistent with the small orthorhombic distortion observed with single-crystal neutron diffraction. The other properties, including thermodynamics, which have been investigated theoretically using tensor networks, point to small residual interactions, potentially due to further couplings and quantum fluctuations. This study highlights Er2Be2GeO7 as a promising platform for investigating exotic magnetic phenomena.

cond-mat.str-el↗
arXiv2025

Confinement, deconfinement, and bound states in the spin-$1$ and spin-$3/2$ generalizations of the Majumdar--Ghosh chain

We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and three-site $J_3$ interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the $J_2$ interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast to the spin-$1/2$ chain, where the spinon continuum dominates the spectral functions, the magnon modes are prominent in the spectral functions of the spin-$1$ and spin-$3/2$ chains. Through single mode approximation and valence bond solid approaches, we disentangle magnon and spinon contributions to the spectral functions. After including the $J_2$ interactions, for the spin-$1$ chain we trace the evolution of the dynamical structure factor along the phase transition line between the Haldane phase and the fully dimerized phase. We find that the excitation spectrum is a continuum along this line and the spectral gap closes as the order of the transition changes from first order to second order. Along the line of first-order transitions, the spinon-like domain walls are deconfined, and the model exhibits their confinement into discrete bound states away from the transition line. A similar phenomenon occurs in the spin-$3/2$ chain across the phase transition between partially dimerized to fully dimerized phases, revealing a universal spinon confinement phenomenon across first-order phase transitions. This study presents the dynamical structure factor corresponding to the ground state phase diagram and establishes a unified quasiparticle framework for understanding the fundamental nature of excitations across distinct quantum phases in frustrated $J_1$-$J_2$-$J_3$ Heisenberg spin chains.

cond-mat.str-el↗
arXiv2025

Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet

We investigate the ground state phase diagram of the spin-$1/2$ antiferromagnetic Heisenberg model on the star lattice using infinite projected entangled pair states (iPEPS) and high-order series expansions. The model includes two distinct couplings: $J_d$ on the dimer bonds and $J_t$ on the trimer bonds. While it is established that the system hosts a valence bond solid (VBS) phase for $J_d \ge J_t$, the ground state phase diagram for $J_d < J_t$ has remained unsettled. Our iPEPS simulations uncover a first-order phase transition at $J_d/J_t \approx 0.18$, significantly lower than previously reported estimates. Beyond this transition, we identify a close competition between two valence bond crystal (VBC) states: a columnar VBC and a $\sqrt{3} \times \sqrt{3}$ VBC, with the latter consistently exhibiting lower energy across all finite bond dimensions. The high-order series expansion supports this by finding that the $\sqrt{3} \times \sqrt{3}$ VBC state indeed becomes energetically favorable, but only at sixth order in perturbation theory, revealing the subtle nature of the competition between candidate states.

cond-mat.str-el↗
arXiv2025

Excitations and dynamical structure factor of $J_1-J_2$ spin-$3/2$ and spin-$5/2$ Heisenberg spin chains

We study the dynamical structure factor of the frustrated spin-$3/2$ $J_1$-$J_2$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid ansatz corroborated by density matrix renormalization group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at $J_2 \approx 0.32J_1$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at $J_2 \approx 0.4J_1$ beyond the Lifshitz point ($J_2 \approx 0.388J_1$). The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-$5/2$ case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

cond-mat.str-el↗
arXiv2025

Slow convergence of spin-wave expansion and magnon dispersion in the 1/3 plateau of the triangular XXZ antiferromagnet

Motivated by recent experiments on the quantum magnet K$_{2}$Co(SeO$_{3}$)$_{2}$, we study theoretically the excitation spectrum of the nearest-neighbour triangular XXZ model in the limit of strong easy-axis anisotropy, within the up-up-down (1/3-plateau) phase. We make an expansion in $α=J_{xy}/J_{zz}$ instead of $1/S$ and calculate the magnon dispersion for any value of the spin $S$ at second order in $α$, with two important conclusions: (i) the 1/S expansion converges very slowly for S=1/2, making spin-wave theory quantitatively inaccurate up to very large orders; (ii) compared to the linear spin-wave predictions, our magnon dispersion presents a much better agreement with experimental results on K$_{2}$Co(SeO$_{3}$)$_{2}$, for which $α\simeq 0.08$.

cond-mat.str-el↗
arXiv2025

Magnetic ordering in out-of-plane artificial spin systems based on the Archimedean lattices

Artificial spin systems, sometimes referred to as artificial spin ices, are arrays of coupled nanoscale magnets that order according to the lattice geometry, nanomagnet shape and magnetic anisotropy. Here we characterize a family of artificial spin systems that are formed by placing arrays of out-of-plane nanomagnets on the vertices of the Archimedean lattices. On demagnetizing these nanomagnet arrays using a magnetic field protocol and subsequently imaging the magnetic configuration using magnetic force microscopy, we observe different types of magnetic order. We compare our experimental results with those predicted by Monte Carlo simulations to assign an effective temperature to each lattice. We find that, for all of the lattices, the assigned effective temperature is above the transition temperature. This reflects the difficulty of obtaining system-spanning order in lattices with out-of-plane nanomagnets. We consider to what extent further-neighbor interactions affect the phase diagram and spin-spin correlations in each lattice, illustrating our results with four example lattices. We can divide the lattices into three main categories: bipartite lattices that admit a perfect antiferromagnetic ground state, frustrated lattices where ordering proceeds via a single step, and frustrated lattices with two-step-ordering. Our work highlights the diversity of magnetic ordering that can be hosted in two-dimensional artificial spin systems with out-of-plane nanomagnets, and demonstrates the importance of including long-range interactions to explain the magnetic ordering. Such insights will be important for incorporating artificial spin systems into novel computing applications.

cond-mat.mes-hall↗
arXiv2025

Bound states and deconfined spinons in the dynamical structure factor of the $J_1 - J_2$ spin-1 chain

Using a time-dependent density matrix renormalization group approach, we study the dynamical structure factor of the $J_1 - J_2$ spin-1 chain. As $J_2$ increases, the magnon mode develops incommensurability. The system undergoes a first-order transition at $J_2 = 0.76 J_1$, and at that point, domain walls lead to a continuum of fractional quasi-particles or spinons. By studying small variations in $J_2$ around the transition point, we observe the confinement of spinons into bound states in the spectral function and find a smooth evolution of the spectrum into magnon modes away from the phase transition. We employ the single-mode approximation to accurately account for the dispersion of the magnon mode away from the phase transition and describe the associated continua and bound states. We extend the single-mode approximation to describe the dispersion of a spinon at the phase transition point and obtain its dispersion throughout the Brillouin zone. This allows us to relate the incommensurability at and around the transition point to the competition between a negative nearest-neighbour hopping amplitude and a positive next-nearest-neighbour one for the domain wall.

cond-mat.str-el↗
arXiv2024

Singularity with and without disorder at AKLT points

The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are non-analytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of SU(N) models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this new possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.

cond-mat.str-el↗
arXiv2024

Weakly first-order melting of the 1/3 plateau in the Shastry-Sutherland model

We investigate the thermal properties of the 1/3 plateau in the Shastry-Sutherland model with infinite projected entangled-pair states (iPEPS) by performing the imaginary time evolution of the infinite temperature density matrix. We show that both the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ broken symmetries of the ground states are restored at a unique temperature where the correlation length has a peak, and that the melting of the plateau occurs via a single weakly first-order transition. We focus on the experimentally relevant coupling constants deep into the 1/3 plateau phase at $h = 1$ and $J'/J = 0.63$, which was estimated to describe the SrCu$_2$(BO$_3$)$_2$ compound. By computing the free energy we are able to locate the transition temperature around $T_c \simeq 4.8$K well above the temperature $T=2$K, at which the 1/3 plateau was observed in experiments. The investigation is supplemented by adding a bias term to the Hamiltonian and studying the induced crossover. We further map the transition line in the field-temperature phase diagram.

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