arXiv subjects

Michel J. P. Gingras

Publications and source records attributed to Michel J. P. Gingras.

At least 19 recordsLinked to original sources

arXiv2026

Fracton Spin Liquid and Exotic Frustrated Phases in Ising-like Octochlore Magnets

For nearly three decades, research on frustrated magnetism in three dimensions (3D) has centered on the pyrochlore lattice of corner-sharing tetrahedra and the classical spin liquid (CSL) known as spin ice. We propose that a lattice of corner-sharing octahedra -- the octochlore lattice -- may provide a next-generation platform for 3D frustrated magnetism, with realizations in anti-perovskite and alkali-rare-earth fluoride compounds. We study the phase diagram of Ising moments on the octochlore lattice, finding a variety of frustrated phases including CSLs and phases with subextensive ground state degeneracy intermediate between spin liquids and long-range order. Utilizing a cluster multipole framework, we present a unified treatment of this variety of frustrated behaviors. In addition to a spin ice CSL, we identify a fracton CSL with excitations restricted to move along one-dimensional (1D) lines, a classical U(1) equivalent of the paradigmatic X-cube model harboring fracton topological order. These "lineon" quasiparticles carry magnetic quadrupole moments, contrasting the famous magnetic monopoles of spin ice. These two CSLs lie at the boundaries of a parent "frustrated chains" phase with subextensive degeneracy. Each CSL corresponds to a condensate of different bound states of 1D ferro-spinons, giving rise to quasi-critical dimensional crossovers near the ends of the frustrated chains phase associated to avoided Kasteleyn-like transitions. We also find a spin nematic phase whose ground states may be viewed as fracton crystals, exhibiting both uniaxial and biaxial orders. The latter is caused by spontaneous dimensional reduction owing to accidental symmetries of the subextensive ground state manifold. This work paves the way for the realization of fracton CSLs and the exploration of other exotic states in underexplored octochlore magnetic materials.

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arXiv2026

Finite-Size Spectral Signatures of Order by Quantum Disorder: A Perspective from Anderson's Tower of States

In frustrated magnetic systems with a subextensive number of classical ground states, quantum zero-point fluctuations can select a unique long-range ordered state, a celebrated phenomenon referred to as \emph{order by quantum disorder} (ObQD). For frustrated spin-$\frac{1}{2}$ models, unbiased numerical methods able to expose ObQD are necessary. We show that ObQD can be identified from exact diagonalization (ED) calculations through an analysis akin to the Anderson tower of states associated with spontaneous symmetry breaking. By defining an effective quantum rotor model, we describe the competition between ObQD-induced localization of the rotor and its tunneling between symmetry-related ground states, identifying the crossover lengthscale from the finite-size regime where the rotor is delocalized, to the infinite system-size limit where it becomes localized. This rotor model relates the characteristic splittings in the ED energy spectrum to the ObQD selection energy scale, providing an estimate that can be compared to spin wave calculations. We demonstrate the general applicability of this approach in one-, two- and three-dimensional frustrated spin models that exhibit ObQD.

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arXiv2025

Anharmonic Collective Oscillations in Isotropic Spin Systems and their Spectroscopic Signatures

Spin waves are the fundamental excitations in magnetically ordered spin systems and are ubiquitously observed in magnetic materials. However, the standard understanding of spin waves as collective spin oscillations in an effective harmonic potential does not consider the possibility of soft modes, such as those due to an effective quartic potential. In this work, we show that such quartic potentials arise under very general conditions in a broad class of isotropic spin systems without a fine-tuning of the interaction parameters. Considering models with spin spiral ground states in two and three spatial dimensions, we numerically demonstrate that quartic amplitude spin oscillations produce a fluctuation-induced spin-wave gap which grows with temperature according to a characteristic power-law. In conjunction with a phenomenological theory, the present work provides a general theoretical framework for describing soft spin modes, extending the previously discussed spin dynamics in the presence of order-by-disorder, and highlighting the important role of finite-size effects. Our predictions of a temperature-dependent gap in spiral spin systems could be tested in inelastic neutron scattering experiments, providing direct spectroscopic evidence for thermal effects arising from soft spin modes in magnetic materials.

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arXiv2025

Universal temperature-dependent power law excitation gaps in frustrated quantum spin systems harboring order-by-disorder

When magnetic moments are subject to competing or frustrated interactions, continuous degeneracies that are not protected by any symmetry of the parent Hamiltonian can emerge at the classical (mean-field) level. Such "accidental" degeneracies are often lifted by both thermal and quantum fluctuations via a mechanism known as order-by-disorder (ObD). The leading proposal to detect and characterize ObD in real materials, in a way that quantitatively distinguishes it from standard energetic selection, is to measure a small fluctuation-induced pseudo-Goldstone gap in the excitation spectrum. While the properties of this gap are known to leading order in the spin wave interactions, in both the zero-temperature and classical limits, the pseudo-Goldstone (PG) gap in quantum magnets at finite temperature has yet to be characterized. Using non-linear spin wave theory, we compute the PG gap to leading order in a $1/S$ expansion at low temperature for a variety of frustrated quantum spin systems. We also develop a formalism to calculate the PG gap in a way that solely uses linear spin-wave theory, circumventing the need to carry out tedious quantum many-body calculations. We argue that, at leading order, the PG gap acquires a distinct power-law temperature dependence, proportional to either $T^{d+1}$ or $T^{d/2+1}$ depending on the gapless dispersion of the PG mode predicted at the mean-field level. Finally, we examine the implications of these results for the pyrochlore oxide compound Er$_2$Ti$_2$O$_7$, for which there is compelling evidence of ObD giving rise to the experimentally observed long-range order.

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arXiv2025

An Atlas of Classical Pyrochlore Spin Liquids

Frustrated magnetism in the pyrochlore lattice magnet has proven to be a most fruitful setting for the experimental and theoretical search for spin liquids. Besides the canonical case of spin ice, recent works have identified a variety of new classical and quantum spin liquids engendered by the generic nearest-neighbor anisotropic spin Hamiltonian for that lattice. However, a general framework for the thorough and systematic classification and characterization of these exotic states of matter has been lacking, as has an exhaustive list of all possible spin liquids that this model can support and, perhaps most interesting, what is the corresponding structure of their emergent field theory description. In this work, we develop such a theoretical framework to identify the interaction parameters stabilizing different classical spin liquids and derive their corresponding effective generalized Gauss's laws at low temperatures. Combining this with Monte Carlo simulations, we systematically identify all classical spin liquids for the general nearest-neighbor anisotropic spin Hamiltonian on the pyrochlore lattice. In doing so, we uncover new spin liquid models with exotic forms of generalized Gauss's law and multipole conservation laws. Our approach allows us to compile an atlas of all spin liquids realized in the phase diagram, providing a global picture of their mutual connections in parameter space and transitions between them. Our work will inform future theoretical and experimental studies of classical and quantum spin liquids on the pyrochlore lattice and help rationalize the exotic properties of pyrochlore magnets.

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arXiv2025

2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects

We introduce a novel geometrically frustrated classical Ising model, dubbed the "spin vorticity model", whose ground state manifold is a novel classical spin liquid, a "2-form Coulomb phase". We study the thermodynamics of this model both analytically and numerically, exposing the presence of algebraically decaying correlations and demonstrating an extensive ground state entropy, and give a comprehensive account of its ground state properties and excitations. Each classical ground state may be decomposed into collections of closed 2-dimensional membranes, supporting fractionalized string excitations attached to the boundaries of open membranes. At finite temperature, the model can then be described as a gas of closed strings in a background of fluctuating membranes. We demonstrate that the emergent gauge structure of the low-temperature phase is naturally captured in the formalism of 2-form electrodynamics, which describes 1-dimensional charged strings coupled to a rank-2 anti-symmetric gauge field. After establishing the classical spin vorticity model, we consider perturbing it with quantum exchange interactions, from which we derive an effective membrane exchange model of the quantum dynamics of these membranes, which maps to a frustrated 2-form U(1) lattice gauge theory. We show the existence of a fine-tuned Rokhsar-Kivelson point where the quantum ground state is an equal weight superposition of all classical ground state configurations. We further demonstrate how to quantize the string excitations, by coupling a 1-form string field to the emergent 2-form U(1) gauge field, thus mapping a quantum spin model to a 2-form gauge-Higgs model. We discuss the stability of the gapless deconfined phase of this gauge theory and the possibility of realizing a novel class of phases of quantum matter: 2-form U(1) quantum spin liquids.

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arXiv2025

Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions

Order-by-disorder, whereby fluctuations lift an accidental classical ground state degeneracy to stabilize a subset of ordered states, is a recurrent and prominent theme in the field of frustrated magnetism where magnetic moments are subject to competing interactions. Thus far, such a phenomenon has been discussed in systems where the quantum ground state is not a classical product state. In such a case, both thermal and quantum fluctuations act to lift the accidental classical degeneracy, begging the question of whether one mechanism of order-by-disorder is possible without the other. In this paper, we present results exposing an uncharted route to order-by-disorder, one without quantum zero-point fluctuations, in the ferromagnetic pyrochlore Heisenberg system with the Dzyaloshinskii-Moriya (DM) interaction as the leading perturbation. We prove that any colinear ferromagnetic state is an exact eigenstate while thermal fluctuations give rise to a preference in the magnetization direction. Using linear spin wave theory, we find that the anisotropy appears at lowest order as a sub-leading term in the low-temperature expansion of the free energy, proportional to $T^{7/2}$. Our results thus show that the phenomenon of thermal order-by-disorder can occur even in the absence of quantum zero-point fluctuations driving quantum order-by-disorder, this being so in particular when the accidentally degenerate ground state of the classical model turns out to be an exact eigenstate of the quantum version of the model. In addition, we find that when the DM interaction is large, the fully polarized ferromagnetic ground state becomes unstable for a spin-$\frac{1}{2}$ system within the framework of non-linear spin wave theory, a result that is presumably closely related to the recent report of a quantum spin liquid in this spin-$\frac{1}{2}$ model reported in [https://doi.org/10.1073/pnas.2403487121].

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arXiv2024

Synthesis and characterization of the novel breathing pyrochlore compound Ba3Tm2Zn5O11

In this study, a novel material from the rare-earth based breathing pyrochlore family, Ba3Tm2Zn5O11, was successfully synthesized. Powder x-ray diffraction and high-resolution powder neutron diffraction confirmed phase purity and the F-43m breathing pyrochlore crystal structure, while thermogravimetric analysis revealed incongruent melting behavior compared to its counterpart, Ba3Yb2Zn5O11. High-quality single crystals of Ba3Tm2Zn5O11 were grown using the traveling solvent floating zone technique and assessed using Laue x-ray diffraction and single crystal x-ray diffraction. Thermodynamic characterization indicated paramagnetic behavior down to 0.05 K, and inelastic neutron scattering measurements identified distinct dispersionless crystal electric field energy bands, with the fitted crystal electric field model predicting a single-ion singlet ground state and an energy gap of ~9 meV separating it from the first excited (singlet) state. Additional low-energy excitation studies on single crystals revealed dispersionless bands at 0.8 and 1 meV. Computed phonon dispersions from first-principles calculations ruled out phonons as the origin of these modes, further illustrating the puzzling and unique properties of Ba3Tm2Zn5O11.

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arXiv2024

Ground state properties of the Heisenberg-compass model on the square lattice

Compass models provide insights into the properties of Mott-insulating materials that host bond-dependent anisotropic interactions between their pseudospin degrees of freedom. In this article, we explore the classical and quantum ground state properties of one such model relevant to certain layered perovskite materials akin to Ba$_2$IrO$_4$ - namely, the Heisenberg-compass model on the square lattice. We first investigate the ground state phase diagram of this model using classical Monte Carlo simulations. These reveal that the low temperature classical phase diagram is divided into six different classes of long-range ordered phases, including four phases that exhibit an order by disorder selection and two phases that are stabilized energetically. This model admits a special duality transformation, known as the Klein duality, conveniently allowing to map one region of coupling parameters onto another and constraining the phase diagram, and which we exploit in our study. From the analysis of the zero-point energy and the free energy of the spin waves, we find that order by quantum disorder at zero temperature and order by thermal disorder select the same orderings as those found from classical Monte Carlo simulations. We further investigate the quantum ground states of this model using numerical exact diagonalization on small clusters by exploiting the translational symmetry of the square lattice. We obtain a ground state phase diagram bearing close resemblance to that found from the classical analysis.

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arXiv2024

Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores

Gauge theories are powerful tools in theoretical physics, allowing complex phenomena to be reduced to simple principles, and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behaviour at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and matrix gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the matrix gauge field, rendering the system spin ice like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and matrix gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers pyrochlore materials.

cond-mat.str-el↗

arXiv2023

Pseudo-Goldstone modes and dynamical gap generation from order-by-thermal-disorder

Accidental ground state degeneracies -- those not a consequence of global symmetries of the Hamiltonian -- are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order-by-thermal-disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, $Δ$, and show that at low temperatures it scales as the square root of temperature, $\sqrt{T} $. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy.

cond-mat.str-el↗

arXiv2023

Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions

We investigate the ground state and critical temperature phase diagrams of the classical and quantum $S=1/2$ pyrochlore lattice with nearest-neighbor Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We consider ferromagnetic and antiferromagnetic Heisenberg exchange as well as direct and indirect DMI. Classically, three ground states are found: all-in/all-out, ferromagnetic and a locally ordered $XY$ phase, known as $Γ_5$, which displays an accidental classical U(1) degeneracy. Quantum zero-point energy fluctuations are found to lift the classical ground state degeneracy and select the $ψ_3$ state in most parts of the $Γ_5$ regime. Likewise, thermal fluctuations treated classically, select the $ψ_3$ state at $T=0^+$. In contrast, classical Monte Carlo finds that the system orders at $T_c$ in the $ψ_2$ state of $Γ_5$ for antiferromagnetic Heisenberg exchange and indirect DMI with a transition from $ψ_2$ to $ψ_3$ at a temperature $T_{Γ_5} <T_c$. The same method finds that the system orders via a single transition at $T_c$ directly into the $ψ_3$ state for most of the region with ferromagnetic Heisenberg exchange and indirect DMI. Such ordering behavior at $T_c$ for the $S=1/2$ quantum model is corroborated by high-temperature series expansion. To investigate the $T=0$ quantum ground states, we apply the pseudo-fermion functional renormalization group (PFFRG). The quantum paramagnetic phase of the pure antiferromagnetic $S=1/2$ Heisenberg model is found to persist over a finite region in the phase diagram for both direct or indirect DMI. We find that near the boundary of ferromagnetism and $Γ_5$ antiferromagnetism the system may potentially realize a quantum ground state lacking conventional magnetic order. Otherwise, for the largest portion of the phase diagram, PFFRG finds the same ordered phases as in the classical model.

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arXiv2022

Pinch-points to half-moons and up in the stars: the kagome skymap

Pinch point singularities, associated with flat band magnetic excitations, are tell-tale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features -- shaped as half-moons and stars -- arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns.

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arXiv2021

Towards understanding the magnetic properties of the breathing pyrochlore compound Ba3Yb2Zn5O11: A single crystal study

Ba3Yb2Zn5O11 is unique among breathing pyrochlore compounds for being in the nearly decoupled limit where inter-tetrahedron interactions are weak, hosting isolated clusters or "molecular magnet" like tetrahedra of magnetic ytterbium (Yb3+) ions. In this work, we present the first study carried out on single-crystal samples of the breathing pyrochlore Ba3Yb2Zn5O11, using a variety of magnetometry and neutron scattering techniques along with theoretical modeling. We employ inelastic neutron scattering to investigate the magnetic dynamics as a function of applied field (with respect to both magnitude and direction) down to a temperature of 70 mK, where inelastic scattering reveals dispersionless bands of excitations as found in earlier powder sample studies, in good agreement with a single-tetrahedron model. However, diffuse neutron scattering at zero field and dc-susceptibility at finite field exhibit features suggesting the presence of excitations at low-energy that are not captured by the single tetrahedron model. Analysis of the local structure down to 2 K via pair distribution function analysis finds no evidence of structural disorder. We conclude that effects beyond the single tetrahedron model are important in describing the low-energy, low temperature physics of Ba3Yb2Zn5O11, but their nature remains undetermined.

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arXiv2021

Probing Flat Band Physics in Spin Ice Systems via Polarized Neutron Scattering

In this paper, we illustrate how polarized neutron scattering can be used to isolate the spin-spin correlations of modes forming flat bands in a frustrated magnetic system hosting a classical spin liquid phase. In particular, we explain why the nearest-neighbor spin ice model, whose interaction matrix has two flat bands, produces a dispersionless (i.e. "flat") response in the non-spin-flip (NSF) polarized neutron scattering channel, and demonstrate that NSF scattering is a highly sensitive probe of correlations induced by weak perturbations which lift the flat band degeneracy. We use this to explain the experimentally measured dispersive (i.e. non-flat) NSF channel of the dipolar spin ice compound $\mathrm{Ho}_2 \mathrm{Ti}_2 \mathrm{O}_7$.

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arXiv2020

Unsupervised Machine Learning of Quenched Gauge Symmetries: A Proof-of-Concept Demonstration

In condensed matter physics, one of the goals of machine learning is the classification of phases of matter. The consideration of a system's symmetries can significantly assist the machine in this goal. We demonstrate the ability of an unsupervised machine learning protocol, the Principal Component Analysis method, to detect hidden quenched gauge symmetries introduced via the so-called Mattis gauge transformation. Our work reveals that unsupervised machine learning can identify hidden properties of a model and may therefore provide new insights into the models themselves.

cond-mat.dis-nn↗

arXiv2019

Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr4O8 and LiGaCr4O8, a spiral spin liquid with two-dimensional degeneracy for CuInCr4Se8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr4S8, LiGaCr4S8 and CuInCr4S8. The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.

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arXiv2019

Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions

We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin $S$ in the presence of nearest-neighbor $J_{1}$ and second-nearest-neighbor $J_{2}$ exchange interactions. By employing the pseudofermion functional renormalization group method, we find, for $S=1/2$ and $S=1$, an extended quantum-spin-liquid phase centered around $J_{2}=0$, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a $J_{2}$ coupling on the nature of the scattering profile, and the pinch points, in particular, are studied. For the magnetic phases of the $J_{1}$-$J_{2}$ model, quantum fluctuations are shown to renormalize phase boundaries compared to the classical model and to modify the ordering wave vectors of spiral magnetic states, while no new magnetic orders are stabilized.

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