arXiv subjects

Paul A. McClarty

Publications and source records attributed to Paul A. McClarty.

At least 19 recordsLinked to original sources

arXiv2026

Classical Kitaev model in a magnetic field

Motivated by experiments on spin-orbit coupled magnets with Kitaev exchange in magnetic fields, we present an analysis of the classical Kitaev honeycomb model in the presence of a magnetic field. We show that there is a spin liquid regime that exists within a finite window of fields from zero up to a finite threshold before transitioning into the polarized paramagnet. We uncover constraints that spins need to satisfy in the ground state and show that they determine the exact limiting zero temperature behavior of the heat capacity and magnetic susceptibility within the spin liquid as a function of field. When the field is finite, both the two-point spin and the quadrupolar correlations are short-ranged, in contrast to the zero-field case. We rationalize an effective mass for the quadrupolar correlations in terms of a coarse-grained theory with fluctuating effective charge degrees of freedom. Finally, we show that weak site-dilution does not change the magnetization within the spin liquid -- a kind of "perfect" compensation of the site dilution.

cond-mat.str-el↗

arXiv2025

Hollow Lattice Tensor Gauge Theories with Bosonic Matter

Higher rank gauge theories are generalizations of electromagnetism where, in addition to overall charge conservation, there is also conservation of higher rank multipoles such as the total dipole moment. In this work we study a four dimensional lattice tensor gauge theory coupled to bosonic matter which has second rank tensor electric and magnetic fields and charge conservation on individual planes. Starting from the Hamiltonian, we derive the lattice action for the gauge fields coupled to $q=1,2$ charged scalars. We use the action formulation to carry out Monte Carlo simulations to map the phase diagram as a function of the gauge ($β$) and matter ($κ$) couplings. We compute the nature of correlators at strong and weak coupling in the pure gauge theory and compare the results to numerical simulations. Simulations show that the naive weak coupling regime (small $κ$, large $β$) does not survive in the thermodynamic limit. Instead, the strong coupling confined phase, spans the whole phase diagram. It is a proliferation of instantons that destroys the weak coupling phase and we show, via a duality transformation, that the expected strong confinement is present in the analog of Wilson line correlators. For finite matter coupling at $q=1$ we find a single thermodynamic phase albeit with a first order phase transition terminating in a critical endpoint.For $q=2$ it is known that the the X-cube model with $\mathbb{Z}_2$ fractonic topological order is recovered deep in the Higgs regime. The simulations indeed reveal a distinct Higgs phase in this case.

hep-lat↗

arXiv2023

Landau Theory of Altermagnetism

We formulate a Landau theory for altermagnets, a class of colinear compensated magnets with spin-split bands. Starting from the non-relativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters and the effect of non-zero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO$_2$, MnTe and CuF$_2$ that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity and magneto-elastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems deriving from the zero spin-orbit coupled limit.

cond-mat.mtrl-sci↗

arXiv2022

Spurious Symmetry Enhancement and Interaction-Induced Topology in Magnons

Linear spin wave theory (LSWT) is the standard technique to compute the spectra of magnetic excitations in quantum materials. In this paper, we show that LSWT, even under ordinary circumstances, may fail to implement the symmetries of the underlying ordered magnetic Hamiltonian leading to spurious degeneracies. In common with pseudo-Goldstone modes in cases of quantum order-by-disorder these degeneracies tend to be lifted by magnon-magnon interactions. We show how, instead, the correct symmetries may be restored at the level of LSWT. In the process we give examples, supported by nonperturbative matrix product based time evolution calculations, where symmetries dictate that there should be a topological magnon gap but where LSWT fails to open up this gap. We also comment on possible spin split magnons in MnF$_2$ and similar rutiles by analogy to recently proposed altermagnets.

cond-mat.other↗

arXiv2022

Quantum Noise as a Symmetry-Breaking Field

We investigate the effect of quantum noise on the measurement-induced quantum phase transition in monitored random quantum circuits. Using the efficient simulability of random Clifford circuits, we find that the transition is broadened into a crossover and that the phase diagram as a function of projective measurements and noise exhibits several distinct regimes. We show that a mapping to a classical statistical mechanics problem accounts for the main features of the random circuit phase diagram. The bulk noise maps to an explicit permutation symmetry breaking coupling; this symmetry is spontaneously broken when the noise is switched off. These results have implications for the realization of entanglement transitions in noisy quantum circuits.

quant-ph↗

arXiv2022

Identifying, and constructing, complex magnon band topology

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path towards coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

cond-mat.mes-hall↗

arXiv2022

Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in mid-spectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the mid-spectrum eigenstates.

cond-mat.stat-mech↗

arXiv2021

Dirac magnons, nodal lines, and nodal plane in elemental gadolinium

We investigate the magnetic excitations of elemental gadolinium (Gd) using inelastic neutron scattering, showing that Gd is a Dirac magnon material with nodal lines at $K$ and nodal planes at half integer $\ell$. We find an anisotropic intensity winding around the $K$-point Dirac magnon cone, which is interpreted to indicate Berry phase physics. Using linear spin wave theory calculations, we show the nodal lines have non-trivial Berry phases, and topological surface modes. We also discuss the origin of the nodal plane in terms of a screw-axis symmetry, and introduce a topological invariant characterizing its presence and effect on the scattering intensity. Together, these results indicate a highly nontrivial topology, which is generic to hexagonal close packed ferromagnets. We discuss potential implications for other such systems.

cond-mat.str-el↗

arXiv2021

Spin exchange Hamiltonian and topological degeneracies in elemental gadolinium

We present a comprehensive study of the magnetic exchange Hamiltonian of elemental Gadolinium. We use neutron scattering to measure the magnon spectrum over the entire Brillouin zone, and fit the excitations to a spin wave model to extract the first 26 nearest neighbor magnetic exchange interactions with rigorously defined uncertainty. We find these exchange interactions to follow RKKY behavior, oscillating from ferromagnetic to antiferromagnetic as a function of distance. Finally, we discuss the topological features and degeneracies in Gd, and HCP ferromagnets in general. We show theoretically how, with asymmetric exchange, topological properties could be tuned with a magnetic field.

cond-mat.str-el↗

arXiv2021

Magnon Interference Tunneling Spectroscopy as a Probe of 2D Magnetism

Probing two-dimensional single-layer quantum magnets remains a significant challenge. In this letter, we propose exploiting tunneling spectroscopy in the presence of magnetic impurities to obtain information about the magnon dispersion relations in analogy to quasiparticle interference in non-magnetic materials. We show this technique can be used to establish the dispersion relations even for frustrated magnets, where the presence of an impurity generally leads to a nontrivial spin texture. Finally, we consider the problem of establishing Chern magnon bands in 2D magnets showing how tuneable impurities allow probing the nature of the surface states.

cond-mat.mes-hall↗

arXiv2021

Information Dynamics in a Model with Hilbert Space Fragmentation

The fully frustrated ladder - a quasi-1D geometrically frustrated spin one half Heisenberg model - is non-integrable with local conserved quantities on rungs of the ladder, inducing the fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets and whose persistence is therefore a consequence of fragmentation. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

cond-mat.stat-mech↗

arXiv2020

Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration

The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flat band systems hosting magnon crystals. We argue that several 1D and 2D models from class (I) exhibit disorder-free localization in high energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of class (II) and (III) exhibit quantum many-body scars -- eigenstates of non-integrable Hamiltonians with finite energy density and anomalously low entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of non-integrable models exhibiting anomalous thermalization in mid-spectrum states.

cond-mat.stat-mech↗

arXiv2020

Statistics of correlation functions in the random Heisenberg chain

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.

cond-mat.dis-nn↗

arXiv2019

Non-Hermitian topology of spontaneous magnon decay

Spontaneous magnon decay is a generic feature of the magnetic excitations of anisotropic magnets and isotropic magnets with non-collinear order. In this paper, we argue that the effect of interactions on one-magnon states can, under many circumstances, be treated in terms of an effective, energy independent, non-Hermitian Hamiltonian for the magnons. In the vicinity of Dirac or Weyl touching points, we show that the spectral function has a characteristic anisotropy arising from topologically protected exceptional points or lines in the non-Hermitian spectrum. Such features can, in principle, be detected using inelastic neutron scattering or other spectroscopic probes. We illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange. We perform interacting spin wave calculations of the structure factor and spectral function of this model, showing good agreement with results from a simple effective non-Hermitian model for the splitting of the Dirac point. Finally, we argue that the zoo of known topological protected magnon band structures may serve as a nearly ideal platform for realizing and exploring non-Hermitian physics in solid-state systems.

cond-mat.str-el↗

arXiv2019

Magnon interactions in the frustrated pyrochlore ferromagnet Yb$_2$Ti$_2$O$_7$

The frustrated rare-earth pyrochlore Yb$_2$Ti$_2$O$_7$ is remarkable among magnetic materials: despite a ferromagnetically ordered ground state it exhibits a broad, nearly gapless, continuum of excitations. This broad continuum connects smoothly to the sharp one-magnon excitations expected, and indeed observed, at high magnetic fields, raising the question: how does this picture of sharp magnons break down as the field is lowered? In this paper, we consider the effects of magnon interactions in Yb$_2$Ti$_2$O$_7$, showing that their inclusion greatly extends the reach of spin-wave theory. First, we show that magnon interactions shift the phase boundary between the (splayed) ferromagnet (SFM) and the antiferromagnetic $Γ_5$ phase so that Yb$_2$Ti$_2$O$_7$ lies very close to it. Next, we show how the high-field limit connects to lower fields; this includes corrections to the critical fields for the $[111]$ and $[1\bar{1}0]$ directions, bringing them closer to the observed experimental values, as well as accounting for the departures from linear spin wave theory that appear in $[001]$ applied fields below 3 T [Thompson et al., Phys. Rev. Lett. 119, 057203 (2017)]. Turning to low-fields, though the extent of the experimentally observed broadening is not quite reproduced, we find a rough correspondence between non-linear spin-wave theory and inelastic neutron scattering data on both a single-crystal sample, as well as on a powder sample [Peçanha-Antonio et al., Phys. Rev. B, 96, 214415 (2017)]. We conclude with an outlook on implications for future experimental and theoretical work on Yb$_2$Ti$_2$O$_7$ and related materials, highlighting the importance of proximity to the splayed ferromagnet-$Γ_5$ phase boundary and its potential role in intrinsic or extrinsic explanations of the low-field physics of Yb$_2$Ti$_2$O$_7$.

cond-mat.str-el↗

arXiv2018

Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets

In systems with competing interactions, continuous degeneracies can appear which are accidental, in that they are not related to any symmetry of the Hamiltonian. Accordingly, the pseudo-Goldstone modes associated with these degeneracies are also unprotected. Indeed, through a process known as "order-by-quantum-disorder", quantum zero-point fluctuations can lift the degeneracy and induce a gap for these modes. We show that this gap can be exactly computed at leading order in $1/S$ in spin-wave theory from the mean curvature of the classical and quantum zero-point energies - without the need to consider any spin-wave interactions. We confirm this equivalence through direct calculations of the spin-wave spectrum to $O(1/S^2)$ in a wide variety of theoretically and experimentally relevant quantum spin models. We prove this equivalence through the use of an exact sum rule that provides the required mixing of different orders of $1/S$. Finally, we discuss some implications for several leading order-by-quantum-disorder candidate materials, clarifying the expected pseudo-Goldstone gap sizes in Er$_2$Ti$_2$O$_7$ and Ca$_3$Fe$_2$Ge$_3$O$_{12}$.

cond-mat.str-el↗

arXiv2018

Eigenstate Thermalization, Random Matrix Theory and Behemoths

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this paper. We report on the construction of highly nonlocal operators, Behemoths, that are building blocks for various kinds of local and non-local operators. The Behemoths have a singular distribution and width $w\sim \mathcal{D}^{-1}$ ($\mathcal{D}$ being the Hilbert space dimension). From them, one may construct local operators with the ordinary Gaussian distribution and $w\sim \mathcal{D}^{-1/2}$ in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with $w\sim \mathcal{D}^{-δ}$, $0<δ<1/2$. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of non-integrable many-body systems.

cond-mat.stat-mech↗

arXiv2013

Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets

The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few experimentally realised examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, the spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterised by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focussing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

cond-mat.str-el↗