Frustrated magnets and fractionalization

One of the attractions of condensed matter physics is how experimental and theoretical developments can go hand-in-hand. In particular, theories can be subjected to experimental tests on reasonable timescales, while experiments frequently throw up puzzles to inspire and challenge theory.

In order to find new types of behaviour, one prerequisite is to find settings where familiar phenomena do not occur. For magnetic system, in order to observe new topological magnetic phases, it is necessary that the conventional types of (anti-)ferromagnetism are sufficiently destabilised to make room for alternative collective instabilities.

A very productive strategy has been to consider magnets where magnetic interactions compete; in the corresponding models, fundamentally new spin liquid phases with very unusual properties have been generated. These include fractionalised phases which, besides exhibiting topological forms of order, also have exotic quasiparticles, including spinons and holons (which independently carry the magnetic and electric aspects of an electron), Majorana Fermions (which are their own antiparticle) and magnetic monopoles (which carry magnetic charge).

Much of our work, besides developing the theoretical underpinnings of these phenomena, is devoted to understanding, interpreting and guiding experimental efforts to realise such phenomena in materials physics.

Avoided quasiparticle decay from strong quantum interactions

Ruben Verresen, Roderich Moessner, Frank Pollmann

Quantum states of matter-such as solids, magnets and topological phases-typically exhibit collective excitations (for example, phonons, magnons and anyons)¹. These involve the motion of many particles in the system, yet, remarkably, act like a single emergent entity-a quasiparticle. Known to be long lived at the lowest energies, quasiparticles are expected to become unstable when encountering the inevitable continuum of many-particle excited states at high energies, where decay is kinematically allowed. Although this is correct for weak interactions, we show that strong interactions generically stabilize quasiparticles by pushing them out of the continuum. This general mechanism is straightforwardly illustrated in an exactly solvable model. Using state-of-the-art numerics, we find it at work in the spin- 1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF). This is surprising given the expectation of magnon decay in this paradigmatic frustrated magnet. Turning to existing experimental data, we identify the detailed phenomenology of avoided decay in the TLHAF material² Ba₃CoSb₂O₉, and even in liquid helium^3,4,5,6,7,8, one of the earliest instances of quasiparticle decay⁹. Our work unifies various phenomena above the universal low-energy regime in a comprehensive description. This broadens our window of understanding of many- body excitations, and provides a new perspective for controlling and stabilizing quantum matter in the strongly interacting regime.

Nature Physics (2019)

Rod motifs in neutron scattering in spin ice

Claudio Castelnovo and Roderich Moessner

In classical and quantum spin ice, rodlike features appear in the neutron-scattering structure factor when the pinch points characteristic of classical spin ice get washed out. We show that these features do not indicate the absence of spin correlations between planes perpendicular to the rods. Rather, they arise because neutron scattering is largely insensitive to the three- dimensional correlations which are present throughout. We present two very simple models which exhibit a pristine incarnation of such scattering rods. This provides a physical picture for their appearance, elucidates the role played by monopole excitations, and identifies conditions conducive to their observation.

Phys. Rev. B 99, 121102(R) (2019)

Spectrum of Itinerant Fractional Excitations in Quantum Spin Ice

Masafumi Udagawa and Roderich Moessner

We study the quantum dynamics of fractional excitations in quantum spin ice. We focus on the density of states in the two-monopole sector, ρ(ω), as this can be connected to the wave-vector-integrated dynamical structure factor accessible in neutron scattering experiments. We find that ρ(ω) exhibits a strikingly characteristic singular and asymmetric structure that provides a useful fingerprint for comparison to experiment. ρ(ω) obtained from the exact diagonalization of a finite cluster agrees well with that, from the analytical solution of a hopping problem on a Husimi cactus representing configuration space, but not with the corresponding result on a face-centered cubic lattice, on which the monopoles move in real space. The main difference between the latter two lies in the inclusion of the emergent gauge field degrees of freedom, under which the monopoles are charged. This underlines the importance of treating both sets of degrees of freedom together, and it presents a novel instance of dimensional transmutation.

Phys. Rev. Lett. 122, 117201 (2019)

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Anyons and fractional quantum Hall effect in fractal dimensions

S. Manna, B. Pal, W. Wang, and A. E. B. Nielsen

The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. We provide analytical wave functions and exact few-body parent Hamiltonians, and we show numerically for several different Hausdorff dimensions between 1 and 2 that the systems host anyons. We also find examples of fractional quantum Hall physics in fractals with Hausdorff dimension 1 and ln(4)/ln(5). Our results suggest that the local structure of the investigated fractals is more important than the Hausdorff dimension to determine whether the systems are in the desired topological phase. The study paves the way for further investigations of strongly correlated topological systems in fractal dimensions.

Phys. Rev. Research 2, 023401 (2020)

Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models

A. E. B. Nielsen, I. Glasser, I. D. Rodriguez

From an experimental point of view, quasielectrons and quasiholes play very similar roles in the fractional quantum Hall effect. Nevertheless, the theoretical description of quasielectrons is known to be much harder than the one of quasiholes. The problem is that one obtains a singularity in the wavefunction if one tries to naively construct the quasielectron as the inverse of the quasihole. Here, we demonstrate that the same problem does not arise in lattice fractional quantum Hall models. This result allows us to make detailed investigations of the properties of quasielectrons, including their braiding statistics and density distribution on lattices on the plane and on the torus. We show that some of the states considered have high overlap with certain fractional Chern insulator states. We also derive few-body Hamiltonians, for which various states containing quasielectrons are exact ground states.

New J. Phys. 20, 033029 (2018)

Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

Sourav Manna, Julia Wildeboer, German Sierra, and Anne E. B. Nielsen

This work concerns Ising quasiholes in Moore-Read type lattice wave functions derived from conformal field theory. We commence with constructing Moore-Read type lattice states and then add quasiholes to them. By use of Metropolis Monte Carlo simulations, we analyze the features of the quasiholes, such as their size, shape, charge, and braiding properties. The braiding properties, which turn out to be the same as in the continuum Moore-Read state, demonstrate the topological attributes of the Moore-Read lattice states in a direct way. We also derive parent Hamiltonians for which the states with quasiholes included are ground states. One advantage of these Hamiltonians lies therein that we can now braid the quasiholes just by changing the coupling strengths in the Hamiltonian since the Hamiltonian is a function of the positions of the quasiholes. The methodology exploited in this article can also be used to construct other kinds of lattice fractional quantum Hall models containing quasiholes, for example, investigation of Fibonacci quasiholes in lattice Read-Rezayi states.

Phys. Rev. B 98, 165147 (2018)

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Pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature

R. Schäfer, I. Hagymási, R. Moessner, and D. J. Luitz

We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore S=1/2 quantum antiferromagnet, at finite temperature T: canonical typicality for a finite cluster of 2×2×2 unit cells (i.e., 32 sites), a finite-T matrix product state method on a larger cluster with 48 sites, and the numerical linked cluster expansion (NLCE) using clusters up to 25 lattice sites, including nontrivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and the static structure factor. We find a pronounced maximum in the specific heat at T=0.57J, which is stable across finite size clusters and converged in the series expansion. At T≈0.25J (the limit of convergence of our method), the residual entropy per spin is 0.47k_B ln 2, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on T of the magnetization at low magnetic fields, reflecting the dominantly nonmagnetic character of the low-energy states. A detailed comparison of our results to measurements for the S=1 material NaCaNi₂F₇ yields a rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material Dy₂Ti₂O₇.

Phys. Rev. B 102, 054408 (2020)

Dynamical Structure Factor of the Three-Dimensional Quantum Spin Liquid Candidate NaCaNi₂F₇

S. Zhang, H. J. Changlani, K. W. Plumb, O. Tchernyshyov, and R. Moessner

We study the dynamical structure factor of the spin-1 pyrochlore material NaCaNi₂F₇, which is well described by a weakly perturbed nearest-neighbour Heisenberg Hamiltonian, Our three approaches-molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory-reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence with the exception of the lowest energies. We discuss two surprising aspects and their implications for quantum spin liquids in general: the complete lack of sharp quasiparticle excitations in momentum space and the success of the linear spin wave theory in a regime where it would be expected to fail for several reasons.

Phys. Rev. Lett. 122, 167203 (2019)

Emergent electrochemistry in spin ice: Debye-Hückel theory and beyond

V. Kaiser, J. Bloxsom, L. Bovo, S. T. Bramwell, P. C. W. Holdsworth, and R. Moessner

We present a detailed theoretical and experimental study to show how a model system for the investigation of classic electrolyte theory emerges in a nonelectrical context. In particular we develop the thermodynamic treatment of spin ice as a “magnetolyte”, a fluid of singly and doubly charged magnetic monopoles. This is equivalent to the electrochemical system 2H₂O = H₃O⁺ + OH^- = H₄O₂⁺ + O₂^-, but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis going beyond Debye-Hückel theory to include Bjerrum pairs. This is accurate at all temperatures and incorporates “Dirac strings” imposed by the microscopic ice rule constraints at the level of Pauling’s approximation. Our theory is in close agreement with the specific heat from numerical simulations as well as new experimental measurements with an improved lattice correction, which we present here, on the spin ice materials Ho₂Ti₂O₇ and Dy₂Ti₂O₇. Our results provide new experimental tests of Debye-Hückel theory and its extensions and yield insights into the electrochemical behavior of water ice and liquid water, which are closely related to the spin ice magnetolyte.

Phys. Rev. B 98, 144413 (2018)

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