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 helium3,4,5,6,7,8, 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)
Frustrated magnets and fractionalization
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
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)
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)
Phys. Rev. Lett. 122, 117201 (2019)
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)
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)
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)
Phys. Rev. B 98, 165147 (2018)
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 0.47kB 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)
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)
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)
Phys. Rev. B 98, 144413 (2018)