30 research outputs found
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.Comment: 4+epsilon page
Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited
We investigate the properties of the XY pyrochlore antiferromagnet with local
planar anisotropy. We find the ground states and show that the
configurational ground state entropy is subextensive. By computing the free
energy due to harmonic fluctuations and by carrying out Monte Carlo
simulations, we confirm earlier work indicating that the model exhibits thermal
order-by-disorder leading to low temperature long-range order consisting of
discrete magnetic domains. We compute the spin wave spectrum and show that
thermal and quantum fluctuations select the same magnetic structure. Using
Monte Carlo simulations, we find that the state selected by thermal
fluctuations in this XY pyrochlore antiferromagnet can survive the addition of
sufficiently weak nearest-neighbor pseudo-dipolar interactions to the spin
Hamiltonian. We discuss our results in relation to the Er2Ti2O7 pyrochlore
antiferromagnet.Comment: 13 pages, 6 figure
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∼D−1 (D being the Hilbert space dimension). From them, one may construct local operators with the ordinary Gaussian distribution and w∼D−1/2 in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with w∼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
Entanglement of mid-spectrum eigenstates of chaotic many-body systems -- 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.Comment: 8 pages, 5 figures, 122 references + 6 pages, 9 figures in 8
Appendice
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 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 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 . Finally, we discuss some implications for
several leading order-by-quantum-disorder candidate materials, clarifying the
expected pseudo-Goldstone gap sizes in ErTiO and
CaFeGeO.Comment: 5 + 26 pages, 3 figures. Corrected discussion of cubic garnet,
expanded supplemental materia
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.Comment: 15 pages, 8 figures; revised version, new figures; accepted for
publication in Physical Review
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 and similar rutiles by analogy to recently proposed altermagnets