[Show abstract][Hide abstract] ABSTRACT: SrCu2(BO3)2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers ±2. SrCu2(BO3)2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.
[Show abstract][Hide abstract] ABSTRACT: Recent experiments on the spin ice Dy$_2$Ti$_2$O$_7$, suggest that the
Pauling "ice entropy", characteristic of its Coulombic spin-liquid state, may
be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)].
However, despite nearly two decades of intensive study, the nature of the
equilibrium ground state of spin-ice remains uncertain. Here we explore how
long-range dipolar interactions $D$, short-range exchange interactions and
quantum fluctuations combine to determine the ground state of dipolar spin ice.
We find that ordered ground states are selected from a set of "chain states" in
which dipolar interactions are exponentially screened. Using both quantum and
classical Monte Carlo simulation, we establish phase diagrams as a function of
quantum tunneling $g$, and temperature $T$, and find that only a very small
$g_c \ll D$ is needed to stabilize a quantum spin-liquid ground state. We
discuss the implications of these results for Dy$_2$Ti$_2$O$_7$, and for the
"quantum spin ice" materials Yb$_2$Ti$_2$O$_7$, Tb$_2$Ti$_2$O$_7$ and
Pr$_2$Zr$_2$O$_7$.
[Show abstract][Hide abstract] ABSTRACT: The celebrated Shastry Sutherland model has a gapped dimer singlet ground
state. The material SrCu$_2$(BO$_3$)$_2$ serves as a good realization of this
model, upto small anisotropies arising from Dzyaloshinskii Moriya (DM)
interactions. The DM interactions admix a triplet component into the singlet
ground state and give rise to weakly dispersing triplon bands. We show that an
applied magnetic field splits the triplon modes and opens band gaps.
Surprisingly, we are left with topological bands with Chern numbers $\pm 2$.
SrCu$_2$(BO$_3$)$_2$ thus supports topologically protected triplonic edge modes
and is a magnetic analogue of the integer quantum Hall effect. At a critical
value of the magnetic field set by the strength of DM interactions, the three
triplon bands touch once again in a spin-1 generalization of a Dirac cone, and
lose their topological character. We predict a strong thermal Hall signature in
the topological regime.
[Show abstract][Hide abstract] ABSTRACT: We study electrons hopping on a kagome lattice at third filling described by
an extended Hubbard Hamiltonian with on-site and nearest-neighbour repulsions
in the strongly correlated limit. As a consequence of the commensurate filling
and the large interactions, each triangle has precisely two electrons in the
effective low energy description, and these electrons form chains of different
lengths. The effective Hamiltonian includes the ring exchange around the
hexagons as well as the nearest- neighbor Heisenberg interaction. Using large
scale exact diagonalization, we find that the effective model exhibits two
different phases: If the charge fluctuations are small, the magnetic
fluctuations confine the charges to short loops around hexagons, yielding a
gapped charge ordered phase. When the charge fluctuations dominate, the system
undergoes a quantum phase transition to a resonating plaquette phase with
ordered spins and gapless spin excitations. We find that a peculiar
conservation law is fulfilled: the electron in the chains can be divided into
two sublattices, and this division is conserved by the ring exchange term.
Physical Review B 02/2014; 90(3). DOI:10.1103/PhysRevB.90.035118 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the effect of the Berry phase on quadrupoles that occur for
example in the low-energy description of spin models. Specifically we study
here the one-dimensional bilinear-biquadratic spin-one model. An open question
for many years about this model is whether it has a non-dimerized fluctuating
nematic phase. The dimerization has recently been proposed to be related to
Berry phases of the quantum fluctuations. We use an effective low-energy
description to calculate the scaling of the dimerization according to this
theory, and then verify the predictions using large scale density-matrix
renormalization group (DMRG) simulations, giving good evidence that the state
is dimerized all the way up to its transition into the ferromagnetic phase. We
furthermore discuss the multiplet structure found in the entanglement spectrum
of the ground state wave functions.
[Show abstract][Hide abstract] ABSTRACT: We investigate the ground-state properties of the highly degenerate
non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on
the triangular lattice with Monte Carlo simulations. For that purpose, we
introduce an Ising pseudospin representation of the ground states, and we use a
simple Metropolis algorithm with local updates, as well as a powerful cluster
algorithm. At sizes that can be sampled with local updates, the presence of
long-range order is surprisingly combined with an algebraic decay of
correlations and the complete disordering of the chirality. It is only thanks
to the investigation of unusually large systems (containing $\sim 10^8$ spins)
with cluster updates that the true asymptotic regime can be reached and that
the system can be proven to consist of equivalent (i.e., equally ordered)
sublattices. These large-scale simulations also demonstrate that the scalar
chirality exhibits long-range order at zero temperature, implying that the
system has to undergo a finite-temperature phase transition. Finally, we show
that the average distance in the order parameter space, which has the structure
of an infinite Cayley tree, remains remarkably small between any pair of
points, even in the limit when the real space distance between them tends to
infinity.
[Show abstract][Hide abstract] ABSTRACT: The SU(4) Heisenberg model can serve as a low energy model of the Mott
insulating state in materials where the spins and orbitals are highly
symmetric, or in systems of alkaline-earth atoms on optical lattice. Recently,
it has been argued that on the honeycomb lattice the model exhibits a unique
spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et
al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the
algebraic spin-orbital liquid toward spontaneous formation of SU(4) singlet
plaquettes (tetramerization). Using a variational Monte Carlo approach to
evaluate the projected wave-function of fermions with $\pi$-flux state, we find
that the algebraic liquid is robust, and that a finite value of the next
nearest exchange is needed to induce tetramerization. We also studied the phase
diagram of a model which interpolates between the nearest neighbor Heisenberg
model and a Hamiltonian for which the singlet-plaquette product state is an
exact ground state.
[Show abstract][Hide abstract] ABSTRACT: Ba2CoGe2O7 is a multiferroic material
where spin waves exhibit giant directional dichroism and natural optical
activity at THz frequencies due to the large ac magnetoelectric effect
[S. Bordacs et al., Nature Physics 8, 734 (2012)]. We studied spin
excitations in the magnetically ordered phase of the noncentrosymmetric
Ba2CoGe2O7 in high magnetic fields up
to 33 T [Penc et al., Phys. Rev. Lett. 108, 257203 (2012)]. In the ESR
and THz absorption spectra we found several spin excitations beyond the
two conventional magnon modes expected for such a two-sublattice
antiferromagnet. A multiboson spin-wave theory describes these
unconventional modes, including spin-stretching modes, characterized by
an oscillating magnetic dipole and quadrupole moment. The lack of
inversion symmetry allows each mode to become electric dipole active.
[Show abstract][Hide abstract] ABSTRACT: Dynamical properties of the lattice structure were studied by optical spectroscopy in ACr2O4 chromium spinel oxide magnetic semiconductors over a broad temperature region of T=10–335 K. The systematic change of the A-site ions (A= Mn, Fe, Co, Ni and Cu) showed that the occupancy of 3d orbitals on the A site has strong impact on the lattice dynamics. For compounds with orbital degeneracy (FeCr2O4, NiCr2O4, and CuCr2O4), clear splitting of infrared-active phonon modes and/or activation of silent vibrational modes have been observed upon the Jahn-Teller transition and at the onset of the subsequent long-range magnetic order. Although MnCr2O4 and CoCr2O4 show multiferroic and magnetoelectric character, no considerable magnetoelasticity was found in spinel compounds without orbital degeneracy as they closely preserve the high-temperature cubic spinel structure even in their magnetic ground state. Aside from lattice vibrations, intra-atomic 3d-3d transitions of the A2+ ions were also investigated to determine the crystal field and Racah parameters and the strength of the spin-orbit coupling.
[Show abstract][Hide abstract] ABSTRACT: Conflicting predictions have been made for the ground state of the SU(3)
Heisenberg model on the honeycomb lattice: Tensor network simulations found a
plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets
are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a
dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)].
In this work we show that the former state is the true ground state by a
systematic study with infinite projected-entangled pair states (iPEPS), for
which the accuracy can be systematically controlled by the so-called bond
dimension $D$. Both competing states can be reproduced with iPEPS by using
different unit cell sizes. For small $D$ the dimer state has a lower
variational energy than the plaquette state, however, for large $D$ it is the
latter which becomes energetically favorable. The plaquette formation is also
confirmed by exact diagonalizations and variational Monte Carlo studies,
according to which both the dimerized and plaquette states are non-chiral flux
states.
[Show abstract][Hide abstract] ABSTRACT: Faraday rotation and magneto-optical absorption spectral measurements
were conducted on a spinel oxide, ZnCr2O4, a
prototype of three-dimensional geometrically frustrated magnet. The
measurements were carried out at temperatures down to 4.6 K under
ultra-high magnetic fields of up to 600 T. The ultra-high magnetic
fields were generated by the electro-magnetic flux compression method.
We obtained a precise magnetization curve up to a fully polarized phase,
where the phase transition takes place above 400 T. The experimental
magnetization curves were compared with those obtained by Monte Carlo
calculations with an effective spin model including spin--lattice
coupling up to fully saturated magnetization. The absorption spectral
peaks of the intra-d-band transitions in Cr3+ ions as well as
the exciton--magnon--phonon transition were used for monitoring the
crystal and magnetic structures subjected to a strong external magnetic
field. A novel magnetic phase was found prior to the fully polarized
phase, which was clarified by the change in magneto-absorption intensity
around 350 T. An umbrella-like magnetic structure was proposed to be the
most plausible candidate for the novel phase. A physical analogy between
the magnetic structures of ZnCr2O4 and the quantum
phases of 4He was discussed based on the similarity of
symmetry breaking.
Journal of the Physical Society of Japan 11/2012; 81(11):4701-. DOI:10.1143/JPSJ.81.114701 · 1.59 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba_{2}CoGe_{2}O_{7} in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S>1/2 spin systems with strong single-ion anisotropy and/or noncentrosymmetric lattice structure.
[Show abstract][Hide abstract] ABSTRACT: In addition to low-energy spin fluctuations, which distinguish them from band
insulators, Mott insulators often possess orbital degrees of freedom when
crystal-field levels are partially filled. While in most situations spins and
orbitals develop long-range order, the possibility for the ground state to be a
quantum liquid opens new perspectives. In this paper, we provide clear evidence
that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a
quantum spin-orbital liquid. The absence of any form of symmetry breaking -
lattice or SU(N) - is supported by a combination of semiclassical and numerical
approaches: flavor-wave theory, tensor network algorithm, and exact
diagonalizations. In addition, all properties revealed by these methods are
very accurately accounted for by a projected variational wave-function based on
the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that
state, correlations are algebraic because of the presence of a Dirac point at
the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the
honeycomb lattice is an algebraic quantum spin-orbital liquid. This model
provides a good starting point to understand the recently discovered
spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest
to choose optical lattices with honeycomb geometry in the search for quantum
liquids in ultra-cold four-color fermionic atoms.
Physical Review X 07/2012; 2(4). DOI:10.1103/PhysRevX.2.041013 · 9.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider the square-lattice antiferromagnetic Heisenberg Hamiltonian
extended with a single-ion axial anisotropy term as a minimal model for the
multiferroic Ba2CoGe2O7. Developing a multiboson spin-wave theory, we
investigate the dispersion of the spin excitations in this spin-3/2 system. As
a consequence of a strong single-ion anisotropy, a stretching (longitudinal)
spin-mode appears in the spectrum. The inelastic neutron scattering spectra of
Zheludev et al. [Phys. Rev. B 68, 024428 (2003)] are successfully reproduced by
the low energy modes in the multiboson spin-wave theory, and we anticipate the
appearance of the spin stretching modes at 4meV that can be identified using
the calculated dynamical spin structure factors. We expect the appearance of
spin stretching modes for any S>1/2 compound where the single-ion anisotropy is
significant.
[Show abstract][Hide abstract] ABSTRACT: We present a numerical study of the SU(N) Heisenberg model with the
fundamental representation at each site for the kagome lattice (for N=3) and
the checkerboard lattice (for N=4), which are the line graphs of the honeycomb
and square lattices and thus belong to the class of bisimplex lattices. Using
infinite projected entangled-pair states (iPEPS) and exact diagonalizations, we
show that in both cases the ground state is a simplex solid state with a
two-fold ground state degeneracy, in which the N spins belonging to a simplex
(i.e. a complete graph) form a singlet. Theses states can be seen as
generalizations of valence bond solid states known to be stabilized in certain
SU(2) spin models.
[Show abstract][Hide abstract] ABSTRACT: We studied spin excitations of the multiferroic Ba2CoGe2O7 in high magnetic
fields up to 33 T. In the electron spin resonance and far infrared absorption
spectra we found several spin excitations beyond the two conventional magnon
modes expected for such a two-sublattice antiferromagnet. We show that a
multi-boson spin-wave theory can capture these unconventional modes, that
include spin-stretching modes associated with an oscillating magnetic dipole
(or only quadrupole) moment. The lack of the inversion symmetry allows these
modes to become electric dipole active. We expect that the spin-stretching
modes can be generally observed in inelastic neutron scattering and light
absorption experiments in a broad class of ordered S > 1/2 spin systems with
strong single-ion anisotropy and/or non-centrosymmetric lattice structure.
[Show abstract][Hide abstract] ABSTRACT: We investigate the zero-temperature behavior of the classical Heisenberg
model on the triangular lattice in which the competition between exchange
interactions of different orders favors a relative angle between neighboring
spins in the interval (0,2pi/3). In this situation, the ground states are
noncoplanar and have an infinite discrete degeneracy. In the generic case, the
set of the ground states is in one to one correspondence (up to a global
rotation) with the non-crossing loop coverings of the three equivalent
honeycomb sublattices into which the bonds of the triangular lattice can be
partitioned. This allows one to identify the order parameter space as an
infinite Cayley tree with coordination number 3. Building on the duality
between a similar loop model and the ferromagnetic O(3) model on the honeycomb
lattice, we argue that a typical ground state should have long-range order in
terms of spin orientation. This conclusion is further supported by the
comparison with the four-state antiferromagnetic Potts model [describing the
case when the angle between neighboring spins is equal to arccos(-1/3)], which
at zero temperature is critical and in terms of the solid-on-solid
representation is located exactly at the point of roughening transition. At
other values of the angle between neighboring spins an additional constraint
appears, whose presence drives the system into an ordered phase (unless this
angle is equal to pi/2, when another constraint is removed and the model
becomes trivially exactly solvable).
[Show abstract][Hide abstract] ABSTRACT: Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin-ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilizing a unique "quantum-ice" ground state-a quantum liquid with excitations described by the Maxwell action of (3+1)-dimensional quantum electrodynamics. We further identify a competing ordered squiggle state, and show how both squiggle and quantum-ice states might be distinguished in neutron scattering experiments on a spin-ice material.
[Show abstract][Hide abstract] ABSTRACT: By applying external magnetic field the square-lattice antiferromagnet
Ba2CoGe2O7 can be transformed to a
chiral form, evidenced by large optical activity when the light is in
resonance with spin excitations at sub-terahertz frequencies. We found
that the magnetochiral effect, the absorption difference for the light
beams propagating parallel and anti-parallel to the applied magnetic
field, has an exceptionally large amplitude close to 100% and persists
to fields up to 30,. All these features are ascribed to the
magnetoelectric nature of spin excitations as they interact both with
the electric and magnetic components of light. We observe a spin flop at
15,, that is consistent with our theoretical calculations.