20 research outputs found
Killing the Hofstadter butterfly, one bond at a time
Electronic bands in a square lattice when subjected to a perpendicular
magnetic field form the Hofstadter butterfly pattern. We study the evolution of
this pattern as a function of bond percolation disorder (removal or dilution of
lattice bonds). With increasing concentration of the bonds removed, the
butterfly pattern gets smoothly decimated. However, in this process of
decimation, bands develop interesting characteristics and features. For
example, in the high disorder limit, some butterfly-like pattern still persists
even as most of the states are localized. We also analyze, in the low disorder
limit, the effect of percolation on wavefunctions (using inverse participation
ratios) and on band gaps in the spectrum. We explain and provide the reasons
behind many of the key features in our results by analyzing small clusters and
finite size rings. Furthermore, we study the effect of bond dilution on
transverse conductivity(). We show that starting from the clean
limit, increasing disorder reduces to zero, even though the
strength of percolation is smaller than the classical percolation threshold.
This shows that the system undergoes a direct transition from a integer quantum
Hall state to a localized Anderson insulator beyond a critical value of bond
dilution. We further find that the energy bands close to the band edge are more
stable to disorder than at the band center. To arrive at these results we use
the coupling matrix approach to calculate Chern numbers for disordered systems.
We point out the relevance of these results to signatures in
magneto-oscillations.Comment: minor typos fixe
Effects of local periodic driving on transport and generation of bound states
We periodically kick a local region in a one-dimensional lattice and
demonstrate, by studying wave packet dynamics, that the strength and the time
period of the kicking can be used as tuning parameters to control the
transmission probability across the region. Interestingly, we can tune the
transmission to zero which is otherwise impossible to do in a time-independent
system. We adapt the non-equilibrium Green's function method to take into
account the effects of periodic driving; the results obtained by this method
agree with those found by wave packet dynamics if the time period is small. We
discover that Floquet bound states can exist in certain ranges of parameters;
when the driving frequency is decreased, these states get delocalized and turn
into resonances by mixing with the Floquet bulk states. We extend these results
to incorporate the effects of local interactions at the driven site, and we
find some interesting features in the transmission and the bound states.Comment: 14 pages, 12 figures; added several references and corrected some
typo
Percolation Transition in a Topological Phase
Transition out of a topological phase is typically characterized by
discontinuous changes in topological invariants along with bulk gap closings.
However, as a clean system is geometrically punctured, it is natural to ask the
fate of an underlying topological phase. To understand this physics we
introduce and study both short and long-ranged toy models where a one
dimensional topological phase is subjected to bond percolation protocols. We
find that non-trivial boundary phenomena follow competing energy scales even
while global topological response is governed via geometrical properties of the
percolated lattice. Using numerical, analytical and appropriate mean-field
studies we uncover the rich phenomenology and the various cross-over regimes of
these systems. In particular, we discuss emergence of "fractured topological
region" where an overall trivial system contains macroscopic number of
topological clusters. Our study shows the interesting physics that can arise
from an interplay of geometrical disorder within a topological phase.Comment: 6+4 pages,7 figure
Dimensional reduction of Kitaev spin liquid at quantum criticality
We investigate the fate of the Kitaev spin liquid (KSL) under the influence
of an external magnetic field in the [001] direction and upon tuning bond
anisotropy of the Kitaev coupling keeping . Guided by
density matrix renormalization group, exact diagonalization, and with insights
from parton mean field theory, we uncover a field-induced gapless-to-gapless
Lifshitz transition from the nodal KSL to an intermediate gapless phase. The
intermediate phase sandwiched between and , which persists for
a wide range of anisotropy , is composed of weakly coupled
one-dimensional quantum critical chains, and asymptotically approaches the
one-dimensional quantum Ising criticality characterized by the (1+1)D conformal
field theory with a central charge as the field approaches the
phase transition at . Beyond the system enters a partially
polarized phase describable as effectively decoupled bosonic chains in which
spin waves propagate along the one-dimensional zigzag direction. Our findings
provide a comprehensive phase diagram and offer insights into the unusual
physics of dimensional reduction generated by a uniform magnetic field in an
otherwise two-dimensional quantum spin liquid.Comment: 12 pages, 8 figure
Correlation-driven non-trivial phases in single bi-layer Kagome intermetallics
Bi-layer Kagome compounds provide an exciting playground where the interplay
of topology and strong correlations can give rise to exotic phases of matter.
Motivated by recent first principles calculation on such systems (Phys. Rev.
Lett 125, 026401), reporting stabilization of a Chern metal with topological
nearly-flat band close to Fermi level, we build minimal models to study the
effect of strong electron-electron interactions on such a Chern metal. Using
approriate numerical and analytical techniques, we show that the topologically
non-trivial bands present in this system at the Fermi energy can realize
fractional Chern insulator states. We further show that if the time-reversal
symmetry is restored due to destruction of magnetism by low dimensionality and
fluctuation, the system can realize a superconducting phase in the presence of
strong local repulsive interactions. Furthermore, we identify an interesting
phase transition from the superconducting phase to a correlated metal by tuning
nearest-neighbor repulsion. Our study uncovers a rich set of non-trivial phases
realizable in this system, and contextualizes the physically meaningful regimes
where such phases can be further explored.Comment: 16 pages, 14 figure
Spectral Form Factors of Topological Phases
Signatures of dynamical quantum phase transitions and chaos can be found in
the time evolution of generalized partition functions such as spectral form
factors (SFF) and Loschmidt echos. While a lot of work has focused on the
nature of such systems in a variety of strongly interacting quantum theories,
in this work, we study their behavior in short-range entangled topological
phases - particularly focusing on the role of symmetry protected topological
zero modes. We show, using both analytical and numerical methods, how the
existence of such zero modes in any representative system can mask the SFF with
large period (akin to generalized Rabi) oscillations hiding any behavior
arising from the bulk of the spectrum. Moreover, in a quenched disordered
system these zero modes fundamentally change the late time universal behavior
reflecting the chaotic signatures of the zero energy manifold. Our study
uncovers the rich physics underlying the interplay of chaotic signatures and
topological characteristics in a quantum system.Comment: 6+4 pages, 6 figure
Gapless state of interacting Majorana fermions in a strain-induced Landau level
Mechanical strain can generate a pseudo-magnetic field, and hence Landau
levels (LL), for low energy excitations of quantum matter in two dimensions. We
study the collective state of the fractionalised Majorana fermions arising from
residual generic spin interactions in the central LL, where the projected
Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and
particle-hole symmetries forbid any bilinear couplings, leading to an
intrinsically strongly interacting system; also, they allow the definition of a
filling fraction, which is fixed at 1/2. We argue that the resulting many-body
state is gapless within our numerical accuracy, implying ultra-short-ranged
spin correlations, while chirality correlators decay algebraically. This
amounts to a Kitaev `non-Fermi' spin liquid, and shows that interacting
Majorana Fermions can exhibit intricate behaviour akin to fractional quantum
Hall physics in an insulating magnet.Comment: 4 pages, 4 figures, Supplemental Material: 4 page
Anyon dynamics in field-driven phases of the anisotropic Kitaev model
The Kitaev model on a honeycomb lattice with bond-dependent Ising
interactions offers an exactly solvable model of a quantum spin liquid (QSL)
with gapped fluxes and gapless linearly dispersing Majorana fermions in
the isotropic limit (). We explore the phase diagram along two
axes, an external magnetic field, , applied out-of-plane of the honeycomb,
and anisotropic interactions, larger than the other two. For
and , the matter Majorana fermions have the largest gap, and the system is
described by a gapped Toric code in which the fluxes form the low
energy bosonic Ising electric (e) and magnetic (m) charges along with their
fermionic bound state . In this regime, we find that a
small out-of-plane magnetic field creates fermions that disperse in
fixed one-dimensional directions before the transition to a valence bond solid
phase, providing a direct dynamical signature of low energy Abelian flux
excitations separated from the Majorana sector. At lower in the center of
the Abelian phase, in a regime we dub the primordial fractionalized (PF)
regime, the field generates a hybridization between the fermions and
the Majorana matter fermions, resulting in a fermion. All the other
phases in the field-anisotropy plane are naturally obtained from this
primordial soup. We show that in the Abelian phase, including the PF
regime, the dynamical structure factors of local spin flip operators reveal
distinct peaks that can be identified as arising from different anyonic
excitations. We present in detail their signatures in energy and momentum and
propose their identification by inelastic light scattering or inelastic
polarized neutron scattering as ``smoking gun" signatures of fractionalization
in the QSL phase.Comment: 16 pages, 6 figures, 1 tabl