69 research outputs found
Symmetry breaking and Landau quantization in topological crystalline insulators
In the recently discovered topological crystalline insulators SnTe and
Pb_{1-x}Sn_{x}(Te,Se), crystal symmetry and electronic topology intertwine to
create topological surface states with many interesting features including
Lifshitz transition, Van-Hove singularity and fermion mass generation. These
surface states are protected by mirror symmetry with respect to the (110)
plane. In this work we present a comprehensive study of the effects of
different mirror-symmetry-breaking perturbations on the (001) surface band
structure. Pristine (001) surface states have four branches of Dirac fermions
at low-energy. We show that ferroelectric-type structural distortion generates
a mass and gaps out some or all of these Dirac points, while strain shifts
Dirac points in the Brillouin zone. An in-plane magnetic field leaves surface
state gapless, but introduces asymmetry between Dirac points. Finally, an
out-of-plane magnetic field leads to discrete Landau levels. We show that the
Landau level spectrum has an unusual pattern of degeneracy and interesting
features due to the unique underlying band structure. This suggests that Landau
level spectroscopy can detect and distinguish between different mechanisms of
symmetry breaking in topological crystalline insulators.Comment: 10 pages, 5 figures, main results are summarized in Table I; (v2)
minor correction
Spectral statistics across the many-body localization transition
The many-body localization transition (MBLT) between ergodic and many-body
localized phase in disordered interacting systems is a subject of much recent
interest. Statistics of eigenenergies is known to be a powerful probe of
crossovers between ergodic and integrable systems in simpler examples of
quantum chaos. We consider the evolution of the spectral statistics across the
MBLT, starting with mapping to a Brownian motion process that analytically
relates the spectral properties to the statistics of matrix elements. We
demonstrate that the flow from Wigner-Dyson to Poisson statistics is a
two-stage process. First, fractal enhancement of matrix elements upon
approaching the MBLT from the metallic side produces an effective power-law
interaction between energy levels, and leads to a plasma model for level
statistics. At the second stage, the gas of eigenvalues has local interaction
and level statistics belongs to a semi-Poisson universality class. We verify
our findings numerically on the XXZ spin chain. We provide a microscopic
understanding of the level statistics across the MBLT and discuss implications
for the transition that are strong constraints on possible theories.Comment: 5 pages, 3 figure
Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
The half filled Landau level is expected to be approximately particle-hole
symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of
the compressible state observed at this filling. Recent work indicates that,
when particle-hole symmetry is preserved, the composite Fermions experience a
quantized -Berry phase upon winding around the composite Fermi-surface,
analogous to Dirac fermions at the surface of a 3D topological insulator. In
contrast, the effective low energy theory of the composite fermion liquid
originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry
phase. In this paper, we explain how thermoelectric transport measurements can
be used to test the Dirac nature of the composite Fermions by quantitatively
extracting this Berry phase. First we point out that longitudinal thermopower
(Seebeck effect) is non-vanishing due to the unusual nature of particle hole
symmetry in this context and is not sensitive to the Berry phase. In contrast,
we find that off-diagonal thermopower (Nernst effect) is directly related to
the topological structure of the composite Fermi surface, vanishing for zero
Berry phase and taking its maximal value for Berry phase. In contrast, in
purely electrical transport signatures the Berry phase contributions appear as
small corrections to a large background signal, making the Nernst effect a
promising diagnostic of the Dirac nature of composite fermions.Comment: 5+4 pages, 2 figures; v2: minor changes, close to published versio
Overscreened Kondo fixed point in S=1 spin liquid
We propose a possible realization of the overscreened Kondo impurity problem
by a magnetic s=1/2 impurity embedded in a two-dimensional S=1 U(1) spin liquid
with a Fermi surface. This problem contains an interesting interplay between
non-Fermi-liquid behavior induced by a U(1) gauge field coupled to fermions and
a non-Fermi-liquid fixed point in the overscreened Kondo problem. Using a
large-N expansion together with an expansion in the dynamical exponent of the
gauge field, we find that the coupling to the gauge field leads to weak but
observable changes in the physical properties of the system at the overscreened
Kondo fixed point. We discuss the extrapolation of this result to a physical
case and argue that the realization of overscreened Kondo physics could lead to
observations of effects due to gauge fields.Comment: 10 pages, 5 figure
Duality approach to quantum annealing of the 3-XORSAT problem
Classical models with complex energy landscapes represent a perspective
avenue for the near-term application of quantum simulators. Until now, many
theoretical works studied the performance of quantum algorithms for models with
a unique ground state. However, when the classical problem is in a so-called
clustering phase, the ground state manifold is highly degenerate. As an
example, we consider a 3-XORSAT model defined on simple hypergraphs. The
degeneracy of classical ground state manifold translates into the emergence of
an extensive number of symmetries, which remain intact even in the
presence of a quantum transverse magnetic field. We establish a general duality
approach that restricts the quantum problem to a given sector of conserved
charges and use it to study how the outcome of the quantum adiabatic
algorithm depends on the hypergraph geometry. We show that the tree hypergraph
which corresponds to a classically solvable instance of the 3-XORSAT problem
features a constant gap, whereas the closed hypergraph encounters a
second-order phase transition with a gap vanishing as a power-law in the
problem size. The duality developed in this work provides a practical tool for
studies of quantum models with classically degenerate energy manifold and
reveals potential connections between glasses and gauge theories
Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
Motivated by recent experiments on Ba3NiSb2O9, we investigate possible
quantum spin liquid ground states for spin S=1 Heisenberg models on the
triangular lattice. We use Variational Monte Carlo techniques to calculate the
energies of microscopic spin liquid wave functions where spin is represented by
three flavors of fermionic spinon operators. These energies are compared with
the energies of various competing three-sublattice ordered states. Our approach
shows that the antiferromagnetic Heisenberg model with biquadratic term and
single-ion anisotropy does not have a low-temperature spin liquid phase.
However, for an SU(3)-invariant model with sufficiently strong ring-exchange
terms, we find a paired chiral quantum spin liquid with a Fermi surface of
deconfined spinons that is stable against all types of ordering patterns we
considered. We discuss the physics of this exotic spin liquid state in relation
with the recent experiment and suggest new ways to test this scenario.Comment: 18 pages, 6 figures; replaced with published versio
Quantum annealing initialization of the quantum approximate optimization algorithm
The quantum approximate optimization algorithm (QAOA) is a prospective
near-term quantum algorithm due to its modest circuit depth and promising
benchmarks. However, an external parameter optimization required in QAOA could
become a performance bottleneck. This motivates studies of the optimization
landscape and search for heuristic ways of parameter initialization. In this
work we visualize the optimization landscape of the QAOA applied to the MaxCut
problem on random graphs, demonstrating that random initialization of the QAOA
is prone to converging to local minima with sub-optimal performance. We
introduce the initialization of QAOA parameters based on the Trotterized
quantum annealing (TQA) protocol, parameterized by the Trotter time step. We
find that the TQA initialization allows to circumvent the issue of false minima
for a broad range of time steps, yielding the same performance as the best
result out of an exponentially scaling number of random initializations.
Moreover, we demonstrate that the optimal value of the time step coincides with
the point of proliferation of Trotter errors in quantum annealing. Our results
suggest practical ways of initializing QAOA protocols on near-term quantum
devices and reveals new connections between QAOA and quantum annealing.Comment: 10 pages, 9 figures; typos corrected, references adde
Non-interacting central site model: localization and logarithmic entanglement growth
We investigate the stationary and dynamical behavior of an Anderson localized
chain coupled to a single central bound state. The coupling to the central site
partially dilutes the Anderson localized peak towards the nearly resonant
sites. In particular, the number of resonantly coupled sites remains finite in
the thermodynamic limit. This is further supported by a multifractal analysis
of eigenstates that shows the frozen spectrum of fractal dimension, which is
characteristic for localized phases in models with power-law hopping. Although
the well-known Fano-resonance problem is seemingly similar to our system, it
fails to describe it because of the absence of level repulsion within the
energy spectrum. For weak coupling strengths to the central site, we identify a
regime with a logarithmic in time transport of particles and information.Comment: 10 pages, 7 figure
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