[Show abstract][Hide abstract] ABSTRACT: By combining the Baeriswyl wavefunction with equilibrium and time-dependent
variational principles, we develop a non-equilibrium formalism to study quantum
quenches for two dimensional spinless fermions with nearest-neighbour hopping
and repulsion. The variational ground state energy and the short time dynamics
agree convincingly with the results of numerically exact simulations. We find
that depending on the initial and final interaction strength, the quenched
system either exhibits undamped oscillations or relaxes to a time independent
steady state. The time averaged expectation value of the CDW order parameter
rises sharply when crossing from the steady state regime to the oscillating
regime, indicating that the system, being non-integrable, shows signs of
thermalization with an effective temperature above or below the equilibrium
critical temperature, respectively.
[Show abstract][Hide abstract] ABSTRACT: The non-equilibrium dynamics beyond linear response of Weyl semimetals is
studied after a sudden switching on of a DC electric field. The resulting
current is a nonmonotonic function of time, with an initial quick increase of
polarization current followed by a power-law decay. Particle-hole creation \`a
la Schwinger dominates for long times when the conduction current takes over
the leading role, with the total current increasing again. The conductivity
estimated from a dynamical calculation within a Drude picture agrees with the
one obtained from Kubo's formula. The full distribution function of
electron-hole pairs changes from Poissonian for short perturbations to a
Gaussian in the long perturbation (Landau-Zener) regime. The vacuum persistence
probability of high energy physics manifests itself in a finite probability of
no pair creation and no induced current at all times.
Physical Review B 05/2015; 92(8). DOI:10.1103/PhysRevB.92.085122 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form in
conventional materials with weak spin orbit coupling, whose spectral width
characterizes the spin relaxation rate. We show that DSS has an unusual
non-Lorentzian form in topological insulators, which are characterized by
strong SOC. At zero temperature, the high frequency part of DSS is universal
and increases in certain directions as $\omega^{d-1}$ with $d=2$ and 3 for
surface states and Weyl semimetals, respectively, while for helical edge
states, the interactions renormalize the exponent as $d=2K-1$ with $K$ the
Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced
from the DSS in contrast to the case of usual metals, which follows from the
strongly entangled spin and charge degrees of freedom in these systems. These
parallel with the optical conductivity of neutral graphene.
[Show abstract][Hide abstract] ABSTRACT: We investigate the Loschmidt echo, the overlap of the initial and final
wavefunctions of Luttinger liquids after a spatially inhomogeneous interaction
quench. In studying the Luttinger model, we obtain an analytic solution of the
bosonic Bogoliubov-de Gennes equations after quenching the interactions within
a finite spatial region. As opposed to the power law temporal decay following a
potential quench, the interaction quench in the Luttinger model leads to a
finite, hardly time dependent overlap, therefore no orthogonality catastrophe
occurs. The steady state value of the Loschmidt echo after a sudden
inhomogeneous quench is the square of the respective adiabatic overlaps. Our
results are checked and validated numerically on the XXZ Heisenberg chain.
[Show abstract][Hide abstract] ABSTRACT: Dynamical phase transitions (DPT) are characterized by nonanalytical time
evolution of the dynamical free energy. For general 2-band systems in one and
two dimensions (eg. SSH model, Kitaev-chain, Haldane model, p+ip
superconductor, etc.), we show that the time evolution of the dynamical free
energy is crucially affected by the ground state topology of both the initial
and final Hamiltonians, implying DPTs when the topology is changed under the
quench. Similarly to edge states in topological insulators, DPTs can be
classified as being topologically protected or not. In 1D systems the number of
topologically protected non-equilibrium time scales are determined by the
difference between the initial and final winding numbers, while in 2D no such
relation exists for the Chern numbers. The singularities of dynamical free
energy in the 2D case are qualitatively different from those of the 1D case,
the cusps appear only in the first time derivative.
Physical Review B 09/2014; 91(15). DOI:10.1103/PhysRevB.91.155127 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the escort probability distribution function of work done during an
interaction quantum quench of Luttinger liquids. It crosses over from the
thermodynamic to the small system limit with increasing $a$, the order of the
escort distribution, and depends on the universal combination
$(|K_i-K_f|/(K_i+K_F))^a$ with $K_i$, $K_f$ the initial and final Luttinger
liquid parameters, respectively. From its characteristic function, the diagonal
R\'enyi entropies and the many body inverse participation ratio (IPR) are
determined to evaluate the information content of the time evolved wavefunction
in terms of the eigenstates of the final Hamiltonian. The hierarchy of overlaps
is dominated by that of the ground states. The IPR exhibits a crossover from
Gaussian to power law decay with increasing interaction quench parameter.
Physical Review B 09/2014; 90(24). DOI:10.1103/PhysRevB.90.245132 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Topological excitations keep fascinating physicists since many decades. While
individual vortices and solitons emerge and have been observed in many areas of
physics, their most intriguing higher dimensional topological relatives,
skyrmions (smooth, topologically stable textures) and magnetic monopoles --
emerging almost necessarily in any grand unified theory and responsible for
charge quantization -- remained mostly elusive. Here we propose that loading a
three-component nematic superfluid such as $^{23}$Na into a deep optical
lattice and thereby creating an insulating core, one can create topologically
stable skyrmion textures and investigate their properties in detail. We show
furthermore that the spectrum of the excitations of the superfluid and their
quantum numbers change dramatically in the presence of the skyrmion, and they
reflect the presence of a trapped monopole, as imposed by the skyrmion's
topology.
[Show abstract][Hide abstract] ABSTRACT: A (single flavor) quadratic band crossing in two dimensions is known to have
a generic instability towards a quantum anomalous Hall (QAH) ground state for
infinitesimal repulsive interactions. Here we introduce a generalization of a
quadratic band crossing which is protected only by rotational symmetry. By
focusing on the representative case of a parabolic and flat band touching,
which also allows for a straightforward lattice realization, the interaction
induced nematic phase is found generally to compete successfully with the QAH
insulator, and to become the dominant instability in certain parts of the phase
diagram already at weak coupling. The full phase diagram of the model, together
with its topological properties, is mapped out using a perturbative
renormalization group, strong coupling analysis, the mean-field theory.
Interestingly, the Berry flux varies continuously in the single flavour limit
with various control parameters.
Physical Review B 02/2014; 90(4). DOI:10.1103/PhysRevB.90.045310 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Dynamical phase transitions (DPT) occur after quenching some global
parameters in quantum systems and are signalled by the non-analytical time
evolution of the dynamical free energy, which is calculated from the Loschmidt
overlap between the initial and time evolved states. In a recent letter (M.
Heyl et al., Phys. Rev. Lett. \textbf{110}, 135704 (2013)), it was suggested
that DPTs are closely related to equilibrium phase transitions (EPT) for the
transverse field Ising model. By studying a minimal model, the XY chain in
transverse magnetic field, we show analytically that this connection does not
hold generally. We present examples where DPT occurs without crossing any
equilibrium critical lines by the quench, and a nontrivial example with no DPT
but crossing a critical line by the quench. Albeit the non-analyticities of the
dynamical free energy on the real time axis do not indicate the presence or
absence of an EPT, the structure of Fisher-lines for complex times reveal a
qualitative difference.
Physical Review B 01/2014; 89(16). DOI:10.1103/PhysRevB.89.161105 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Spintronics is an emerging paradigm with the aim to replace conventional electronics by using electron spins as information carriers. Its utility relies on the magnitude of the spin-relaxation, which is dominated by spin-orbit coupling (SOC). Yet, SOC induced spin-relaxation in metals and semiconductors is discussed for the seemingly orthogonal cases when inversion symmetry is retained or broken by the so-called Elliott-Yafet and D'yakonov-Perel' spin-relaxation mechanisms, respectively. We unify the two theories on general grounds for a generic two-band system containing intra- and inter-band SOC. While the previously known limiting cases are recovered, we also identify parameter domains when a crossover occurs between them, i.e. when an inversion symmetry broken state evolves from a D'yakonov-Perel' to an Elliott-Yafet type of spin-relaxation and conversely for a state with inversional symmetry. This provides an ultimate link between the two mechanisms of spin-relaxation.
[Show abstract][Hide abstract] ABSTRACT: We study the non-equilibrium dynamics of the Luttinger model after a quantum
quench, when the initial state is a finite temperature thermal equilibrium
state. The diagonal elements of the density matrix in the steady state show
thermal features for high temperature initial states only, otherwise retain
highly non-thermal character. The time evolution of Uhlmann fidelity, which
measures the distance between the time evolved and initial states, is evaluated
for arbitrary initial temperatures and quench protocols. In the long time
limit, the overlap between the time evolved and initial system decreases
exponentially with the temperature with a universal prefactor. Within
perturbation theory, the statistics of final total energy and work are
numerically evaluated in the case of a sudden quench, which yield identical
distributions at zero temperature. In both statistics, temperature effects are
more significant in small systems. The Dirac-delta peak at the adiabatic ground
state energy remains present in the probability distribution of the total
energy, but disappears from the work distribution at non-zero initial
temperatures.
Physical Review B 07/2013; 88(15). DOI:10.1103/PhysRevB.88.155115 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry.
[Show abstract][Hide abstract] ABSTRACT: The persistent current in strictly one-dimensional Dirac systems is
investigated within two different models, defined in the continuum and on a
lattice, respectively. The object of the study is the effect of a single
magnetic or nonmagnetic impurity in the two systems. In the continuum Dirac
model, an analytical expression for the persistent current flowing along a ring
with a single delta-like magnetic impurity is obtained after regularization of
the unbounded negative energy states. The predicted decay of the persistent
agrees with the lattice simulations. The results are generalized to finite
temperatures. To realize a single Dirac massless fermion, the lattice model
breaks the time-reversal symmetry, and, in contrast with the continuum model, a
pointlike nonmagnetic impurity can lead to a decay in the persistent current.
Physical Review B 07/2013; 88(20). DOI:10.1103/PhysRevB.88.205401 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The manipulation and movement of Dirac points in the Brillouin zone by the
electron-electron interaction is considered within leading order perturbation
theory. At the merging point, an infinitesimal interaction is shown to cause
opening of the gap or splitting of the Dirac points, depending on the inter- or
intrasublattice nature of the merging and the sign of the interaction. The
topology of the spectrum can therefore be efficiently changed by simply tuning
the interaction between particles, as opposed to the usual careful band
structure engineering. This is illustrated around the merging transition of
one, two, and three dimensional Dirac-Weyl fermions. A simple Weyl-like
Hamiltonian that describes the quadratic band-crossing in three dimensions is
also proposed, and its stability under interactions is addressed.
[Show abstract][Hide abstract] ABSTRACT: Several lattices, such as the dice or the Lieb lattice, possess Dirac cones
and a flat band crossing the Dirac point, whose effective model is the
pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in
the presence of disorder by focusing on the density of states (DOS) and dc
conductivity. While the central hub-site does not reveal the presence of the
flat band, the sublattice resolved DOS on the non-central sites exhibits a
narrow peak with height ~ 1/\sqrt{g} with g the dimensionless disorder
variance. Although the group velocity is zero on the flat band, the dc
conductivity diverges as ln(1/g) with decreasing disorder due to interband
transitions around the band touching point between the propagating and the flat
band. Generalizations to higher pseudospin are given.
Physical Review B 05/2013; 88(16). DOI:10.1103/PhysRevB.88.161413 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Topological insulators represent unique phases of matter with insulating bulk
and conducting edge or surface states, immune to small perturbations such as
backscattering due to disorder. This stems from their peculiar band structure,
which provides topological protections. While conventional tools (pressure,
doping etc.) to modify the band structure are available, time periodic
perturbations can provide tunability by adding time as an extra dimension
enhanced to the problem. In this short review, we outline the recent research
on topological insulators in non equilibrium situations. Firstly, we introduce
briefly the Floquet formalism that allows to describe steady states of the
electronic system with an effective time-independent Hamiltonian. Secondly, we
summarize recent theoretical work on how light irradiation drives semi-metallic
graphene or a trivial semiconducting system into a topological phase. Finally,
we show how photons can be used to probe topological edge or surface states.
physica status solidi (RRL) - Rapid Research Letters 02/2013; 7(1-2). DOI:10.1002/pssr.201206451 · 2.14 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ)
chain, starting at the XX point. This is equivalent to switching on a nearest
neighbour interaction for hard-core bosons or an interaction quench for free
fermions. The physical observables we investigate are: the energy pumped into
the system during the quench, the spin-flip correlation function, and the
bipartite fluctuations of the z component of the spin in a box. We find
excellent agreement between exact numerics (infinite system time-evolving block
decimation, iTEBD) and analytical results from bosonization, as a function of
the quench time, spatial coordinate and interaction strength. This provides a
stringent and much-needed test of Luttinger liquid theory in a non-equilibrium
situation.
[Show abstract][Hide abstract] ABSTRACT: We present a unified treatment of the Elliott-Yafet (EY) and the
D'yakonov-Perel' (DP) spin-relaxation mechanisms using the Mori-Kawasaki
formula, which gives the spin-relaxation rate to lowest order in the spin-orbit
coupling (SOC) but to infinite order in the quasi-particle scattering rate,
Gamma. We consider a four-state Hamiltonian of the conduction and a nearby
(valence) band with spin degeneracy, including SOC between adjacent bands
(inter-SOC) and within the same band (intra-SOC). We find in agreement with the
expectations that intra-SOC yields the DP- whereas the inter-SOC the EY-like
result. However, we identify parameter domains of Gamma and the band structure
where a crossover occurs between the two types of spin-relaxation mechanisms.
The result ultimately connects the EY and the DP spin-relaxation mechanisms
into a unified description and it leads to a better understanding of
spin-relaxation in strongly correlated systems and where band degeneracy plays
a role such as e.g. in graphene.
[Show abstract][Hide abstract] ABSTRACT: The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases. Particularly strong disorder effects have been predicted to occur at zero-temperature quantum phase transitions. Here, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in Sr(1-x)Ca(x)RuO3 is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. Using a magneto-optical technique, we map the magnetic phase diagram in the composition-temperature space. We find that the ferromagnetic phase is significantly extended by the disorder and develops a pronounced tail over a broad range of the composition x. These findings are explained by a microscopic model of smeared quantum phase transitions in itinerant magnets. Moreover, our theoretical study implies that correlated disorder is even more powerful in promoting ferromagnetism than random disorder.
[Show abstract][Hide abstract] ABSTRACT: Temperature dependent electron spin resonance (ESR) measurements are reported
on stage 1 potassium doped graphite, a model system of biased graphene. The ESR
linewidth is nearly isotropic and although the g-factor has a sizeable
anisotropy, its majority is shown to arise due to macroscopic magnetization.
Albeit the homogeneous ESR linewidth shows an unusual, non-linear temperature
dependence, it appears to be proportional to the resistivity which is a
quadratic function of the temperature. These observations suggests the validity
of the Elliott-Yafet relaxation mechanism in KC8 and allows to place KC8 on the
empirical Beuneu-Monod plot among ordinary elemental metals.