33,531 research outputs found
Geometric phase and phase diagram for non-Hermitian quantum XY model
We study the geometric phase for the ground state of a generalized
one-dimensional non-Hermitian quantum XY model, which has
transverse-field-dependent intrinsic rotation-time reversal symmetry. Based on
the exact solution, this model is shown to have full real spectrum in multiple
regions for the finite size system. The result indicates that the phase diagram
or exceptional boundary, which separates the unbroken and broken symmetry
regions corresponds to the divergence of the Berry curvature. The scaling
behaviors of the groundstate energy and Berry curvature are obtained in an
analytical manner for a concrete system.Comment: 6 pages, 3 figure
Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
We theoretically study the non-Hermitian systems, the non-Hermiticity of
which arises from the unequal hopping amplitude (UHA) dimers. The
distinguishing features of these models are that they have full real spectra if
all of the eigenvectors are time-reversal (T) symmetric rather than
parity-time-reversal (PT) symmetric, and that their Hermitian counterparts are
shown to be an experimentally accessible system, which have the same
topological structures as that of the original ones but modulated hopping
amplitudes within the unbroken region. Under the reflectionless transmission
condition, the scattering behavior of momentum-independent reflectionless
transmission (RT) can be achieved in the concerned non-Hermitian system. This
peculiar feature indicates that, for a certain class of non-Hermitian systems
with a balanced combination of the RT dimers, the defects can appear fully
invisible to an outside observer.Comment: 9 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1008.5306 by other author
Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
We systematically study the non-Hermitian version of the one-dimensional
anisotropic XY model, which in its original form, is a unique exactly solvable
quantum spin model for understanding the quantum phase transition. The
distinguishing features of this model are that it has full real spectrum if all
the eigenvectors are intrinsic rotation-time reversal (RT) symmetric rather
than parity-time reversal (PT) symmetric, and that its Hermitian counterpart is
shown approximately to be an experimentally accessible system, an isotropic XY
spin chain with nearest neighbor coupling. Based on the exact solution,
exceptional points which separated the unbroken and broken symmetry regions are
obtained and lie on a hyperbola in the thermodynamic limit. It provides a nice
paradigm to elucidate the complex quantum mechanics theory for a quantum spin
system.Comment: 7 pages, 3 figure
Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
Unlike a Chern number in D and D topological system, Zak phase takes a
subtle role to characterize the topological phase in D. On the one hand, it
is not a gauge invariant, on the other hand, the Zak phase difference between
two quantum phases can be used to identify the topological phase transitions. A
non-Hermitian system may inherit some characters of a Hermitian system, such as
entirely real spectrum, unitary evolution, topological energy band, etc. In
this paper, we study the influence of non-Hermitian term on the Zak phase for a
class of non-Hermitian systems. We show exactly that the real part of the Zak
phase remains unchanged in a bipartite lattice. In a concrete example, D
Su-Schrieffer-Heeger (SSH) model, we find that the real part of Zak phase can
be obtained by an adiabatic process. To demonstrate this finding, we
investigate a scattering problem for a time-dependent scattering center, which
is a magnetic-flux-driven non-Hermitian SSH ring. Owing to the nature of the
Zak phase, the intriguing features of this design are the wave-vector
independence and allow two distinct behaviors, perfect transmission or
confinement, depending on the timing of a flux impulse threading the ring. When
the flux is added during a wavepacket travelling within the ring, the
wavepacket is confined in the scatter partially. Otherwise, it exhibits perfect
transmission through the scatter. Our finding extends the understanding and
broaden the possible application of geometric phase in a non-Hermitian system.Comment: 11 pages, 7 figure
EPR pairing dynamics in Hubbard model with resonant
We study the dynamics of the collision between two fermions in Hubbard model
with on-site interaction strength . The exact solution shows that the
scattering matrix for two-wavepacket collision is separable into two
independent parts, operating on spatial and spin degrees of freedom,
respectively. The S-matrix for spin configuration is equivalent to that of
Heisenberg-type pulsed interaction with the strength depending on and
relative group velocity . This can be applied to create distant
EPR pair, through a collision process for two fermions with opposite spins in
the case of ,\ without the need for
temporal control and measurement process. Multiple collision process for many
particles is also discussed.Comment: 7 pages, 3 figure
Asymmetric transmission through a flux-controlled non-Hermitian scattering center
We study the possibility of asymmetric transmission induced by a
non-Hermitian scattering center embedded in a one-dimensional waveguide,
motivated by the aim of realizing quantum diode in a non-Hermitian system. It
is shown that a symmetric non-Hermitian scattering center always
has symmetric transmission although the dynamics within the isolated center can
be unidirectional, especially at its exceptional point. We propose a concrete
scheme based on a flux-controlled non-Hermitian scattering center, which
comprises a non-Hermitian triangular ring threaded by an Aharonov-Bohm flux.
The analytical solution shows that such a complex scattering center acts as a
diode at the resonant energy level of the spectral singularity, exhibiting
perfect unidirectionality of the transmission. The connections between the
phenomena of the asymmetric transmission and reflectionless absorption are also
discussed.Comment: 6 pages, 5 figure
Dynamical topological invariant for non-Hermitian Rice-Mele model
We study a non-Hermitian Rice-Mele model without breaking time-reversal
symmetry, with the non-Hermiticity arising from imbalanced hopping rates. The
Berry connection, Berry curvature and Chern number are introduced in the
context of biorthonormal inner product. It is shown that for a bulk system,
although the Berry connection can be complex numbers, the Chern number is still
quantized, as topological invariant. For an opened chain system, the mid-gap
edge modes are obtained exactly, obeying the bulk-edge correspondence.
Furthermore, we also introduce a local current in the context of biorthonormal
inner product to measure the pumping charge generated by a cyclic adiabatic
evolution. Analytical analysis and numerical simulation of the time evolution
of the mid-gap states show that the pumping charge can be a dynamical
topological invariant in correspondence with the Chern number. It indicates
that the geometric concepts for Hermitian topological insulator can be extended
to the non-Hermitian regime
Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field
In the Hermitian regime, a Berry phase is always the real number. It may be
imaginary for a non-Hermitian system, which leads to amplitude amplification or
attenuation of an evolved quantum state. We study the dynamics of the
non-Hermitian Rice-Mele model driven by a time-dependent external field. The
exact results show that it can have full real spectrum for any value of the
field. Several rigorous results are presented for the Berry phase with respect
to the varying field. We show that the Berry phase is the same complex constant
for any initial state in a single sub-band. Numerical simulation indicates that
the amplitude control of a state can be accomplished by a quasi-adiabatic
process within a short time
Non-Hermitian description of the dynamics of inter-chain pair tunnelling
We study inter-chain pair tunnelling dynamics based on an exact two-particle
solution for a two-leg ladder. We show that the Hermitian Hamiltonian shares a
common two-particle eigenstate with a corresponding non-Hermitian Hubbard
Hamiltonian in which the non-Hermiticity arises from an on-site interaction of
imaginary strength. Our results provides that the dynamic processes of
two-particle collision and across-legs tunnelling are well described by the
effective non-Hermitian Hubbard Hamiltonian based on the eigenstate
equivalence. We also find that any common eigenstate is always associated with
the emergence of spectral singularity in the non-Hermitian Hubbard model. This
result is valid for both Bose and Fermi systems and provides a clear physical
implication of the non-Hermitian Hubbard model.Comment: 10 pages, 4 figure
Dynamical signature of moire pattern in non-Hermitian ladder
We study the dynamical behavior of a non-Hermitian moire superlattice system,
which consists of two-coupled SSH chains with staggered imaginary on-site
potentials. There are two main spatial regions, in which systems are in
unbroken symmetric phases with fully real spectrum, appearing periodically
along the ladder. We show that the two quantum phases are dimerized and
tetramerized, which determine the distinct dynamical behaviors. Dirac
probability can oscillate periodically, increase quadratically and increase
exponentially, which correspond to the unbroken phase, exceptional point and
the broken phase of the tetramerized region. In comparison, the Dirac
probability can exhibit high-frequency oscillation in the dimerized region.
These phenomena demonstrate the dynamical signature and provide insightful
information of the moire pattern in the non-Hermitian regime.Comment: 10 pages, 5 figure
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