27 research outputs found
Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
We focus on the biorthogonal work statistics of the interacting many-body
Hatano-Nelson model after switching on the imaginary vector potential. We
introduce a generalized Loschmidt echo utilizing the biorthogonal metric
operator. It is well suited for numerical analysis and its Fourier transform
yields the probability distribution of work done. The statistics of work
displays several universal features, including an exponential decay with the
square of both the system size and imaginary vector potential for the
probability to stay in the ground state. Additionally, its high energy tail
follows a universal power law with exponent . This originates from the
peculiar temporal power law decay of with a time dependent exponent. The
mean and the variance of work scale linearly and logarithmically with system
size while all higher cumulants are non-extensive. Our results are relevant for
non-unitary field theories as well.Comment: 7 pages, 3 figure
Correlations at higher-order exceptional points in non-Hermitian models
We investigate the decay of spatial correlations of -symmetric
non-Hermitian one-dimensional models that host higher-order exceptional points.
Beyond a certain correlation length, they develop anomalous power-law behavior
that indicates strong suppression of correlations in the non-Hermitian setups
as compared to the Hermitian ones. The correlation length is also reflected in
the entanglement entropy where it marks a change from logarithmic growth at
short distance to a constant value at large distance, characteristic of an
insulator, despite the spectrum being gapless. Two different families of models
are investigated, both having a similar spectrum constrained by particle-hole
symmetry. The first model offers an experimentally attractive way to generate
arbitrary higher-order exceptional points and represents a non-Hermitian
extension of the Dirac Hamiltonian for general spin. At the critical point it
displays a decay of the correlations and irrespective of
the order of the exceptional point. The second model is constructed using
unidirectional hopping and displays enhanced suppression of correlations , with a power law that depends on the order of the exceptional
point.Comment: 19 pages, 11 figure
Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
We investigate the quantum quench dynamics of the interacting Hatano-Nelson
model with open boundary conditions using both abelian bosonization and
numerical methods. Specifically, we follow the evolution of the particle
density and current profile in real space over time by turning the imaginary
vector potential on or off in the presence of weak interactions. Our results
reveal spatio-temporal Friedel oscillations in the system with light cones
propagating ballistically from the open ends, accompanied by local currents of
equal magnitude for both switch off and on protocols. Remarkably, the
bosonization method accurately accounts for the density and current patterns
with a single overall fitting parameter. The continuity equation is satisfied
by the long wavelength part of the density and current, despite the non-unitary
time evolution when the Hatano-Nelson term is switched on.Comment: 9 pages, 4 figure