9 research outputs found
Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
Using the framework of infinite Matrix Product States, the existence of an
\textit{anomalous} dynamical phase for the transverse-field Ising chain with
sufficiently long-range interactions was first reported in [J.~C.~Halimeh and
V.~Zauner-Stauber, arXiv:1610:02019], where it was shown that
\textit{anomalous} cusps arise in the Loschmidt-echo return rate for
sufficiently small quenches within the ferromagnetic phase. In this work we
further probe the nature of the anomalous phase through calculating the
corresponding Fisher-zero lines in the complex time plane. We find that these
Fisher-zero lines exhibit a qualitative difference in their behavior, where,
unlike in the case of the regular phase, some of them terminate before
intersecting the imaginary axis, indicating the existence of smooth peaks in
the return rate preceding the cusps. Additionally, we discuss in detail the
infinite Matrix Product State time-evolution method used to calculate Fisher
zeros and the Loschmidt-echo return rate using the Matrix Product State
transfer matrix. Our work sheds further light on the nature of the anomalous
phase in the long-range transverse-field Ising chain, while the numerical
treatment presented can be applied to more general quantum spin chains.Comment: Journal article. 9 pages and 6 figures. Includes in part what used to
be supplemental material in arXiv:1610:0201
Quasiparticle origin of dynamical quantum phase transitions
Considering nonintegrable quantum Ising chains with exponentially decaying
interactions, we present matrix product state results that establish a
connection between low-energy quasiparticle excitations and the kind of
nonanalyticities in the Loschmidt return rate. When domain walls in the
spectrum of the quench Hamiltonian are energetically favored to be bound rather
than freely propagating, anomalous cusps appear in the return rate regardless
of the initial state. In the nearest-neighbor limit, domain walls are always
freely propagating, and anomalous cusps never appear. As a consequence, our
work illustrates that models in the same equilibrium universality class can
still exhibit fundamentally distinct out-of-equilibrium criticality. Our
results are accessible to current ultracold-atom and ion-trap experiments.Comment: 9 pages, 8 figures, accepted versio
Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
We numerically study the dynamics after a parameter quench in the
one-dimensional transverse-field Ising model with long-range interactions
( with distance ), for finite chains and also directly
in the thermodynamic limit. In nonequilibrium, i.e., before the system settles
into a thermal state, we find a long-lived regime that is characterized by a
prethermal value of the magnetization, which in general differs from its
thermal value. We find that the ferromagnetic phase is stabilized dynamically:
as a function of the quench parameter, the prethermal magnetization shows a
transition between a symmetry-broken and a symmetric phase, even for those
values of for which no finite-temperature transition occurs in
equilibrium. The dynamical critical point is shifted with respect to the
equilibrium one, and the shift is found to depend on as well as on the
quench parameters.Comment: 6 pages, 4 figure