39 research outputs found
Softening of Majorana edge states by long-range couplings
The inclusion of long-range couplings in the Kitaev chain is shown to modify
the universal scaling of topological states close to the critical point. By
means of the scattering approach, we prove that the Majorana states soften,
becoming increasingly delocalised at a universal rate which is only determined
by the interaction range. This edge mechanism can be related to a change in the
value of the bulk topological index at criticality, upon careful redefinition
of the latter. The critical point turns out to be topologically akin to the
trivial phase rather than interpolating between the two phases. Our treatment
moreover showcases how various topological aspects of quantum models can be
investigated analytically.Comment: 6 + 6 pages (main body + appendices), 3 figure
Universal scaling in fractional dimension
The concept of universality has shaped our understanding of many-body
physics, but is mostly limited to homogenous systems. Here, we present a first
study of universality on a non-homogeneous graph, the long-range diluted graph
(LRDG). Its scaling theory is controlled by a single parameter, the spectral
dimension , which plays the role of the relevant parameter on complex
geometries. The graph under consideration allows us to tune the value of the
spectral dimension continuously and find the universal exponents as continuous
functions of the dimension. By means of extensive numerical simulations, we
probe the scaling exponents of a simple instance of O(N) symmetric models on
the LRDG showing quantitative agreement with the theoretical prediction of
universal scaling in fractional dimensions.Comment: 10 pages, 9 figure
Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
Experimental progress in atomic, molecular, and optical platforms in the last
decade has stimulated strong and broad interest in the quantum coherent
dynamics of many long-range interacting particles. The prominent collective
character of these systems enables novel non-equilibrium phenomena with no
counterpart in conventional quantum systems with local interactions. Much of
the theory work in this area either focussed on the impact of variable-range
interaction tails on the physics of local interactions or relied on
mean-field-like descriptions based on the opposite limit of all-to-all
infinite-range interactions. In this Report, we present a systematic and
organic review of recent advances in the field. Working with prototypical
interacting quantum spin lattices without disorder, our presentation hinges
upon a versatile theoretical formalism that interpolates between the few-body
mean-field physics and the many-body physics of quasi-local interactions. Such
a formalism allows us to connect these two regimes, providing both a formal
quantitative tool and basic physical intuition. We leverage this unifying
framework to review several findings of the last decade, including the peculiar
non-ballistic spreading of quantum correlations, counter-intuitive slowdown of
entanglement dynamics, suppression of thermalization and equilibration,
anomalous scaling of defects upon traversing criticality, dynamical phase
transitions, and genuinely non-equilibrium phases stabilized by periodic
driving. The style of this Report is on the pedagogical side, which makes it
accessible to readers without previous experience in the subject matter.Comment: Review article, 88 + 43 pages and 32 figures. Comments are welcom
Dynamical criticality and domain-wall coupling in long-range Hamiltonians
Dynamical quantum phase transitions hold a deep connection to the underlying
equilibrium physics of the quench Hamiltonian. In a recent study [J.~C.~Halimeh
\textit{et al.}, arXiv:1810.07187], it has been numerically demonstrated that
the appearance of anomalous cusps in the Loschmidt return rate coincides with
the presence of bound domain walls in the spectrum of the quench Hamiltonian.
Here, we consider transverse-field Ising chains with power-law and
exponentially decaying interactions, and show that by removing domain-wall
coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with
long-range hopping and pairing, anomalous dynamical criticality is no longer
present. This indicates that bound domain walls are necessary for anomalous
cusps to appear in the Loschmidt return rate. We also calculate the dynamical
phase diagram of the Kitaev chain with long-range hopping and pairing, which in
the case of power-law couplings is shown to exhibit rich dynamical criticality
including a doubly critical dynamical phase.Comment: journal article, 11 pages, 5 figure
Vortex supersolid in the XY model with tunable vortex fugacity
In this paper, we investigate the XY model in the presence of an additional
potential term that independently tunes the vortex fugacity. By increasing the
strength of this term and thereby the vortex chemical potential , we
observe significant changes in the phase diagram with the emergence of a normal
vortex-antivortex lattice as well as a superconducting vortex-antivortex
crystal (supersolid) phase. We examine the transition lines between these two
phases and the conventional non-crystalline one as a function of both the
temperature and the chemical potential. Our findings suggest the possibility of
a peculiar tricritical point where second-order, first-order, and
infinite-order transition lines meet. We discuss the differences between the
present phase diagram and previous results for two-dimensional Coulomb gas
models. Our study provides important insights into the behaviour of the
modified XY model and opens up new possibilities for investigating the
underlying physics of unconventional phase transitions
Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution
and possibly complex energy eigenvalues, which can lead to a rich phenomenology
with no Hermitian counterpart. In this work, we study the dynamics of an
exactly solvable non-Hermitian system, hosting both -symmetric
and -broken modes subject to a linear quench. Employing a fully
consistent framework, in which the Hilbert space is endowed with a nontrivial
dynamical metric, we analyze the dynamics of the generated defects. In contrast
to Hermitian systems, our study reveals that PT -broken time evolution leads to
defect freezing and hence the violation of adiabaticity. This physics
necessitates the so-called metric framework, as it is missed by the oft used
approach of normalizing quantities by the time-dependent norm of the state. Our
results are relevant for a wide class of experimental systems.Comment: Main text: 7 pages and 3 figure
Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes universal
vortex unbinding in many two-dimensional systems, including the paradigmatic XY
model. However, most of these systems present a complex interplay between
excitations at different length scales that complicates theoretical
calculations of nonuniversal thermodynamic quantities. These difficulties may
be overcome by suitably modifying the initial conditions of the BKT flow
equations to account for noncritical fluctuations at small length scales. In
this work, we perform a systematic study of the validity and limits of this
two-step approach by constructing optimised initial conditions for the BKT
flow. We find that the two-step approach can accurately reproduce the results
of Monte-Carlo simulations of the traditional XY model. In order to
systematically study the interplay between vortices and spin-wave excitations,
we introduce a modified XY model with increased vortex fugacity. We present
large-scale Monte-Carlo simulations of the spin stiffness and vortex density
for this modified XY model and show that even at large vortex fugacity, vortex
unbinding is accurately described by the nonperturbative functional
renormalisation group
Out-of-equilibrium phase diagram of long-range superconductors
Within the ultimate goal of classifying universality in quantum many-body
dynamics, understanding the relation between out-of-equilibrium and equilibrium
criticality is a crucial objective. Models with power-law interactions exhibit
rich well-understood critical behavior in equilibrium, but the
out-of-equilibrium picture has remained incomplete, despite recent experimental
progress. We construct the rich dynamical phase diagram of free-fermionic
chains with power-law hopping and pairing, and provide analytic and numerical
evidence showing a direct connection between nonanalyticities of the return
rate and zero crossings of the string order parameter. Our results may explain
the experimental observation of so-called \textit{accidental} dynamical
vortices, which appear for quenches within the same topological phase of the
Haldane model, as reported in [Fl\"aschner \textit{et al.}, Nature Physics
\textbf{14}, 265 (2018)]. Our work is readily applicable to modern
ultracold-atom experiments, not least because state-of-the-art quantum gas
microscopes can now reliably measure the string order parameter, which, as we
show, can serve as an indicator of dynamical criticality.Comment: 17 pages, 9 figures, accepted versio