134 research outputs found
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
Riemannian optimization of isometric tensor networks
Several tensor networks are built of isometric tensors, i.e. tensors
satisfying . Prominent examples include matrix
product states (MPS) in canonical form, the multiscale entanglement
renormalization ansatz (MERA), and quantum circuits in general, such as those
needed in state preparation and quantum variational eigensolvers. We show how
gradient-based optimization methods on Riemannian manifolds can be used to
optimize tensor networks of isometries to represent e.g. ground states of 1D
quantum Hamiltonians. We discuss the geometry of Grassmann and Stiefel
manifolds, the Riemannian manifolds of isometric tensors, and review how
state-of-the-art optimization methods like nonlinear conjugate gradient and
quasi-Newton algorithms can be implemented in this context. We apply these
methods in the context of infinite MPS and MERA, and show benchmark results in
which they outperform the best previously-known optimization methods, which are
tailor-made for those specific variational classes. We also provide open-source
implementations of our algorithms.Comment: 18 pages + appendices, 3 figures; v3 submission to SciPost; v4 expand
preconditioning discussion and add polish, resubmit to SciPos
Beelden van vertrouwen: het vertrouwen in politie en justitie in perspectief geplaatst (locomotieftekst).
Deze bijdrage handelt over de mate van vertrouwen die de burger stelt in politie en justitie, twee belangrijke instituties die de fundamenten van de democratische rechtsstaat dienen te waarborgen. In een internationale context is al heel wat diepgaand onderzoek gevoerd naar het vertrouwen van de burger in zowel politie als justitie. De justitiebarometer buiten beschouwing gelaten hinkt België wat achterop. In deze locomotieftekst wensen we een beschrijvend overzicht te bieden van het vertrouwen van de burger in de Belgische justitie en politie, waarbij we de mate van vertrouwen in politie en justitie vergelijken, enerzijds door de tijd heen, en anderzijds met het vertrouwen in andere overheidsinstituties in ons land en in een Europese context. Tot slot worden enkele kanttekeningen geformuleerd bij de studie van vertrouwen
Quasiparticles in quantum spin chains with long-range interactions
We study quasiparticle excitations for quantum spin chains with long-range
interactions using variational matrix product state techniques. It is confirmed
that the local quasiparticle ansatz is able to capture those excitations very
accurately, even when the correlation length becomes very large and in the case
of topological nontrivial excitation such as spinons. It is demonstrated that
the breaking of the Lieb-Robinson bound follows from the appearance of cusps in
the dispersion relation, and evidence is given for a crossover between
different quasiparticles as the long-range interactions are tuned
Local measures of dynamical quantum phase transitions
In recent years, dynamical quantum phase transitions (DQPTs) have emerged as a useful theoretical concept to characterize nonequilibrium states of quantum matter. DQPTs are marked by singular behavior in an effective free energy lambda(t), which, however, is a global measure, making its experimental or theoretical detection challenging in general. We introduce two local measures for the detection of DQPTs with the advantage of requiring fewer resources than the full effective free energy. The first, called the real-local effective free energy lambda(M)(t), is defined in real space and is therefore suitable for systems where locally resolved measurements are directly accessible such as in quantum-simulator experiments involving Rydberg atoms or trapped ions. We test lambda(M)(t) in Ising chains with nearest-neighbor and power-law interactions, and find that this measure allows extraction of the universal critical behavior of DQPTs. The second measure we introduce is the momentum-local effective free energy lambda(k)(t), which is targeted at systems where momentum-resolved quantities are more naturally accessible, such as through time-of-flight measurements in ultracold atoms. We benchmark lambda(k)(t) for the Kitaev chain, a paradigmatic system for topological quantum matter, in the presence of weak interactions. Our introduced local measures for effective free energies can further facilitate the detection of DQPTs in modern quantum-simulator experiments
Anatomy of Dynamical Quantum Phase Transitions
Global quenches of quantum many-body models can give rise to periodic
dynamical quantum phase transitions (DQPTs) directly connected to the zeros of
a Landau order parameter (OP). The associated dynamics has been argued to bear
close resemblance to Rabi oscillations characteristic of two-level systems.
Here, we address the question of whether this DQPT behavior is merely a
manifestation of the limit of an effective two-level system or if it can arise
as part of a more complex dynamics. We focus on quantum many-body scarring as a
useful toy model allowing us to naturally study state transfer in an otherwise
chaotic system. We find that a DQPT signals a change in the dominant
contribution to the wave function in the degenerate initial-state manifold,
with a direct relation to an OP zero only in the special case of occurring at
the midpoint of an evenly degenerate manifold. Our work generalizes previous
results and reveals that, in general, periodic DQPTs comprise complex many-body
dynamics fundamentally beyond that of two-level systems.Comment: Accepted versio
Tangent-space methods for truncating uniform MPS
A central primitive in quantum tensor network simulations is the problem of
approximating a matrix product state with one of a lower bond dimension. This
problem forms the central bottleneck in algorithms for time evolution and for
contracting projected entangled pair states. We formulate a tangent-space based
variational algorithm to achieve this for uniform (infinite) matrix product
states. The algorithm exhibits a favourable scaling of the computational cost,
and we demonstrate its usefulness by several examples involving the
multiplication of a matrix product state with a matrix product operator
Efficient MPS methods for extracting spectral information on rings and cylinders
Based on the MPS formalism, we introduce an ansatz for capturing excited
states in finite systems with open boundary conditions, providing a very
efficient method for computing, e.g., the spectral gap of quantum spin chains.
This method can be straightforwardly implemented on top of an existing DMRG or
MPS ground-state code. Although this approach is built on open-boundary MPS, we
also apply it to systems with periodic boundary conditions. Despite the
explicit breaking of translation symmetry by the MPS representation, we show
that momentum emerges as a good quantum number, and can be exploited for
labeling excitations on top of MPS ground states. We apply our method to the
critical Ising chain on a ring and the classical Potts model on a cylinder.
Finally, we apply the same idea to compute excitation spectra for 2-D quantum
systems on infinite cylinders. Again, despite the explicit breaking of
translation symmetry in the periodic direction, we recover momentum as a good
quantum number for labeling excitations. We apply this method to the 2-D
transverse-field Ising model and the half-filled Hubbard model; for the latter,
we obtain accurate results for, e.g., the hole dispersion for cylinder
circumferences up to eight sites
Real-time scattering of interacting quasiparticles in quantum spin chains
We develop a method based on tensor networks to create localized single-particle excitations on top of strongly correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing the gauge freedom of momentum excitations on top of matrix product states. The corresponding wave packets propagate almost dispersionlessly. The time-dependent variational principle is used to scatter two such wave packets, and we extract the phase shift from the collision data. We also study reflection and transmission coefficients of a wave packet impinging on an impurity
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