369 research outputs found
Classical spin systems and the quantum stabilizer formalism: general mappings and applications
We present general mappings between classical spin systems and quantum
physics. More precisely, we show how to express partition functions and
correlation functions of arbitrary classical spin models as inner products
between quantum stabilizer states and product states, thereby generalizing
mappings for some specific models established in [Phys. Rev. Lett. 98, 117207
(2007)]. For Ising- and Potts-type models with and without external magnetic
field, we show how the entanglement features of the corresponding stabilizer
states are related to the interaction pattern of the classical model, while the
choice of product states encodes the details of interaction. These mappings
establish a link between the fields of classical statistical mechanics and
quantum information theory, which we utilize to transfer techniques and methods
developed in one field to gain insight into the other. For example, we use
quantum information techniques to recover well known duality relations and
local symmetries of classical models in a simple way, and provide new classical
simulation methods to simulate certain types of classical spin models. We show
that in this way all inhomogeneous models of q-dimensional spins with pairwise
interaction pattern specified by a graph of bounded tree-width can be simulated
efficiently. Finally, we show relations between classical spin models and
measurement-based quantum computation.Comment: 24 pages, 5 figures, minor corrections, version as accepted in JM
Renormalization algorithm with graph enhancement
We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.Comment: 4 pages, 1 figur
Spaced training enhances memory and prefrontal ensemble stability in mice
It is commonly acknowledged that memory is substantially improved when learning is distributed over time, an effect called the "spacing effect". So far it has not been studied how spaced learning affects the neuronal ensembles presumably underlying memory. In the present study, we investigate whether trial spacing increases the stability or size of neuronal ensembles. Mice were trained in the "everyday memory"task, an appetitive, naturalistic, delayed matching-to-place task. Spacing trials by 60 min produced more robust memories than training with shorter or longer intervals. c-Fos labeling and chemogenetic inactivation established the involvement of the dorsomedial prefrontal cortex (dmPFC) in successful memory storage. In vivo calcium imaging of excitatory dmPFC neurons revealed that longer trial spacing increased the similarity of the population activity pattern on subsequent encoding trials and upon retrieval. Conversely, trial spacing did not affect the size of the total neuronal ensemble or the size of subpopulations dedicated to specific task-related behaviors and events. Thus, spaced learning promotes reactivation of prefrontal neuronal ensembles processing episodic-like memories
Dielectric screening in extended systems using the self-consistent Sternheimer equation and localized basis sets
We develop a first-principles computational method for investigating the
dielectric screening in extended systems using the self-consistent Sternheimer
equation and localized non-orthogonal basis sets. Our approach does not require
the explicit calculation of unoccupied electronic states, only uses two-center
integrals, and has a theoretical scaling of order O(N^3). We demonstrate this
method by comparing our calculations for silicon, germanium, diamond, and LiCl
with reference planewaves calculations. We show that accuracy comparable to
planewaves calculations can be achieved via a systematic optimization of the
basis set.Comment: 6 pages, 3 figure
Pinwheel stabilization by ocular dominance segregation
We present an analytical approach for studying the coupled development of
ocular dominance and orientation preference columns. Using this approach we
demonstrate that ocular dominance segregation can induce the stabilization and
even the production of pinwheels by their crystallization in two types of
periodic lattices. Pinwheel crystallization depends on the overall dominance of
one eye over the other, a condition that is fulfilled during early cortical
development. Increasing the strength of inter-map coupling induces a transition
from pinwheel-free stripe solutions to intermediate and high pinwheel density
states.Comment: 10 pages, 4 figure
Microscopic theory for the light-induced anomalous Hall effect in graphene
We employ a quantum Liouville equation with relaxation to model the recently
observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of
circularly polarized light. In the weak-field regime, we demonstrate that the
Hall effect originates from an asymmetric population of photocarriers in the
Dirac bands. By contrast, in the strong-field regime, the system is driven into
a non-equilibrium steady state that is well-described by topologically
non-trivial Floquet-Bloch bands. Here, the anomalous Hall current originates
from the combination of a population imbalance in these dressed bands together
with a smaller anomalous velocity contribution arising from their Berry
curvature. This robust and general finding enables the simulation of electrical
transport from light-induced Floquet-Bloch bands in an experimentally relevant
parameter regime and creates a pathway to designing ultrafast quantum devices
with Floquet-engineered transport properties
Local renormalization method for random systems
In this paper, we introduce a real-space renormalization transformation for
random spin systems on 2D lattices. The general method is formulated for random
systems and results from merging two well known real space renormalization
techniques, namely the strong disorder renormalization technique (SDRT) and the
contractor renormalization (CORE). We analyze the performance of the method on
the 2D random transverse field Ising model (RTFIM).Comment: 12 pages, 13 figures. Submitted to the Special Issue on "Quantum
Information and Many-Body Theory", New Journal of Physics. Editors: M.B.
Plenio, J. Eiser
Common microscopic origin of the phase transitions in Ta<sub>2</sub>NiS<sub>5</sub> and the excitonic insulator candidate Ta<sub>2</sub>NiSe<sub>5</sub>
The structural phase transition in Ta2NiSe5 has been envisioned as driven by the formation of an excitonic insulating phase. However, the role of structural and electronic instabilities on crystal symmetry breaking has yet to be disentangled. Meanwhile, the phase transition in its complementary material Ta2NiS5 does not show any experimental hints of an excitonic insulating phase. We present a microscopic investigation of the electronic and phononic effects involved in the structural phase transition in Ta2NiSe5 and Ta2NiS5 using extensive first-principles calculations. In both materials the crystal symmetries are broken by phonon instabilities, which in turn lead to changes in the electronic bandstructure also observed in the experiment. A total energy landscape analysis shows no tendency towards a purely electronic instability and we find that a sizeable lattice distortion is needed to open a bandgap. We conclude that an excitonic instability is not needed to explain the phase transition in both Ta2NiSe5 and Ta2NiS5
- …