151 research outputs found
From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
An exponential deformation of 1D critical Hamiltonians gives rise to ground
states whose entanglement entropy satisfies a volume-law. This effect is
exemplified in the XX and Heisenberg models. In the XX case we characterize the
crossover between the critical and the maximally entangled ground state in
terms of the entanglement entropy and the entanglement spectrum.Comment: Accepted for the Special Issue: Quantum Entanglement in Condensed
Matter Physics. 11 pages, 9 figures (with enhanced size to focus on the
details) and new reference
Entanglement in low-energy states of the random-hopping model
We study the low-energy states of the 1D random-hopping model in the strong
disordered regime. The entanglement structure is shown to depend solely on the
probability distribution for the length of the effective bonds , whose
scaling and finite-size behavior are established using renormalization-group
arguments and a simple model based on random permutations. Parity oscillations
are absent in the von Neumann entropy with periodic boundary conditions, but
appear in the higher moments of the distribution, such as the variance. The
particle-hole excited states leave the bond-structure and the entanglement
untouched. Nonetheless, particle addition or removal deletes bonds and leads to
an effective saturation of entanglement at an effective block size given by the
expected value for the longest bond
Entanglement detachment in fermionic systems
This article introduces and discusses the concept of entanglement detachment.
Under some circumstances, enlarging a few couplings of a Hamiltonian can
effectively detach a (possibly disjoint) block within the ground state. This
detachment is characterized by a sharp decrease in the entanglement entropy
between block and environment, and leads to an increase of the internal
correlations between the (possibly distant) sites of the block. We provide some
examples of this detachment in free fermionic systems. The first example is an
edge-dimerized chain, where the second and penultimate hoppings are increased.
In that case, the two extreme sites constitute a block which disentangles from
the rest of the chain. Further examples are given by (a) a superlattice which
can be detached from a 1D chain, and (b) a star-graph, where the extreme sites
can be detached or not depending on the presence of an external magnetic field,
in analogy with the Aharonov-Bohm effect. We characterize these detached blocks
by their reduced matrices, specially through their entanglement spectrum and
entanglement Hamiltonian
Many-body Lattice Wavefunctions From Conformal Blocks
We introduce a general framework to construct many-body lattice wavefunctions
starting from the conformal blocks (CBs) of rational conformal field theories
(RCFTs). We discuss the different ways of encoding the physical degrees of
freedom of the lattice system using both the internal symmetries of the theory
and the fusion channels of the CBs. We illustrate this construction both by
revisiting the known Haldane-Shastry model and by providing a novel
implementation for the Ising RCFT. In the latter case, we find a connection to
the Ising transverse field (ITF) spin chain via the Kramers-Wannier duality and
the Temperley-Lieb-Jones algebra. We also find evidence that the ground state
of the finite-size critical ITF Hamiltonian corresponds exactly to the
wavefunction obtained from CBs of spin fields
Power accretion in social systems
We consider a model of power distribution in a social system where a set of agents plays a simple game on
a graph: The probability of winning each round is proportional to the agent’s current power, and the winner
gets more power as a result. We show that when the agents are distributed on simple one-dimensional and
two-dimensional networks, inequality grows naturally up to a certain stationary value characterized by a clear
division between a higher and a lower class of agents. High class agents are separated by one or several lower
class agents which serve as a geometrical barrier preventing further flow of power between them. Moreover,
we consider the effect of redistributive mechanisms, such as proportional (nonprogressive) taxation. Sufficient
taxation will induce a sharp transition towards a more equal society, and we argue that the critical taxation level
is uniquely determined by the system geometry. Interestingly, we find that the roughness and Shannon entropy
of the power distributions are a very useful complement to the standard measures of inequality, such as the Gini
index and the Lorenz curveWe acknowledge financial support from the Spanish Government through
Grants No. FIS2015-69167-C2-1-P, No. FIS2015-66020-C2-
1-P, and No. PGC2018-094763-B-I0
- …