125,293 research outputs found
Bound states and entanglement in the excited states of quantum spin chains
We investigate entanglement properties of the excited states of the spin-1/2
Heisenberg (XXX) chain with isotropic antiferromagnetic interactions, by
exploiting the Bethe ansatz solution of the model. We consider eigenstates
obtained from both real and complex solutions ("strings") of the Bethe
equations. Physically, the former are states of interacting magnons, whereas
the latter contain bound states of groups of particles. We first focus on the
situation with few particles in the chain. Using exact results and
semiclassical arguments, we derive an upper bound S_MAX for the entanglement
entropy. This exhibits an intermediate behavior between logarithmic and
extensive, and it is saturated for highly-entangled states. As a function of
the eigenstate energy, the entanglement entropy is organized in bands. Their
number depends on the number of blocks of contiguous Bethe-Takahashi quantum
numbers. In presence of bound states a significant reduction in the
entanglement entropy occurs, reflecting that a group of bound particles behaves
effectively as a single particle. Interestingly, the associated entanglement
spectrum shows edge-related levels. At finite particle density, the
semiclassical bound S_MAX becomes inaccurate. For highly-entangled states
S_A\propto L_c, with L_c the chord length, signaling the crossover to extensive
entanglement. Finally, we consider eigenstates containing a single pair of
bound particles. No significant entanglement reduction occurs, in contrast with
the few-particle case.Comment: 39 pages, 10 figure. as published in JSTAT. Invited submission to
JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physic
Phase diagram of the anti-ferromagnetic xxz model in the presence of an external magnetic field
The anisotropic s=1/2 anti-ferromagnetic Heisenberg chain in the presence of
an external magnetic field is studied by using the standard quantum
renormalization group. We obtain the critical line of the transition from
partially magnetized (PM) phase to the saturated ferromagnetic (SFM) phase. The
crossover exponent between the PM phase and anti-ferromagnetic Ising (AFI)
phase is evaluated. Our results show that the anisotropy(\d) term is relevant
and causes crossover. These results indicate that the standard RG approach
yields fairly good values for the critical points and their exponents. The
magnetization curve, correlation functions and the ground state energy per site
are obtained and compared with the known exact results.Comment: A LaTex file(20 pages) and 9 PS figure
Entanglement of Solitons in the Frenkel-Kontorova Model
We investigate entanglement of solitons in the continuum-limit of the
nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons
manifests particle-like behavior as they are characterized by localization of
entanglement. The von-Neumann entropy of solitons mixes critical with
noncritical behaviors. Inside the core of the soliton the logarithmic increase
of the entropy is faster than the universal increase of a critical field,
whereas outside the core the entropy decreases and saturates the constant value
of the corresponding massive noncritical field. In addition, two solitons
manifest long-range entanglement that decreases with the separation of the
solitons more slowly than the universal decrease of the critical field.
Interestingly, in the noncritical regime of the Frenkel-Kontorova model,
entanglement can even increase with the separation of the solitons. We show
that most of the entanglement of the so-called internal modes of the solitons
is saturated by local degrees of freedom inside the core, and therefore we
suggest using the internal modes as carriers of quantum information.Comment: 16 pages, 22 figure
Hubbard model: Pinning of occupation numbers and role of symmetries
Fermionic natural occupation numbers do not only obey Pauli's exclusion
principle, but are even further restricted by so-called generalized Pauli
constraints. Such restrictions are particularly relevant whenever they are
saturated by given natural occupation numbers . For
few-site Hubbard models we explore the occurrence of this pinning effect. By
varying the on-site interaction for the fermions we find sharp transitions
from pinning of to the boundary of the allowed region to
nonpinning. We analyze the origin of this phenomenon which turns out be either
a crossing of natural occupation numbers or
a crossing of -particle energies. Furthermore, we emphasize the relevance of
symmetries for the occurrence of pinning. Based on recent progress in the field
of ultracold atoms our findings suggest an experimental set-up for the
realization of the pinning effect.Comment: published versio
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