378 research outputs found
Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
We examine the phase diagram of the half-filled one-dimensional extended
Hubbard model using quantum information entropies within the density-matrix
renormalization group. It is well known that there is a charge-density-wave
phase at large nearest-neighbor and small on-site Coloumb repulsion and a
spin-density-wave at small nearest-neighbor and large on-site Coloumb
repulsion. At intermediate Coulomb interaction strength, we find an additional
narrow region of a bond-order phase between these two phases. The phase
transition line for the transition out of the charge-density-wave phase changes
from first-order at strong coupling to second-order in a parameter regime where
all three phases are present. We present evidence that the additional
phase-transition line between the spin-density-wave and bond-order phases is
infinite order. While these results are in agreement with recent numerical
work, our study provides an independent, unbiased means of determining the
phase boundaries by using quantum information analysis, yields values for the
location of some of the phase boundaries that differ from those previously
found, and provides insight into the limitations of numerical methods in
determining phase boundaries, especially those of infinite-order transitions.Comment: 8 pages, 7 figure
Braid group statistics implies scattering in three-dimensional local quantum physics
It is shown that particles with braid group statistics (Plektons) in
three-dimensional space-time cannot be free, in a quite elementary sense: They
must exhibit elastic two-particle scattering into every solid angle, and at
every energy. This also implies that for such particles there cannot be any
operators localized in wedge regions which create only single particle states
from the vacuum and which are well-behaved under the space-time translations
(so-called temperate polarization-free generators). These results considerably
strengthen an earlier "NoGo-theorem for 'free' relativistic Anyons".
As a by-product we extend a fact which is well-known in quantum field theory
to the case of topological charges (i.e., charges localized in space-like
cones) in d>3, namely: If there is no elastic two-particle scattering into some
arbitrarily small open solid angle element, then the 2-particle S-matrix is
trivial.Comment: 25 pages, 4 figures. Comment on model-building added in the
introductio
An Algebraic Jost-Schroer Theorem for Massive Theories
We consider a purely massive local relativistic quantum theory specified by a
family of von Neumann algebras indexed by the space-time regions. We assume
that, affiliated with the algebras associated to wedge regions, there are
operators which create only single particle states from the vacuum (so-called
polarization-free generators) and are well-behaved under the space-time
translations. Strengthening a result of Borchers, Buchholz and Schroer, we show
that then the theory is unitarily equivalent to that of a free field for the
corresponding particle type. We admit particles with any spin and localization
of the charge in space-like cones, thereby covering the case of
string-localized covariant quantum fields.Comment: 21 pages. The second (and crucial) hypothesis of the theorem has been
relaxed and clarified, thanks to the stimulus of an anonymous referee. (The
polarization-free generators associated with wedge regions, which always
exist, are assumed to be temperate.
The Spin-Statistics Theorem for Anyons and Plektons in d=2+1
We prove the spin-statistics theorem for massive particles obeying braid
group statistics in three-dimensional Minkowski space. We start from first
principles of local relativistic quantum theory. The only assumption is a gap
in the mass spectrum of the corresponding charged sector, and a restriction on
the degeneracy of the corresponding mass.Comment: 21 pages, 2 figures. Citation added; Minor modifications of Appendix
Modular Localization of Massive Particles with "Any" Spin in d=2+1
We discuss a concept of particle localization which is motivated from quantum field theory, and has been proposed by Brunetti, Guido and Longo and by Schroer. It endows the single particle Hilbert space with a family of real subspaces indexed by the space-time regions, with certain specific properties reflecting the principles of locality and covariance. We show by construction that such a localization structure exists also in the case of massive anyons in d=2+1, i.e. for particles with positive mass and with arbitrary spin s in the reals. The construction is completely intrinsic to the corresponding ray representation of the (proper orthochronous) Poincare group. Our result is of particular interest since there are no free fields for anyons, which would fix a localization structure in a straightforward way. We present explicit formulas for the real subspaces, expected to turn out useful for the construction of a quantum field theory for anyons. In accord with well-known results, only localization in string-like, instead of point-like or bounded, regions is achieved. We also prove a single-particle PCT theorem, exhibiting a PCT operator which acts geometrically correctly on the family of real subspaces
On the extension of stringlike localised sectors in 2+1 dimensions
In the framework of algebraic quantum field theory, we study the category
\Delta_BF^A of stringlike localised representations of a net of observables O
\mapsto A(O) in three dimensions. It is shown that compactly localised (DHR)
representations give rise to a non-trivial centre of \Delta_BF^A with respect
to the braiding. This implies that \Delta_BF^A cannot be modular when
non-trival DHR sectors exist. Modular tensor categories, however, are important
for topological quantum computing. For this reason, we discuss a method to
remove this obstruction to modularity.
Indeed, the obstruction can be removed by passing from the observable net
A(O) to the Doplicher-Roberts field net F(O). It is then shown that sectors of
A can be extended to sectors of the field net that commute with the action of
the corresponding symmetry group. Moreover, all such sectors are extensions of
sectors of A. Finally, the category \Delta_BF^F of sectors of F is studied by
investigating the relation with the categorical crossed product of \Delta_BF^A
by the subcategory of DHR representations. Under appropriate conditions, this
completely determines the category \Delta_BF^F.Comment: 36 pages, 1 eps figure; v2: appendix added, minor corrections and
clarification
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