arXiv subjects

W. Thirring

Publications and source records attributed to W. Thirring.

8 recordsLinked to original sources

arXiv2002

A Geometric Picture of Entanglement and Bell Inequalities

We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S subset H_s of separable states. This violation equals the euclidean distance in H_s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.

quant-ph↗

arXiv2001

Thermal correlators of anyons in two dimensions

The anyon fields have trivial $α$-commutator for $α$ not integer. For integer $α$ the commutators become temperature-dependent operator valued distributions. The $n$-point functions do not factorize as for quasifree states.

math-ph↗

arXiv2000

Laughlin type wave function for two-dimensional anyon fields in a KMS-state

The correlation functions of two-dimensional anyon fields in a KMS-state are studied. For T=0 the $n$-particle wave functions of noncanonical fermions of level $α$, $α$ odd, are shown to be of Laughlin type of order $α$. For $T>0$ they are given by a simple finite-temperature generalization of Laughlin's wave function. This relates the first and second quantized pictures of the fractional quantum Hall effect.

hep-th↗

arXiv2000

A mixed mean-field/BCS phase with an energy gap at high $T_c$

We construct a pair potential which in a scaling limit leads to a Hamiltonian that generates co-existing mean-field and superconducting phases. Depending on the relative values of the coupling constants, the superconducting phase may exist at arbitrarily high temperatures.

math-ph↗

arXiv1999

Anyons and the Bose-Fermi duality in the finite-temperature Thirring model

Solutions to the Thirring model are constructed in the framework of algebraic QFT. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is $λ=\sqrt{2(2n+1)π}, n\in {\bf N}$. These fermions are inequivalent and only for $n=1$ they are canonical fields. In the general case solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces and obey dynamical equations (of the type of Heisenberg's "Urgleichung") characterized by the corresponding values of the statistic parameter. Thus statistic parameter turns out to be related to the coupling constant $λ$ and the whole Hilbert space becomes non-separable with a different "Urgleichung" satisfied in each of its sectors. This feature certainly cannot be seen by any power expansion in $λ$. Moreover, since the latter is tied to the statistic parameter, it is clear that such an expansion is doomed to failure and will never reveal the true structure of the theory. The correlation functions in the temperature state for the canonical dressed fermions are shown by us to coincide with the ones for bare fields, that is in agreement with the uniqueness of the $τ$-KMS state over the CAR algebra ($τ$ being the shift automorphism). Also the $α$-anyon two-point function is evaluated and for scalar field it reproduces the result that is known from the literature.

math-ph↗

arXiv1999

A pair potential supporting a mixed mean-field / BCS- phase

We construct a Hamiltonian which in a scaling limit becomes equivalent to one that can be diagonalized by a Bogoliubov transformation. There may appear simultaneously a mean-field and a superconducting phase. They influence each other in a complicated way. For instance, an attractive mean field may stimulate the superconducting phase and a repulsive one may destroy it.

math-ph↗

arXiv1998

The Thirring model 40 years later

Solutions to the Thirring model are constructed in the framework of algebraic QFT. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is $λ= \sqrt{2(2n+1)π}, n\in \bf N$, otherwise solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces, so the whole Hilbert space becomes non-separable and in each of its sectors a different Urgleichung holds. This feature certainly cannot be seen by any power expansion in $λ$. Moreover, if the statistic parameter is tied to the coupling constant it is clear that such an expansion is doomed to failure and will never reveal the true structure of the theory. On the basis of the model in question, it is not possible to decide whether fermions or bosons are more fundamental since dressed fermions can be constructed either from bare fermions or directly from the current algebra.

hep-th↗

arXiv1998

Do anyons solve Heisenberg's Urgleichung in one dimension

We construct solutions to the chiral Thirring model in the framework of algebraic quantum field theory. We find that for all positive temperatures there are fermionic solutions only if the coupling constant is $λ= \sqrt{2(2n + 1)π}, n \in \bf N$.

hep-th↗