arXiv subjects

Meik Hellmund

Publications and source records attributed to Meik Hellmund.

14 recordsLinked to original sources

arXiv2012

Entanglement and output entropy of the diagonal map

We review some properties of the convex roof extension, a construction used, e.g., in the definition of the entanglement of formation. Especially we consider the use of symmetries of channels and states for the construction of the convex roof. As an application we study the entanglement entropy of the diagonal map for permutation symmetric real N=3 states $ω(z)$ and solve the case $z<0$ where $z$ is the non-diagonal entry in the density matrix. We also report a surprising result about the behaviour of the output entropy of the diagonal map for arbitrary dimensions $N$; showing a bifurcation at N=6.

quant-ph↗

arXiv2009

Concurrence and Entanglement Entropy of Stochastic 1-Qubit Maps

Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1-qubit maps are presented. We construct the relevant convex roof patterns by a new method. We conclude that two component optimal decompositions always exist. Our results can be transferred to 2xN-quantumsystems providing the concurrence for all rank two density operators as well as lower and upper bounds for their entanglement of formation. We apply these results to a study of the entanglement entropy of 1-qubit stochastic maps which preserve axial symmetry. Using analytic and numeric results we analyze the bifurcation patterns appearing in the convex roof of optimal decompositions and give results for the one-shot (Holevo-Schumacher-Westmoreland) capacity of those maps.

quant-ph↗

arXiv2009

An Entropy Inequality

Let $S(ρ)=- Tr (ρ\logρ)$ be the von Neumann entropy of an $N$-dimensional quantum state $ρ$ and $e_2(ρ)$ the second elementary symmetric polynomial of the eigenvalues of $ρ$. We prove the inequality $S(ρ) \le c(N) \sqrt{e_2(ρ)} $ where $c(N)=\log(N) \sqrt{\frac{2N}{N-1}}$. This generalizes an inequality given by Fuchs and Graaf \cite{fuchsgraaf} for the case of one qubit, i.e., N=2. Equality is achieved if and only if $ρ$ is either a pure or the maximally mixed state. This inequality delivers new bounds for quantities of interest in quantum information theory, such as upper bounds for the minimum output entropy and the entanglement of formation as well as a lower bound for the Holevo channel capacity.

quant-ph↗

arXiv2008

Concurrence of Stochastic 1-Qubit Maps

Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1-qubit maps are presented. By a new method we find the relevant convex roof pattern. We conclude that two component optimal decompositions always exist. Our results can be transferred to $2 \times n$-quantum systems providing the concurrence for all rank two density operators as well as a lower bound for their entanglement of formation.

quant-ph↗

arXiv2006

High-temperature series expansions for the $q$-state Potts model on a hypercubic lattice and critical properties of percolation

We present results for the high-temperature series expansions of the susceptibility and free energy of the $q$-state Potts model on a $D$-dimensional hypercubic lattice $\mathbb{Z}^D$ for arbitrary values of $q$. The series are up to order 20 for dimension $D\leq3$, order 19 for $D\leq 5$ and up to order 17 for arbitrary $D$. Using the $q\to 1$ limit of these series, we estimate the percolation threshold $p_c$ and critical exponent $γ$ for bond percolation in different dimensions. We also extend the 1/D expansion of the critical coupling for arbitrary values of $q$ up to order $D^{-9}$.

cond-mat.stat-mech↗

arXiv2006

High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions

In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d = 3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d = 4$ is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the \sus to be $γ=1.305(5)$ at the random fixed point.

cond-mat.stat-mech↗

arXiv2005

High-Temperature Series Expansions for Random Potts Models

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2002

Star-graph expansions for bond-diluted Potts models

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond $q$-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength $p$ as well as the dimension $d$ as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the $(p,d)$ parameter space for any value of $q$. For the bond-diluted 4-state Potts model in three dimensions, which exhibits a rather strong first-order phase transition in the undiluted case, we present results for the transition temperature and the effective critical exponent $γ$ as a function of $p$ as obtained from the analysis of susceptibility series up to order 18. A comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev. E64, 036120(2001)) shows signals for the softening to a second-order transition at finite disorder strength.

cond-mat.stat-mech↗

arXiv1997

Static solitons with non-zero Hopf number

We investigate a generalized non-linear O(3) $σ$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.

hep-th↗

arXiv1997

Unpolarized quasielectrons and the spin polarization at filling fractions between 1/3 and 2/5

We prove that for a hard core interaction the ground state spin polarization in the low Zeeman energy limit is given by $P=2/ν-5$ for filling fractions in the range $ 1/3 \leqν\leq 2/5 $. The same result holds for a Coulomb potential except for marginally small magnetic fields. At the magnetic fields $B<20T$ unpolarized quasielectrons can manifest themselves by a characteristic peak in the I-V characteristics for tunneling between two $ν=1/3$ ferromagnets.

cond-mat↗

arXiv1996

Transition from ν=8/5 to ν=5/3 in the low Zeeman energy limit

Skyrmions in the FQHE at filling fractions above ν=1/3 are studied within the anyon model and by exact diagonalization. Relations to the composite fermion theory are pointed out. We find that unpolarized quasiparticles above ν=1/3 are stable below B\approx 0.02T. At low Zeeman energy the polarization in the range ν=8/5 ... 5/3 is found to be a linear function of the filling factor. We also reexamine the energy and wave function of skyrmions at ν=1 by a new method.

cond-mat.mes-hall↗

arXiv1996

Interaction dependence of composite fermion effective masses

We estimate the composite fermion effective mass for a general two particle potential r^{-α} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction ν=1/2 as well as estimates of the excitation gap at ν=1/3, 2/5 and 3/7 show that m_eff \sim α^{-1}.

cond-mat.mes-hall↗

arXiv1994

A comparison of FQHE quasi electron trial wave functions on the sphere

We study Haldane's and Jain's proposals for the quasiparticle wave function on the sphere. The expectation values of the energy and the pair angular momenta distribution are calculated at filling factor 1/3 and compared with the data of an exact numerical diagonalization for up to 10 electrons with Coulomb and truncated quasipotential interaction.

cond-mat↗

arXiv1994

Sphaleron Effects Near the Critical Temperature

We discuss one-loop radiative corrections to the sphaleron-induced baryon number-violating transition rate near the electroweak phase transition in the standard model. We emphasize that in the case of a first-order transition a rearrangement of the loop expansion is required close to the transition temperature. The corresponding expansion parameter, the effective 3-dimensional gauge coupling approaches a finite $λ$ dependent value at the critical temperature. The $λ$ (Higgs mass) dependence of the 1-loop radiative corrections is discussed in the framework of the heat kernel method. Radiative corrections are small compared to the leading sphaleron contribution as long as the Higgs mass is small compared to the W mass. To 1-loop accuracy, there is no Higgs mass range compatible with experimental limits where washing-out of a B+L asymmetry could be avoided for the minimal standard model with one Higgs doublet.

hep-ph↗