Macroscopic Entanglement and Phase Transitions

This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.Comment: 9 pages, 7 figures (color), Submitted to special OSID issue, Proceedings of the 38th Symposium on Mathematical Physics - Quantum Entanglement & Geometry, Torun (Poland), June 200

Enhancement of superconductive critical temperatures in almost empty or full bands in two dimensions: possible relevance to beta-HfNCl, C60 and MgB2

We examine possibility of enhancement of superconductive critical temperature in two-dimensions. The weak coupling BCS theory is applied, especially when the Fermi level is near the edges of the electronic bands. The attractive interaction depends on ${\bf k}$ due to screening. The density of states(DOS) does not have a peak near the bottom of the band, but $k$-dependent contribution to DOS (electron density on the Fermi surface) has a diverging peak at the bottom or top. These features lead to significant enhancement of the critical temperatures. The results are qualitatively consistent with the superconductive behaviors of HfNCl (\Tc \le 25K) and ZrNCl(\Tc \le 15K), C$_{60}$ with a field-effect transistor configuration (\Tc = 52K), and MgB$_2$ (\Tc \approx 40K) which have the unexpectedly high superconductive critical transition temperatures.Comment: 5 pages,4 figure

Noninvasiveness and time symmetry of weak measurements

Measurements in classical and quantum physics are described in fundamentally different ways. Nevertheless, one can formally define similar measurement procedures with respect to the disturbance they cause. Obviously, strong measurements, both classical and quantum, are invasive -- they disturb the measured system. We show that it is possible to define general weak measurements, which are noninvasive: the disturbance becomes negligible as the measurement strength goes to zero. Classical intuition suggests that noninvasive measurements should be time symmetric (if the system dynamics is reversible) and we confirm that correlations are time-reversal symmetric in the classical case. However, quantum weak measurements -- defined analogously to their classical counterparts -- can be noninvasive but not time symmetric. We present a simple example of measurements on a two-level system which violates time symmetry and propose an experiment with quantum dots to measure the time-symmetry violation in a third-order current correlation function.Comment: 19 pages, 5 figures, more information at http://www.fuw.edu.pl/~abednorz/tasym

Proposal for a cumulant-based Bell test for mesoscopic junctions

The creation and detection of entanglement in solid state electronics is of fundamental importance for quantum information processing. We prove that second-order quantum correlations can be always interpreted classically and propose a general test of entanglement based on the violation of a classically derived inequality for continuous variables by fourth-order quantum correlation functions. Our scheme provides a way to prove the existence of entanglement in a mesoscopic transport setup by measuring higher order cumulants without requiring the additional assumption of a single charge detectionComment: 6 pages, 1 figure, detailed proof of weak positivity and Bell-type inequalit

Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions

The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of noncommuting observables in mesoscopic transport experiments, using a quasiprobablistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters.Comment: 4 pages, published versio

Bipolarons in the Extended Holstein Hubbard Model

We numerically and analytically calculate the properties of the bipolaron in an extended Hubbard Holstein model, which has a longer range electron-phonon coupling like the Fr\" ohlich model. In the strong coupling regime, the effective mass of the bipolaron in the extended model is much smaller than the Holstein bipolaron mass. In contrast to the Holstein bipolaron, the bipolaron in the extended model has a lower binding energy and remains bound with substantial binding energy even in the large-U limit. In comparison with the Holstein model where only a singlet bipolaron is bound, in the extended Holstein model a triplet bipolaron can also form a bound state. We discuss the possibility of phase separation in the case of finite electron doping.Comment: 5 pages, 3 figure

3D wedge filling and 2D random-bond wetting

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively.Comment: 7 pages, 3 figures, accepted for publication in Europhysics Letter

Chiral Plaquette Polaron Theory of Cuprate Superconductivity

Ab-initio density functional calculations on explicitly doped La(2-x)Sr(x)CuO4 find doping creates localized holes in out-of-plane orbitals. A model for superconductivity is developed based on the assumption that doping leads to the formation of holes on a four-site Cu plaquette composed of the out-of-plane A1 orbitals apical O pz, planar Cu dz2, and planar O psigma. This is in contrast to the assumption of hole doping into planar Cu dx2-y2 and O psigma orbitals as in the t-J model. Interaction of holes with the d9 spin background leads to chiral polarons with either a clockwise or anti-clockwise charge current. When the polaron plaquettes percolate through the crystal at x~0.05 for LaSrCuO, a Cu dx2-y2 and planar O psigma band is formed. Spin exchange Coulomb repulsion with chiral polarons leads to D-wave superconductivity. The equivalent of the Debye energy in phonon superconductivity is the maximum energy separation between a chiral polaron and its time-reversed partner. An additive skew-scattering contribution to the Hall effect is induced by chiral polarons and leads to a temperature dependent Hall effect that fits the measured values for LaSrCuO. The integrated imaginary susceptibility satisfies omega/T scaling due to chirality and spin-flip scattering of polarons along with a uniform distribution of polaron energy splittings. The derived functional form is compatible with experiments. The static spin structure factor is computed and is incommensurate with a separation distance from (pi,pi) given by ~(2pi)x. Coulomb scattering of the x2-y2 band with polarons leads to linear resistivity. Coupling of the x2-y2 band to the undoped Cu d9 spins leads to the ARPES pseudogap and its doping and temperature dependence.Comment: 32 pages, 17 figure

Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.Comment: 14 pages, 12 fig

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behavior in temperature dependencies of some observables in $(s+id)$-wave BCS superconductivity in the presence of a weak $s$ wave. There also could appear a second second-order phase transition. As temperature is lowered past the usual critical temperature $T_c$, a less ordered superconducting phase is created in $d$ wave, which changes to a more ordered phase in $(s+id)$ wave at $T_{c1}$ ($< T_c$). The presence of two phase transitions manifest in two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of susceptibility, penetration depth, and thermal conductivity also confirm the new phase transition.Comment: 6 pages, 5 post-script figures