Partially gapped fermions in 2D

We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.Comment: v1: 36 pages, 10 figures, v2: minor corrections; equation references to arXiv:0903.0055 updated

No Evidence that 2D:4D is Related to the Number of CAG Repeats in the Androgen Receptor Gene

The length ratio of the second to the fourth digit (2D:4D) is a putative marker of prenatal testosterone (T) effects. The number of CAG repeats (CAGn) in the AR gene is negatively correlated with T sensitivity in vitro. Results regarding the relationship between 2D:4D and CAGn are mixed but have featured prominently in arguments for and against the validity of 2D:4D. Here, I present random-effects meta-analyses on 14 relevant samples with altogether 1,904 subjects. Results were homogeneous across studies. Even liberal estimates (upper limit of the 95% CI) were close to zero and therefore suggested no substantial relationship of CAGn with either right-hand 2D:4D, left-hand 2D:4D, or the difference between the two. However, closer analysis of the effects of CAGn on T dependent gene activation in vitro and of relationships between CAGn and T dependent phenotypic characteristics suggest that normal variability of CAGn has mostly no, very small, or inconsistent effects. Therefore, the lack of a clear association between CAGn and 2D:4D has no negative implications for the latter’s validity as a marker of prenatal T effects

Violation of Luttinger's Theorem in the Two-Dimensional t-J Model

We have calculated the high temperature series for the momentum distribution function n_k of the 2D t-J model to 12th order in inverse temperature. By extrapolating the series to T=0.2J we searched for a Fermi surface of the 2D t-J model. We find that three criteria used for estimating the location of a Fermi surface violate Luttinger's Theorem, implying the 2D t-J model does not have an adiabatic connection to a non-interacting model.Comment: 4 pages, 5 figures. Version with grayscale figures available upon reques

Crossover from the 2D Heisenberg to the 1D Quantum Spin Ladder Regime in Underdoped High Tc Cuprates

The enigmatic scaling behaviour of the normal state properties of the high Tc cuprates has been explained by assuming that a crossover from the two- dimensional Heisenberg (2D-H) to the one-dimensional spin ladder (1D-SL) regime takes place at temperature T=T*. For T<T* stripe formation results in the quantum 1D transport with the characteristic inelastic length L_phi being fully controlled by the magnetic correlation length xi_m of the even-chain SL, whereas for T> T* the 2D quantum transport is realized with L_\phi governed by the 2D-H correlations L_phi=xi_m=exp(J/T)$. Therefore, the pseudogap found in underdoped (p<p_opt) high Tc's is the spin-gap Delta(p) in even-chain 1D-SL.Comment: 5 pages, 5 EPS figures, submitted to PR

Magnetic properties of the 2D t-t'-Hubbard model

The two-dimensional (2D) t-t'-Hubbard model is studied within the slave-boson (SB) theory. At half-filling, a paramagnetic to antiferromagnetic phase transition of first order at a finite critical interaction strength U_c(t'/t) is found. The dependences on U/t and t'/t of the sublattice magnetization and of the local magnetic moment are calculated. Our results reasonably agree with recent (Projector) Quantum Monte Carlo data. The SB ground-state phase diagram reveals a t'-induced electron-hole asymmetry, and, depending on the ratio t'/t, the antiferromagnetic or ferromagnetic phases are stable down to U=0 at a critical hole doping.Comment: 2 pages, 3 Postscript figure, submitted to Int. Conf. M2S-HTSC-V Beijing 97, to appear in Physica

An operator extension of the parallelogram law and related norm inequalities

We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr's inequality and present several norm inequalities. More precisely, let ${\mathfrak A}$ be a $C^*$-algebra, $T$ be a locally compact Hausdorff space equipped with a Radon measure $\mu$ and let $(A_t)_{t\in T}$ be a continuous field of operators in ${\mathfrak A}$ such that the function $t \mapsto A_t$ is norm continuous on $T$ and the function $t \mapsto \|A_t\|$ is integrable. If $\alpha: T \times T \to \mathbb{C}$ is a measurable function such that $\bar{\alpha(t,s)}\alpha(s,t)=1$ for all $t, s \in T$, then we show that \begin{align*} \int_T\int_T&\left|\alpha(t,s) A_t-\alpha(s,t) A_s\right|^2d\mu(t)d\mu(s)+\int_T\int_T\left|\alpha(t,s) B_t-\alpha(s,t) B_s\right|^2d\mu(t)d\mu(s) \nonumber &= 2\int_T\int_T\left|\alpha(t,s) A_t-\alpha(s,t) B_s\right|^2d\mu(t)d\mu(s) - 2\left|\int_T(A_t-B_t)d\mu(t)\right|^2\,. \end{align*}Comment: 9 pages; To appear in Math. Inequal. Appl. (MIA

Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids

While it is well-known that the electron-electron (\emph{ee}) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T^2 behavior. The T^2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T^2 term can result only from a combined--but distinct from quantum-interference corrections-- effect of the electron-impurity and \emph{ee} interactions. Whether the T^2 term is present depends on 1) dimensionality (two dimensions (2D) vs three dimensions (3D)), 2) topology (simply- vs multiply-connected), and 3) shape (convex vs concave) of the FS. In particular, the T^2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T^2 term is also absent for a convex and simply-connected but otherwise arbitrarily anisotropic FS in 2D. The origin of this nullification is approximate integrability of the electron motion on a 2D FS, where the energy and momentum conservation laws do not allow for current relaxation to leading --second--order in T/E_F (E_F is the Fermi energy). If the T^2 term is nullified by the conservation law, the first non-zero term behaves as T^4. The same applies to a quantum-critical metal in the vicinity of a Pomeranchuk instability, with a proviso that the leading (first non-zero) term in the resistivity scales as T^{\frac{D+2}{3}} (T^{\frac{D+8}{3}}). We discuss a number of situations when integrability is weakly broken, e.g., by inter-plane hopping in a quasi-2D metal or by warping of the FS as in the surface states of Bi_2Te_3 family of topological insulators.Comment: Submitted to a special issue of the Lithuanian Journal of Physics dedicated to the memory of Y. B. Levinso