No Arabic abstract
The Optimized Perturbation Theory (OPT) method, at finite temperature and finite chemical potential, is applied to the field theory model for polyacetylene. The critical dopant concentration in trans-polyacetylene is evaluated and compared with the available experimental data and with previous calculations. The results obtained within the OPT go beyond the standard mean field (or large-N) approximation (MFA) by explicitly including finite N effects. A critical analysis of the possible theoretical prescriptions to implement and interpret these corrections to the mean field results, given the available data, is given. For typical temperatures probed in the laboratory, our results show that the critical dopant concentration is only weakly affected by thermal effects.
In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction $V(Omega_m) propto 1/|Omega_m|^gamma$ (the $gamma$-model). We analyze both the original model and its extension, in which we introduce an extra parameter $N$ to account for non-equal interactions in the particle-hole and particle-particle channel. In two previous papers(arXiv:2004.13220 and arXiv:2006.02968), we considered the case $0 < gamma <1$ and argued that (i) at $T=0$, there exists an infinite discrete set of topologically different gap functions, $Delta_n (omega_m)$, all with the same spatial symmetry, and (ii) each $Delta_n$ evolves with temperature and terminates at a particular $T_{p,n}$. In this paper, we analyze how the system behavior changes between $gamma <1$ and $gamma >1$, both at $T=0$ and a finite $T$. The limit $gamma to 1$ is singular due to infra-red divergence of $int d omega_m V(Omega_m)$, and the system behavior is highly sensitive to how this limit is taken. We show that for $N =1$, the divergencies in the gap equation cancel out, and $Delta_n (omega_m)$ gradually evolve through $gamma=1$ both at $T=0$ and a finite $T$. For $N eq 1$, divergent terms do not cancel, and a qualitatively new behavior emerges for $gamma >1$. Namely, the form of $Delta_n (omega_m)$ changes qualitatively, and the spectrum of condensation energies, $E_{c,n}$ becomes continuous at $T=0$. We introduce different extension of the model, which is free from singularities for $gamma >1$.
In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V(Omega_m) = {bar g}^gamma/|Omega_m|^gamma$ (the $gamma$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous Papers I-V we analyzed the $gamma$ model for $gamma leq 2$ and argued that the ground state is an ordinary superconductor for $gamma <1$, a peculiar one for $1<gamma <2$, when the phase of the gap function winds up along real frequency axis due to emerging dynamical vortices in the upper half-plane of frequency, and that there is a quantum phase transition at $gamma =2$, when the number of dynamical vortices becomes infinite. In this paper we consider larger $2< gamma <3$ and address the issue what happens on the other side of this quantum transition. We argue that the system moves away from criticality in that the number of dynamical vortices becomes finite and decreases with increasing $gamma$. The ground state is again a superconductor, however a highly unconventional one with a non-integrable singularity in the density of states at the lower edge of the continuum. This implies that the spectrum of excited states now contains a level with a macroscopic degeneracy, proportional to the total number of states in the system. We argue that the phase diagram in variables $(T,gamma)$ contains two distinct superconducting phases for $gamma <2$ and $gamma >2$, and an intermediate pseudogap state of preformed pairs.
We present the global phase diagram of the extended boson Hubbard model on a simple cubic lattice by quantum Monte Carlo simulation with worm update algorithm. Four kinds of phases are supported by this model, including superfluid, supersolid, Mott, and charge density wave (CDW) states, which are identified in the phase diagram of chemical potential $mu$ versus nearest neighbor interaction V . By changing the chemical potential, a continuous transition is found from the Mott phase to a superfluid phase without breaking the translational symmetry. For an insulating CDW state, adding particles to it gives rise to a continuous transition to a supersolid phase, while removing particles usually leads to a first-order one to either supersolid or superfluid phase. By tuning the nearest neighbor interaction, one can realize the transition between two insulating phases, Mott and CDW with the same particle density, which turns out to be of the first-order. We also demonstrate that a supersolid phase with average particle density less than 1/2 can exist in a small region of $mu$ - V phase diagram.
Single crystals of (Ca1-xLax)10(Pt3As8)(Fe2As2)5 (x = 0 to 0.182) superconductors have been grown and characterized by X-ray, microprobe, transport and thermodynamic measurements. Features in the magnetic susceptibility, specific heat and two kinks in the derivative of the electrical resistivity around 100 K in the x = 0 compound support the existence of decoupled structural and magnetic phase transitions. With La doping, the structural/magnetic phase transitions are suppressed and a half-dome of superconductivity with a maximal Tc around 26 K is observed in the temperature-concentration phase diagram.
A first principle prediction of the binary nanoparticle phase diagram assembled by solvent evaporation has eluded theoretical approaches. In this paper, we show that a binary system interacting through Lennard-Jones (LJ) potential contains all experimental phases in which nanoparticles are effectively described as quasi hard spheres. We report a phase diagram consisting of 53 equilibrium phases, whose stability is quite insensitive to the microscopic details of the potentials, thus giving rise to some type of universality. Furthermore, we show that binary lattices may be understood as consisting of certain particle clusters, i.e. motifs, which provide a generalization of the four conventional Frank-Kasper polyhedral units. Our results show that meta-stable phases share the very same motifs as equilibrium phases. We discuss the connection with packing models, phase diagrams with repulsive potentials and the prediction of likely experimental superlattices.