Search Results (42)

The Ising model is famous in condensed matter and statistical physics. In this work we present a free-fermion formulation of the two-dimensional classical Ising models on honeycomb, triangular and Kagomé lattices. Each Ising model is studied in the cases of a zero field and of an imaginary field $i(\pi /2)k_{B}T$. We employ the decorated lattice technique, star-triangle transformation, and weak-graph expansion method to exactly map each Ising model in both cases into an eight-vertex model on the square lattice. The resulting vertex weights are shown to satisfy the free-fermion condition. In the zero-field case, each Ising model is an even free-fermion model. In the case of the imaginary field, the Ising model on the honeycomb lattice is an even free-fermion model, while the models on the triangular and Kagomé lattices are odd free-fermion models. We obtain the exact solution of the Kagomé lattice Ising model under the imaginary field $i(\pi /2)k_{B}T$, a result not previously reported in the literature. We also show that the frustrated Ising models on the triangular and Kagomé lattices in the imaginary field still exhibit a non-zero residual entropy. Full article

The dynamic phosphorylation of the human RNA Pol II CTD establishes a code applicable to all eukaryotic transcription processes. However, the ability of these specific post-translational modifications to convey molecular signals through structural changes remains unclear. We previously explained that each gene can be modeled as a combination of n circuits connected in parallel. RNA Pol II accesses these circuits and, through a series of pulses, matches the resonance frequency of the DNA qubits, enabling it to extract genetic information and quantum teleport it. Negatively charged phosphates react under RNA Pol II catalysis, which increases the electron density on the deoxyribose acceptor carbon (2’C in the DNA sugar backbone). The phosphorylation effect on the stability of a carbon radical connects tyrosine to the nitrogenous base, while the subsequent pulses link the protein to molecular water through hydrogen bonds. The selective activation of inert C(sp³)–H bonds begins by reading the quantum information stored in the nitrogenous bases. The coupling of hydrogen proton transfer with electron transfer in water generates a supercurrent, which is explained by the correlation of pairs of the same type of fermions exchanging a boson. All these changes lead to the formation of a molecular protein–DNA–water transcriptional condensate. Full article

We investigate the time evolution of the quark condensate toward a chiral symmetry broken phase in hot and dense quark matter using a field-theoretic quark model with nonlocal chiral-invariant four-fermion coupling. By purposely selecting a parameter set in which inhomogeneous phases are energetically disfavored, we nonetheless observe the emergence of metastable patterned configurations that appear to persist for remarkably long timescales. These findings suggest that even when not fully stable, inhomogeneous phases may play a significant role in the dynamics of chiral symmetry breaking and restoration. To gain deeper insight into these phenomena, we also analyze the impact of the dimensionality of coordinate space on both the formation and stability of inhomogeneous chiral condensates. Full article

In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness ($C_f$) in a finite model of N interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate $C_f$ with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of $C_f$ on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion–fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science. Full article

In our review, we analyze the scaling of the condensation energy $E_{\mathsf{\Delta }}$ divided by $\gamma$, $E_{\mathsf{\Delta }}/\gamma \simeq N\left(0\right){\mathsf{\Delta }}_1^2/\gamma$, and quasiparticles of both conventional and unconventional superconductors, where $N\left(0\right)$ is the density of states at zero temperature $T=0$, ${\mathsf{\Delta }}_1$ is the maximum value of the superconducting gap, and $\gamma$ is the Sommerfeld coefficient. It is shown that Bogoliubov quasiparticles act in superconducting states of unconventional and conventional superconductors. At the same time, quasiparticles are also present in the normal state of unconventional superconductors. We briefly describe the difference between unconventional superconductors and conventional ones, such as the resistivity in normal states and the difference in superfluid density in superconducting states. For the first time, we theoretically show that the universal scaling of $E_{\mathsf{\Delta }}/\gamma \propto T_c^2$ applies equally to both conventional and unconventional superconductors. Our consideration is based on two experimental facts: Bogoliubov quasiparticles act in conventional and non-conventional superconductors and the corresponding flat band is deformed by the non-conventional superconducting state. As a result, our theoretical observations based on the theory of fermion condensation agree well with the experimental facts. Full article

An attempt is made to describe from first principles the large-scale structure of the confining vacuum in quantum chromodynamics. Starting from our previous variational studies of the SU(2) pure gauge theory in an external Abelian chromomagnetic field and extending Feynman’s qualitative analysis in (2+1)-dimensional SU(2) gauge theory, we show that the SU(3) vacuum in three-space and one-time dimensions behaves like a disordered chromomagnetic condensate. Color confinement is assured by the presence of a mass gap together with the absence of color long-range correlations. We offer a clear physical picture for the formation of the flux tube between static quark charges that allows us to determine the color structure and the transverse profile of the flux-tube chromoelectric field. The transverse profile of the flux-tube chromoelectric field turns out to be in reasonable agreement with lattice data. We, also, show that our quantum vacuum allows for both the color and ordinary Meissner effect. We find that for massless quarks, the quantum vacuum can accommodate a finite non-zero density of fermion zero modes leading to the dynamical breaking of the chiral symmetry. Full article

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be described by chiral perturbation theory (ChPT), which predicts a second-order phase transition with Bose-Einstein condensation of diquarks at $\mu =m_{\pi }/2$. At larger baryon chemical potentials, the interactions between baryons become important, and ChPT is not applicable anymore. At sufficiently large baryon chemical potential, the Fermi sphere composed of quarks is formed, and diquarks are condensed on the surface of this sphere. In this region, two-color baryon matter reveals properties similar to those of the Quarkyonic phase. Particular attention in this review is paid to lattice studies of dense two-color QCD phase diagram. In the low-density region, the results of lattice studies are in agreement with ChPT predictions. At sufficiently large baryon densities, lattice studies observe a Fermi sphere composed of quarks and condensation of diquarks on its surface. Thus, available lattice studies support most of the theoretical predictions. Finally, we discuss the status of the deconfinement in cold dense two-color matter, which was observed in lattice simulation with staggered fermions. Full article

In this review, we consider the impact of magnetic field on the properties of strongly correlated heavy-fermion compounds such as heavy-fermion metals and frustrated insulators with quantum spin liquid. Magnetic field B can be considered a universal tool, allowing the exploration of the physics controlling the remarkable properties of heavy-fermion compounds. These vivid properties are $T/B$ scaling, exhibited under the application of magnetic field B and at fixed temperature T, and the emergence of Landau Fermi liquid behavior under the application of magnetic field. We analyze the influence of quasiparticle–hole asymmetry on the properties of heavy-fermion (HF) compounds such as the universal scaling behavior of the thermopower $S/T$ exhibited under the application of magnetic field B. We show that universal scaling is demonstrated by different HF compounds such as $\beta$-${\mathrm{YbAlB}}_4$, ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, and strongly correlated layered cobalt oxide $\left[{\mathrm{BiBa}}_{0.66}{\mathrm{K}}_{0.36}{\mathrm{O}}_2\right]{\mathrm{CoO}}_2$. Analyzing ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, we show that the $T/B$ scaling behavior of $S/T$ is violated at the antiferromagnetic phase (AF) transition. The residual resistivity ${\rho }_0$ and the density of states $N_0$ experience jumps at the AF transition, causing two jumps in the thermopower and its sign reversal. Our consideration is based on the flattening of the single-particle spectrum that strongly affects ${\rho }_0$ and $N_0$ and leads to the violation of particle–hole symmetry. The particle–hole asymmetry generates the asymmetrical part $\mathsf{\Delta }{\sigma }_d\left(V\right)$ of tunneling differential conductivity ${\sigma }_d\left(V\right)$, $\mathsf{\Delta }{\sigma }_d\left(V\right)={\sigma }_d\left(V\right)-{\sigma }_d(-V)$, where V is the voltage bias. We demonstrate that in the presence of magnetic field, the quasiparticle–hole asymmetry vanishes, the LFL behavior is restored, and the asymmetry disappears. Our calculations of the mentioned properties of HF compounds, based on the fermion condensation theory, are in good agreement with the experiment and support our conclusion that the fermion condensation theory is capable of describing the properties of HF compounds, including those exhibited under the application of magnetic field. Full article

An extensive review of recent results concerning the quantum field theory of particle mixing in curved spacetime is presented. The rich mathematical structure of the theory for both fermions and bosons, stemming from the interplay of curved space quantization and field mixing, is discussed, and its phenomenological implications are shown. Fermionic and bosonic oscillation formulae for arbitrary globally hyperbolic spacetimes are derived and the transition probabilities are explicitly computed on some metrics of cosmological and astrophysical interest. The formulae thus obtained are characterized by a pure QFT correction to the amplitudes, which is absent in quantum mechanics, where only the phase of the oscillations is affected by the gravitational background. Their deviation from the flat space probabilities is demonstrated, with the aid of numerical analyses. The condensate structure of the flavor vacuum of mixed fermions is studied, assessing its role as a possible dark matter component in a cosmological context. It is shown that the flavor vacuum behaves as a barotropic fluid, satisfying the equation of the state of cold dark matter. New experiments on the cosmic neutrino background, as PTOLEMY, may validate these theoretical results. Full article

We discuss the hadron–quark crossover accompanied by the formation of Cooper triples (three-body counterpart of Cooper pairs) by analogy with the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer crossover in two-component fermionic systems. Such a crossover is different from a phase transition, which often involves symmetry breaking. We calculate the in-medium three-body energy from the three-body T-matrix with a phenomenological three-body force characterizing a bound hadronic state in vacuum. With increasing density, the hadronic bound-state pole smoothly undergoes a crossover toward the Cooper triple phase where the in-medium three-body clusters coexist with the quark Fermi sea. The relation to the quarkyonic matter model can also be found in a natural manner. Full article

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated. Full article

While the identification of skyrmions as the low energy description of baryons in $N_f\ge 2$ QCD is known for decades, a parallel construction for the case of $N_f=1$ is more mysterious. In the case of one fermionic flavor, there is no chiral symmetry breaking, no non-linear sigma model, and the conventional construction of skyrmions fails to work. In this article, I will review developments from the last couple of years trying to identify baryons as certain singular configurations in the large $N_c$ limit of $N_f=1$ QCD. We will give various arguments supporting this identification, and discuss some of its applications. Unlike skyrmions, the new baryons are not contained completely inside the low energy effective theory. They give rise to a singular ring on which the chiral condensate must vanish, with new degrees of freedom living on this ring. These configurations may serve as a bridge between the UV and the IR, and hopefully shed some light on the connection between different phases of QCD. Full article

Since the discovery of the quantum Hall effect in 1980, it has attracted intense interest in condensed matter physics and has led to a new type of metrological standard by utilizing the resistance quantum. Graphene, a true two-dimensional electron gas material, has demonstrated the half-integer quantum Hall effect and composite-fermion fractional quantum Hall effect due to its unique massless Dirac fermions and ultra-high carrier mobility. Here, we use a monolayer graphene encapsulated with hexagonal boron nitride and few-layer graphite to fabricate micrometer-scale graphene Hall devices. The application of a graphite gate electrode significantly screens the phonon scattering from a conventional SiO₂/Si substrate, and thus enhances the carrier mobility of graphene. At a low temperature, the carrier mobility of graphene devices can reach 3 × 10⁵ cm²/V·s, and at room temperature, the carrier mobility can still exceed 1 × 10⁵ cm²/V·s, which is very helpful for the development of high-temperature quantum Hall effects under moderate magnetic fields. At a low temperature of 1.6 K, a series of half-integer quantum Hall plateaus are well-observed in graphene with a magnetic field of 1 T. More importantly, the ν = ±2 quantum Hall plateau clearly persists up to 150 K with only a few-tesla magnetic field. These findings show that graphite-gated high-mobility graphene devices hold great potential for high-sensitivity Hall sensors and resistance metrology standards for the new Système International d’unités. Full article

With the continuous development of topological properties in condensed matter systems, the current research focus has been expanded into phononic bosonic states. Compared with the conventional electronic fermions, topological phonons exhibit very distinct features. In this study, based on density functional calculations, we have systematically investigated the topological phonons in the ternary phosphide compound BaLiP. Coincident nodal line and nodal surface states are revealed in the middle part of the phononic spectrum and they are formed by the same two phonon bands. Detailed band structure mechanism and symmetry operation formalism are provided. More importantly, evident surface states are observed from the entire nodal line and they are all well separated from the bulk state projection, very beneficial and preferable for future experimental investigation. Lastly, the mechanical properties are also examined and several important parameters are provided, which can be very useful for the practical application. Considering the multiple advantages of the topological nodal states in this material, the corresponding experimental study can be immediately inspired. Full article

Relativistic plasma can be formed in strong electromagnetic or gravitational fields. Such conditions exist in compact astrophysical objects, such as white dwarfs and neutron stars, as well as in accretion discs around neutron stars and black holes. Relativistic plasma may also be produced in the laboratory during interactions of ultra-intense lasers with solid targets or laser beams between themselves. The process of thermalization in relativistic plasma can be affected by quantum degeneracy, as reaction rates are either suppressed by Pauli blocking or intensified by Bose enhancement. In addition, specific quantum phenomena, such as Bose–Einstein condensation, may occur in such a plasma. In this review, the process of plasma thermalization is discussed and illustrated with several examples. The conditions for quantum condensation of photons are formulated. Similarly, the conditions for thermalization delay due to the quantum degeneracy of fermions are analyzed. Finally, the process of formation of such relativistic plasma originating from an overcritical electric field is discussed. All these results are relevant for relativistic astrophysics as well as for laboratory experiments with ultra-intense lasers. Full article