We study the ground-state magnetic phase diagram of a spin
S
= 1/2 antiferromagnetic two-leg ladder with period two lattice units modulated Dzyaloshinskii-Moriya (DM) interaction along the legs. We ...consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto an effective spin
σ
= 1/2
XXZ
chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation
M
= 0 and to its saturation value per rung
M
=
M
sat
= 1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization
M
= 0.5
M
sat
. The width of the magnetization plateau at
M
= 0.5
M
sat
, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as (
D
0
D
1
/
J
2
)
α
where
D
0
,
D
1
are uniform and staggered components of the DM term,
J
is the intraleg exchange and
α
≤ 3∕4 and weakly depends on the DM couplings.
Graphical abstract
This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with ...quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in Lu3Cu2Sb3O14 and quasi-one dimensional (1D) quantum spin liquid in both YbAlO3 and Cu(C4H4N2)(NO3)2 with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal α-YbAl1-xFexB4, with x=0.014, and on its sister compounds β-YbAlB4 and YbCo2Ge4, carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of α-YbAl1-xFexB4 and in its sister compounds β-YbAlB4 and YbCo2Ge4 emerge, as well as establish connection of these (HF) metals with insulators Lu3Cu2Sb3O14, Cu(C4H4N2)(NO3)2 and YbAlO3. We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields.
This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals ...that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.
Based on the novel prescription for the power function, (x+iy)m, the new expression for Ψ(x,y|m), the eigenfunction of the operator of the third component of the angular momentum, M^z, is presented. ...These functions are normalizable, single valued and, distinct to the traditional presentation, (x+iy)m=ρmeimϕ, are invariant under the rotations at 2π for any, not necessarily integer, m—the eigenvalue of M^z. For any real m the functions Ψ(x,y|m) form an orthonormal set, therefore they may serve as a quantum mechanical eigenfunction of M^z. The eigenfunctions and eigenvalues of the angular momentum operator squared, M^2, derived for the two different prescriptions for the square root, (m2)1/2, (m2)1/2=|m| and (m2)1/2=±m, are reported. The normalizable eigenfunctions of M^2 are presented in terms of hypergeometric functions, admitting integer as well as non-integer eigenvalues. It is shown that the purely integer spectrum is not the most general solution but is just the artifact of a particular choice of the Legendre functions as the pair of linearly independent solutions of the eigenvalue problem for the M^2.
In our review, we focus on the quantum spin liquid (QSL), defining the thermodynamic, transport, and relaxation properties of geometrically frustrated magnet (insulators) represented by ...herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 . The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless parts in the fermionic quasiparticle spectrum, so-called flat bands. QSL is a quantum state of matter having neither magnetic order nor gapped excitations even at zero temperature. QSL along with heavy fermion metals can form a new state of matter induced by the topological fermion condensation quantum phase transition. The observation of QSL in actual materials such as herbertsmithite is of fundamental significance both theoretically and technologically, as it could open a path to the creation of topologically protected states for quantum information processing and quantum computation. It is therefore of great importance to establish the presence of a gapless QSL state in one of the most prospective materials, herbertsmithite. In this respect, the interpretation of current theoretical and experimental studies of herbertsmithite are controversial in their implications. Based on published experimental data augmented by our theoretical analysis, we present evidence for the the existence of a QSL in the geometrically frustrated insulator herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 , providing a strategy for unambiguous identification of such a state in other materials. To clarify the nature of QSL in herbertsmithite, we recommend measurements of heat transport, low-energy inelastic neutron scattering, and optical conductivity σ ¯ in ZnCu 3 ( OH ) 6 Cl 2 crystals subject to an external magnetic field at low temperatures. Our analysis of the behavior of σ ¯ in herbertsmithite justifies this set of measurements, which can provide a conclusive experimental demonstration of the nature of its spinon-composed quantum spin liquid. Theoretical study of the optical conductivity of herbertsmithite allows us to expose the physical mechanisms responsible for its temperature and magnetic field dependence. We also suggest that artificially or spontaneously introducing inhomogeneity at nanoscale into ZnCu 3 ( OH ) 6 Cl 2 can both stabilize its QSL and simplify its chemical preparation, and can provide for tests that elucidate the role of impurities. We make predictions of the results of specified measurements related to the dynamical, thermodynamic, and transport properties in the case of a gapless QSL.
We consider the dimerized spin‐1/2 Heisenberg chain with spin hexameric distortion of the exchange pattern and study the zero‐temperature phase diagram in the parameter space (J1, J2, J3) by a ...continuum‐limit bosonization approach and the exact diagonalization method. The phase diagram is rich and has two gapped dimer phases. We obtain an estimate of the critical line separating the different gapped dimer phases by the bosonization approach. The existence of the transition line and the difference between dimer phases is checked numerically. The behavior of the energy gap and the dimer order parameter supports the exact location of the gapless line.
Previous detections of individual astrophysical sources of neutrinos are limited to the Sun and the supernova 1987A, whereas the origins of the diffuse flux of high-energy cosmic neutrinos remain ...unidentified. On 22 September 2017, we detected a high-energy neutrino, IceCube-170922A, with an energy of ~290 tera-electron volts. Its arrival direction was consistent with the location of a known γ-ray blazar, TXS 0506+056, observed to be in a flaring state. An extensive multiwavelength campaign followed, ranging from radio frequencies to γ-rays. These observations characterize the variability and energetics of the blazar and include the detection of TXS 0506+056 in very-high-energy γ-rays. This observation of a neutrino in spatial coincidence with a γ-ray-emitting blazar during an active phase suggests that blazars may be a source of high-energy neutrinos.
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