From thermodynamics, local spin density approximation Hubbard U studies and exact diagonalizations of a five-band Hubbard model on CuO 2 stripes we find that Li 2 ZrCuO 4 (Li 2 CuZrO 4 in traditional notation) is close to a ferromagnetic critical point. Analyzing its susceptibility T and specific heat c p T; H within a Heisenberg model, we show that the ratio of the 2nd to the 1st neighbor exchange integrals ÿJ 2 =J 1 0:3 is close to the critical value c 1 4 . Comparing with related chain cuprates we explain the rather strong field dependence of c p , the monotonic downshift of the peak of T, and its increase for ! c 0.

During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role. PACS

Using a model of an open spin chain that is exactly soluble by means of a Bethe ansatz, we study the effects of a boundary magnetic field and an impurity spin coupled to the chain. An impurity spin only scatters forward, while the boundary is purely a back-scatterer. Two parameters for the impurity and one for the boundary permit us to mimic the effect of real magnetic impurity, with both forward and backward scattering.

Capper t u g d a t e become. antiterromagnetically ordered below 23.0(2) K and ibs magnetic structure has been determined I " singl-ystal unpolarized neutron diffraction measurements at 5 K. The chemical unit cell is triclinic Pi, with (L = 4.694(1), 6 = 5.830(1). c = 4.877(1) A, OT = 91.€4(1), @ = 92.41(2) and r = 82.91(1)o at 15 K. The magnetic propagation vector is ( $ 0 0 ) and the magnetic space group P 2 . i . The two equivalent copper ions within the unit cell have magnetic moments of 0.67(1) pg aligned ferromagnetically at the sphuiorl polar ang l s B = 121(2)O and d = 52(2)', the polar axis being parallel to e and Q being measured from the =-a* plane. This direaim coincides, within experimudal error, with the axis of elongation o f the Jahn-Teller distorted octahedmn of oxygen a t o m about the Cu't ion. A multipole refinement of the moment distribution, to order two on quantum u e s Z parallel to the moment direction and X , Y directed towards the four close oxygen neighbours, shows that Y20 is the only significant multipole.Its sign indicates that the moment distribution approximates to an oblate ellipsoid of revolution with its axis parallel to Z. Only two of the six oxygen neighbours of the Cuz+ ion carry a significant transferred moment of 0.06(1) pg . These ohservatiors a r e related to the exchange paths and covalency in the compound.

An explanation is provided for the heavy quasiparticle excitations in LiV2O4. It differs considerably from that of other known heavy-fermion systems. Main ingredients of our theory are the cubic spinel structure of the material and strong short-range correlations of the d electrons. The large γ coefficient is shown to result from excitations of Heisenberg spin 1 2 rings and chains. The required coupling constant is calculated from LDA+U calculations and is found to be of the right size. Also the calculated Sommerfeld-Wilson ratio is reasonably close to the observed one. Dedicated to E. Müller-Hartmann on the occasion of his 60th birthday.The low-temperature properties of the metal LiV 2 O 4 show many of the characteristic features of heavy-fermion systems like CeAl 3 or CeRu 2 Si 2 [1-3]. The coefficient γ of the lowtemperature specific heat C = γT is large, i.e., γ = 0.35-0.42 J/mol K 2 [1], depending on samples, and C(T ) shows a broad maximum around 16 K. The large γ value implies a high density of fermionic low-energy excitations. In fact, when C(T ) is integrated up to 60 K it is found that the associated entropy is close to 2R ln 2, where R is the gas constant. This suggests that there is roughly one excitation per V ion in the system when it is heated up to that temperature, a finding inconceivable for a conventional, partially filled conduction band of d electrons. In fact, the γ-value obtained from ab initio band structure calculations [4-7] turns out to be too small by a factor of 25. In accordance with the observed large γ-value, it is found that also the spin susceptibility χ sp (T ) is similarly enhanced [2]. It is nearly T -independent below T ≈ 30 K with a shallow broad maximum around 16 K and a sample-dependent increase

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An electron spin resonance (ESR) study of the heavy fermion compound YbRh2Si2 for fields up to ∼ 8 T reveals a strongly anisotropic signal below the single ion Kondo temperature TK ∼ 25 K. A remarkable similarity between the T -dependence of the ESR parameters and that of the specific heat and the 29 Si nuclear magnetic resonance data gives evidence that the ESR response is given by heavy fermions which are formed below TK and that ESR properties are determined by their field dependent mass and lifetime. The signal anisotropy, otherwise typical for Yb 3+ ions, suggests that, owing to a strong hybridization with conduction electrons at T < TK, the magnetic anisotropy of the 4f states is absorbed in the ESR of heavy quasiparticles. Tuning the Kondo effect on the 4f states with magnetic fields ∼ 2 − 8 T and temperature 2 − 25 K yields a gradual change of the ESR g-factor and linewidth which reflects the evolution of the Kondo state in this Kondo lattice system. PACS numbers: 71.27.+a, 75.20.Hr, Strong electron-electron (EE) interactions in metals yield a fascinating variety of novel and often interrelated quantum phenomena, such as quantum phase transitions, breakdown of the Landau Fermi-liquid (LFL) state, unconventional superconductivity, etc. (for an overview see, e.g., [1]). In intermetallic compounds where 4f (5f ) magnetic ions (e.g. Yb, Ce, U etc.) build up a regular Kondo lattice, strong EE correlations are established by the coupling of local f -magnetic moments with the conduction electrons (CE). As a consequence, a large effective mass enhancement of the quasiparticles (QP) hallmarks the properties of paramagnetic heavy fermion metals. A competing interaction, the so-called RKKY-interaction between the local f -states via the sea of CE, favors a magnetically ordered ground state.An important realization of a system where the delicate balance between Kondo and RKKY interactions can be investigated is the intermetallic compound YbRh 2 Si 2 where antiferromagnetic order, quantum criticality, heavy fermion-and non-LFL (NFL) behavior can be tuned by a magnetic field B and temperature T [2,3,4,5,6] (Fig. 1). In the parameter domain where these remarkable electronic crossovers take place a strong hybridization of 4f electrons with CE significantly broadens the otherwise atomically sharp f -states. That is why the observation of a narrow electron spin resonance (ESR) signal in the Kondo state of YbRh 2 Si 2 was very surprising [7]. While the reported pronounced anisotropy of the signal is indeed in accordance with an ESR of localized Yb 3+ 4f moments, a non-local picture is suggested by the observation of this signal down to the lowest accessible temperatures of 0.69 K [8] where the single ion Kondo effect is expected to screen the magnetic moments. On the other hand the conduction electron ESR seems also unlikely because in this compound comprising heavy metal elements the spin-orbit (SO) coupling drastically shortens the electron spin lifetime [9].To unravel a controversial nature of this resonance response w...