Effect of doping on the magnetic ordering of quasi-one-dimensional antiferromagnets

We have studied theoretically how nonmagnetic dopants, which change the local coupling of spins to the host, affect the low-temperature thermodynamic characteristics of quasi-one-dimensional (Q1D) quantum spin antiferromagnets. Our theory qualitatively and, in some cases, quantitatively describe the behavior of the magnetic susceptibility and specific heat of the Q1D system BaCu₂(Si₁₋xGex)₂O₇. We have shown that in some cases the strong disorder in the distribution of characteristics of magnetic impurities in quantum antiferromagnetic spin chains can be the cause of magnetic ordering, if such chains are weakly coupled to each other, while for homogeneous chains and chains with a weak disorder a small enough coupling between chains does not produce magnetic ordering. For other values of the parameters, magnetic impurities can decrease the Neel temperature compared to that of the homogeneous Q1D spin system

Boundary bound states in the Bose–Hubbard-like chain

The degenerate Hubbard-like chain with open boundary conditions is studied with the help of the Bethe ansatz. The special case of the Bose–Hubbard-like chain is studied in detail. Boundary bound states, which appear as the consequence of the local potential(s), applied to the edge(s) of the open chain are studied in the ground stat

Spin-orbit interaction in the supersymmetric antiferromagnetic t-J chain with a magnetic impurity

The effect of spin-orbit interaction in the strongly correlated exactly solvable electron model with magnetic impurity is studied. The considered magnetic impurity reveals the property of a “mobile” one. It is shown that the asymptotics of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by both, the spin-orbit coupling, and by the magnetic impurity

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

During recent years the interest to frustrated magnets has grown considerably. Such systems reveal very peculiar properties which distinguish them from standard paramagnets, magnetically ordered regular systems (like ferro-, ferri-, and antiferromagnets), or spin glasses. In particular great amount of attention has been devoted to the so-called spin ices, in which magnetic frustration together with the large value of the single-ion magnetic an-isotropy of a special kind, yield peculiar behavior. One of the most exciting features of spin ices is related to low-energy emergent excitations, which from many viewpoints can be considered as analogies of Dirac's mono-poles. In this article we review the main achievements of theory and experiment in this field of physics

NMR relaxation rate of a quantum spin chain with an impurity

The relaxation rate of the nuclear magnetic resonance is calculated exactly for a model spin-1/2 chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's g-factor from the values of the host chain yield special features in the temperature and magnetic field behavior for the relaxation rate

Majorana bound states in the finite-length chain

Recent experiments investigating edge states in ferromagnetic atomic chains on superconducting substrate are analyzed. In particular, finite size effects are considered. It is shown how the energy of the Majorana bound state depends on the length of the chain, as well as on the parameters of the model. Oscillations of the energy of the bound edge state in the chain as a function of the length of the chain, and as a function of the applied voltage (or the chemical potential) are studied. In particular, it has been shown that oscillations can exist only for some values of the effective potential

Dynamical quantum phase transitions (Review Article)

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

To the theory of spin–charge separation in one-dimensional correlated electron systems

Spin—charge separation is considered to be one of the key properties that distinguish low-dimensional electron systems from others. Three-dimensional correlated electron systems are described by the Fermi liquid theory. There, low-energy excitations (quasiparticles) are reminiscent of noninteracting electrons: They carry charges e and spins 1/2. It is believed that for any one-dimensional correlated electron system, low-lying electron excitations carry either only spin and no charge, or only charge without spin. That is why recent experiments looked for such low-lying collective electron excitations, one of which carries only spin, and the other carries only charge. Here we show that despite the fact that for exactly solvable one-dimensional correlated electron models there exist excitations which carry only spin and only charge, in all these models with short-range interactions the low-energy physics is described by low-lying collective excitations, one of which carries both spin and charge

Commensurate-incommensurate phase transitions for multichain quantum spin models: exact results

The behavior in an external magnetic field is studied exactly for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate-incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exactly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in the limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearence of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrable theories are calculated

Macroscopic thermal entanglement in a spin chain caused by the magnetic field: Inhomogeneity effect

The influence of the inhomogeneity on the macroscopic thermal pairwise entanglement for the system of coupled spins 1/2 (qubits) has been studied. The most important effect of the inhomogeneity on the thermal entanglement is in the new role of the external potential (magnetic field), which can produce nonzero entanglement for qubits, situated not far from the inhomogeneity