Exact thermodynamics of pairing and charge–spin separation crossovers in small Hubbard nanoclusters

The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and ferromagnetism in nanoclusters. The phase diagram off half filling strongly suggests the existence of quantum critical points and subsequent transitions from electron pairing into unsaturated and saturated ferromagnetic Mott–Hubbard like insulators, driven by electron repulsion. Rigorous criteria for the existence of quantum critical points and crossover temperatures are formulated. The phase diagram for 2×4$2\times 4$-site clusters illustrates how these features are scaled with cluster size. The phase separation and electron pairing, monitored by a magnetic field and electron doping, surprisingly resemble phase diagrams in the family of doped high-Tc$T_c$ cuprates.     

Exact quantum critical points and phase separation instabilities in Betts Hubbard nanoclusters

Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in U>0 Hubbard model including the next nearest neighbor coupling are calculated with the emphasis on the two-dimensional (square) lattices generated by 8- and 10-site Betts unit cells. The exact theory yields insights into the nature of quantum critical points, continuous transitions, dramatic phase separation instabilities and electron condensation in spatially inhomogeneous systems. The picture of coupled antiparallel (singlet) spins and paired charged holes suggests full Bose condensation and coherent pairing in real space at zero temperature of electrons complied with the Bose-Einstein statistics. Separate pairing of charge and spin degrees at distinct condensation temperatures offers a new route to superconductivity different from the BCS scenario. The conditions for spin liquid behavior coexisting with unsaturated and saturated Nagaoka ferromagnetism due to spin-charge separation are established. The phase separation critical points and classical criticalities found at zero and finite temperatures resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen near optimally doped high-T_c cuprates, pnictides and CMR nanomaterials.     

Stripe like inhomogeneities,spectroscopies, pairing and coherence in the high Tc cuprates

It is found that the carriers of the high-T_c cuprates are polaron-like ‘stripons’ carrying charge and located in stripe-like inhomogeneities, ‘quasi-electrons’ carrying charge and spin, and ‘svivons’ carrying spin and lattice distortion. This is shown to result in the observed anomalous spectroscopic properties of the cuprates. The AF/stripe-like inhomogeneities result from the Bose condensation of the svivon field, and the speed of their dynamics is determined by the width of the double-svivon neutron-resonance peak. Pairing results from transitions between pair states of stripons and quasi-electrons through the exchange of svivons. The obtained pairing symmetry is of the d_x²−y² type; however, sign reversal through the charged stripes results in features not characteristic of this symmetry. The phase diagram is determined by a pairing and a coherence line, associated with a Mott transition, and the pseudogap state corresponds to incoherent pairing.     

Stripe fluctuations, carriers, spectroscopies, transport, and BCS-BEC crossover in the high-Tc cuprates

The quasiparticles of the high-T_c cuprates are found to consist of: polaron-like ‘stripons’ carrying charge, and associated primarily with large-U orbitals in stripe-like inhomogeneities; ‘quasi-electrons’ (QE) carrying charge and spin, and associated with hybridized small-U and large-U orbitals; and ‘svivons’ carrying spin and lattice distortion. It is shown that this electronic structure leads to the systematic behavior of spectroscopic and transport properties of the cuprates. High-T_c pairing results from transitions between pair states of stripons and QEs through the exchange of svivons. The cuprates fall in the regime of crossover between BCS and preformed-pairs Bose-Einstein condensation behaviors.     

Pairing enhancement in Betts lattices with next nearest neighbor couplings: Exact results

Electron instabilities in the Hubbard model with the next nearest neighbor coupling are calculated by exact diagonalization in finite, two-dimensional Betts cells (lattices). A viable spin and charge coherent pairing, signaled by quantum critical points and a negative charge gap region, is found in 8- and 10-site Betts lattices at small and moderate U regions consistent with our exact results in elementary bipartite geometries [Phys. Rev. B 78 (2008) 075431]. The contour isolines for continuous temperature driven-crossover between the Mott-Hubbard insulating and coherent pairing phases are demonstrated. The criteria for smooth and abrupt phase transitions are found for systematic enhancement of coherent pairing by optimization of the next nearest neighbor coupling parameter.     

A comparative analysis of the spectral characteristics of triplet self-trapped excitons and F 2 centers in alkali halide crystals

A comparative analysis of the spectral characteristics of self-trapped excitons (STE) and F ₂ centers in the states with the same spin multiplicity is carried out. Based on the analysis, a criterion for the separation of the triplet-triplet (T-T) absorptive transitions in the electronic and hole components of the STE in any alkali halide crystal is proposed. It is concluded that inhomogeneities in the form of a homological cation or anion impurity in the nearest coordination shells of the spatial position of the STE, rather than hole, affect the spectral position of the T-T transitions in the electron component of the STE.     

Pairing modulations and phase separation instabilities in Bi2Sr2CaCu2O8 + δ

There is growing evidence that the unconventional spatial inhomogeneities in the doped high-_Tc$T_c$ superconductors are accompanied by the pairing of electrons, subsequent phase transitions and condensation into coherent states. We show that such pairing states can be obtained from phase separation instabilities near level crossings. Conditions for coherent pairing instabilities are examined using exact diagonalization of Hubbard-like pyramid structures under variation of coupling and interaction strengths. We also evaluate the behavior of the energy charge gap in the vicinity of level crossings using a parametrization of coupling to the apical site to represent out-of-plane effects. These results provide a simple microscopic explanation of (correlation induced) supermodulation of the coherent pairing gap observed in scanning tunneling microscopy measurements at atomic scale in Bi₂Sr₂CaCu₂O_8 + δ.     

Ground States of Quantum Antiferromagnets in Two Dimensions

We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (1990, Mod. Phys. Lett. B4, 1043). The minimal model for square lattice antiferromagnets is a lattice discretization of the quantum nonlinear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Néel order at weak coupling and a confining paramagnetic ground state with bond charge (e.g., spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry groups is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring noncollinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.     

Structural phase transitions and sodium ordering in Na0.5CoO2: a combined electron diffraction and Raman spectroscopy study

The nonstoichiometric Na_xCoO₂ system exhibits extraordinary physical properties that correlate with temperature and Na concentration in its layered lattice without evident long-range structure modification when conventional crystallographic techniques are applied. For instance, Na_0.7CoO₂, a thermodynamically stable phase, shows large thermoelectric power; water-intercalated Na_0.33CoO₂·1.3H₂O is a newly discovered superconductor with T_c∼4 K, and Na_0.5CoO₂ exhibits an unexpected charge ordering transition at around T_co∼55 K. Recent studies suggest that the transport and magnetic properties in the Na_xCoO₂ system strongly depend on the charge carrier density and local structural properties. Here we report a combined variable temperature transmission electron microscopy and Raman scattering investigation on structural transformations in Na_0.5CoO₂ single crystals. A series of structural phase transitions in the temperature range from 80 to 1000 K are directly identified and the observed superstructures and modulated phases can be interpreted by Na-ordering. The Raman scattering measurements reveal phase separation and a systematic evolution of active modes along with phase transitions. Our work demonstrates that the high mobility and ordering of sodium cations among the CoO₂ layers are a key factor for the presence of complex structural properties in Na_xCoO₂ materials, and also demonstrate that the combination of electron diffraction and Raman spectroscopy measurements is an efficient way for studying the cation ordering and phase transitions in related systems.     

Investigation on phase and shape transitions in the hot rotating nucleus <Superscript>154</Superscript>Dy

A statistical theory for hot rotating nuclei incorporating deformation, collective and non-collective rotational degrees of freedom, shell effects and pairing correlations is used to investigate the occurrence of phase and shape transitions in the hot rotating deformed nucleus ¹⁵⁴Dy . The interplay of various degrees of freedom and their influence on the behavior of nuclei formed as fused compounds in heavy-ion reactions are studied. A phase transition from the superfluid to normal state in the nucleus with increasing temperature and angular momentum is observed. The effect of pairing on the level density parameter and nucleon separation energy has been analyzed and is found to be substantial. The neutron and proton separation energies extracted as a function of the angular momentum and temperature is found to decrease sharply for particular angular momentum states of the nucleus due to shape transitions from prolate collective to oblate non-collective at higher temperatures.     

Localized charge inhomogeneities and phase separation near a second-order phase transition

Localized charge inhomogeneities and phase separation are described in the framework of the phenomenological theory of phase transitions. It is shown that Coulomb interaction determines the charge distribution and the characteristic size of the emerging inhomogeneities. Phase separation associated with charge segregation becomes possible because of a high dielectric constant and a low excess charge density in the localization region. The phase diagram of the system is calculated, and estimates are obtained for the gain in energy associated with the emerging state. The role of Coulomb interaction is exposed, and corresponding estimates are given.     

Study on the competition between density waves, singlet, and triplet pairing superconductivity in organic conductors (TMTSF)2X

We study the effect of dimerization of TMTSF molecules and the effect of magnetic field (Zeeman splitting) on the phase competition in quasi one-dimensional organic superconductors (TMTSF)₂X by applying the random phase approximation method. As for the dimerization effect, we conclude that due to the decrease of the dimerization, which corresponds to applying the pressure and cooling, spin and charge density wave states are suppressed and give way to a superconducting state. As for the magnetic field effect, we find generally that spin-triplet pairing mediated by a coexistence of 2k_F spin and 2k_F charge fluctuations can be strongly enhanced by applying magnetic field rather than triplet pairing due to a ferromagnetic spin fluctuations. Applying the above idea to (TMTSF)₂X compounds, a magnetic field induced singlet-triplet transition is consistent with above mechanism in (TMTSF)₂ClO₄.     

N@C60 and P@C60 as quantum bits

Due to their long electron spin relaxation times, the endohedral fullerenes N@C₆₀ and P@C₆₀ are good candidates for the implementation of qubits in an electron spin quantum computer. A central operation in this context is the rotation of the spin direction by an arbitrary angle. In the present experiment, this nutation behavior was studied in pulsed electron spin resonance measurements. We show that, even at room temperature, about 50 Rabi oscillations (about 100 qubit operations) can be performed without refocusing the spin system, although inhomogeneities are present. A special feature of the group V endohedral fullerenes is the electron spinS=3/2, which complicates the nutation behavior. The zero-field splitting at low temperature gives rise to different nutation frequencies for the (1/2,?1/2) transition and the (±3/2, ±1/2) transitions. The frequency ratio is 2/3^1/2.     

Spin-triplet superconductivity induced by off-site Coulomb interaction in a triangular lattice

In order to study how superconductivity emerges when the charge fluctuation coexists with the spin fluctuation in a triangular lattice, we obtain a phase diagram against the nearest-neighbor Coulomb repulsion V and band filling n on the extended Hubbard model using the fluctuation exchange (FLEX) approximation. We find that a charge density wave (CDW) phase exists in the region where the value of V is large, and the f-wave spin-triplet pairing mediated by a strong charge fluctuation is dominant near the CDW phase.     

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.     

Spin and charge order in Mott insulators and d-wave superconductors

We argue that aspects of the anomalous, low temperature, spin and charge dynamics of the high temperature superconductors can be understood by studying the corresponding physics of undoped Mott insulators. Such insulators display a quantum transition from a magnetically ordered Néel state to a confining paramagnet with a spin gap; the latter state has bond-centered charge order, a low energy S=1 spin exciton, confinement of S=1/2 spinons, and a free S=1/2 moment near non-magnetic impurities. We discuss how these characteristics, and the quantum phase transitions, evolve upon doping the insulator into a d-wave superconductor. This theoretical framework was used to make a number of predictions for STM measurements and for the phase diagram of the doped Mott insulator in an applied magnetic field.     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

Discrete and generalized phase space techniques in critical quantum spin chains

We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\frac{1}{2}$ systems. We develop a general formula relating the phase space techniques and the thermodynamical quantities of spin models, which we apply to single, bipartite and multi-partite systems governed by the XY and the XXZ models. Our approach allows us to introduce a novel way to represent, detect, and distinguish first-, second- and infinite-order quantum phase transitions. Furthermore, we show that the factorization phenomenon of the XY model is only directly detectable by quantities based on the square root of the bipartite reduced density matrix. We establish that phase space techniques provide a simple, experimentally promising tool in the study of many-body systems and we discuss their relation with measures of quantum correlations and quantum coherence.     

Large triplet pairing mixing in the FFLO state of spin fluctuation mediated superconductivity in Q1D systems

We study the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state of spin fluctuation mediated superconductivity and focus on the effect of coexisting charge fluctuations. We find that (i) consecutive transitions from singlet pairing to FFLO and further to S_z=1 triplet pairing can generally take place upon increasing the magnetic field when strong charge fluctuations coexist with spin fluctuations and (ii) the enhancement of the charge fluctuations lead to a significant increase of the parity mixing in the FFLO state, where the triplet/singlet component ratio in the gap function can be close to unity. We propose that such consecutive pairing state transition and strong parity mixing in the FFLO state may take place in a quasi-one-dimensional organic superconductor (TMTSF)₂X.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998