Algebraic properties of an integrable t-J model with impurities

We investigate the algebraic structure of a recently proposed integrable t-J model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz states are highest weight vectors of the underlying gl(2′1) supersymmetry algebra. By acting with the gl(2′1) generators we construct a complete set of states for the model.     

Unitary transformation treatment of a single hole in an Ising antiferromagnet

The behavior of a single hole in a two-dimensional Ising antiferromagnet (t-J ^z model), is studied in the generalized Dyson-Maleev representation, where the spins are mapped on boson operators and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that thet-J ^z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. Our approach yields an upper bound to the exact ground state energy, as well as the corresponding ground state eigenvector. Fork=0 our energy bound is remarkably close to the result of the self-consistent Born approximation over a wide range of the coupling parameter, which includes the range typically assumed for the high-T _c materials. The ground state eigenvector is used to calculate the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obtained in previous work, showing that our ground state eigenvector accounts quite well for the small size of the “spin polaron” in thet-J ^z model.     

Coherent motion of a hole in the copper-oxygen planes of high-temperature superconductors

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional (CuO₂) _N system is discussed. The (CuO_2)N planes constitute the most important structural element in the high-T _c superconducting materials. The system is described by the Kondo-Heisenberg Hamiltonian, which is a simplified version of the extended Hubbard or Emery model. The calculations are based on the introduction of a trial wave function in the unitary space of the Cu spins and the O degrees of freedom. They generalize an approach recently proposed for the coherent motion of a hole in thet-J model. The propagation is mainly determined by the spin-fluctuation part of the superexchange between the copper spins. Minor contributions to the coherent hole motion are due to an effective tunneling of the hole to second and third nearest neighbors along spiral paths in the (CuO₂) _N plane. This mechanism can be considered as the analogue of a mechanism for coherent hole motion in thet-J model first discussed by Trugman. For the dispersion relation a cosine-band-like form is found similar to that for thet-J model. The band width, however, is somewhat increased. Except for this difference, our results seem to support the point of view of Zhang and Rice, who have claimed that there exists a one-to-one mapping between the low-lying states of the two-band model and the effectivet-J model.     

Single-hole state in half-filled 2D Hubbard model

Summary We have investigated the ground state of a single hole in the half-filled Hubbard model on a 2D square lattice using the coupled-cluster method. In particular we obtained an analytical expression of the hole energy dispersion function ɛ(k) which is consistent with earlier studies on thet-J model in the strong-coupling limit. An appreciable discrepancy on the hole energy bandwidth is, however, observed between the Hubbard model and thet-J model. We believe that this discrepancy is due to the absence of the three-site interaction term in thet-J model.     

Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method

The power-Lanczos (PL) method is one kind of Green's function Monte Carlo simulation, which is improved by Lanczos iterations. The ground state energies of strongly-correlated models can be evaluated by this method quite accurately. In this report, the boundary of phase separation (PS) of the two-dimensional t-J model is investigated by the power-Lanczos method and Maxwell construction. The energies are compared with the results evaluated by other methods. Our conclusion is that there is no phase separation for J/t≤0.4.     

Effective interactions and the nature of Cooper instability of spin polarons in the 2D Kondo lattice

It has been shown that two-and three-center interactions arise in the strong-coupling regime for the 2D Kondo lattice; these interactions both induce and suppress the Cooper instability. It is important that, in contrast to the t-J* model, the three-center interactions promote the Cooper pairing and ensure the appearance of the superconducting phase with a high critical temperature T _c. The calculated concentration dependences of T _c agree well with the experimental data for the cuprate superconductors.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Mutual Chern-Simons theory and its applications in condensed matter physics

In this paper, the mutual Chern-Simons (MCS) theory is introduced as a new kind of topological gauge theory in 2+1 dimensions. We use the MCS theory in gapped phase as an effective low energy theory to describe the Z ₂ topological order of the Kitaev-Wen model. Our results show that the MCS theory can catch the key properties for the Z ₂ topological order. On the other hand, we use the MCS theory as an effective model to deal with the doped Mott insulator. Based on the phase string theory, the t-J model reduces to a MCS theory for spinons and holons. The related physics in high T _c cuprates is discussed.      

Effective Hamiltonian and properties of the normal and superconducting phases of <Emphasis Type="Italic">n</Emphasis>-type cuprates

An effective low-energy Hamiltonian is derived from a microscopic multiband p-d model in the regime of strong electron correlations. The parameters of the p-d model are determined by comparison with the ARPES data for undoped Nd₂CuO₄. The Hamiltonian is the t-J* model in which hopping and exchange slowly decay with distance and are taken into account up to the fifth coordination sphere. The quasiparticle band structure is calculated as a function of the doping concentration with regard to short-range magnetic order, and the superconductivity theory with the spin-fluctuation pairing mechanism is constructed. Assuming that the parameters of the model do not depend on the doping level, we obtained quantitative agreement with the properties observed experimentally for the normal and superconducting phases without introducing fitting parameters.     

Properties of the t-J model in the dynamical mean field theory: One-particle properties in the antiferromagnetic phase

We study the one-particle properties of the t-J model within the framework of Vollhardt's dynamical mean field theory. By introducing an AB-sublattice structure we explicitly allow for a broken symmetry for the spin degrees of freedom and are thus able to calculate the one-particle spectral function in the antiferromagnetic phase. We observe surprisingly rich structures in the one-particle density of states for T < T _N at finite doping up to 15%. These structures can be related to the well known results for one single hole in the Néel background. We are thus able to establish the relevance of this at a first sight academic limit to physical properties of the t-J model with a finite density of holes in the thermodynamical limit.     

Theory of the electronic structure and spin susceptibility of La2−x SrxCuO4

We solve the problem of the effect of strong electron correlations on the homogeneous spin susceptibility of current carriers in CuO₂ planes. We show that the dependence of the spin susceptibility χ(T) of high-T _c superconductors of the La_2−x Sr_xCuO₄ type on temperature and the doping index x can be explained fairly well by the two-band model suggested earlier (the singlet-correlated oxygen band plus the lower Hubbard band of copper). The model has features in common with the phenomenological t-J model but cannot be reduced to the latter completely. In contrast to the t-J model, the density of states of the oxygen holes has a peak near the bottom of the band. It is the presence of this peak together with the non-Fermi-liquid properties that explain the unusual behavior of the spin susceptibility of La_2−x Sr_xCuO₄. Zh. éksp. Teor. Fiz. 112, 1763–1777 (November 1997)     

Variational approximations for stationary states of Ising-like models

The derivation of spin-effective actions is envisaged for the Hubbard model with infinite Coulomb repulsion for a very low concentration of holes with a slave fermion representation for electronic operators. For that, spinless charge variables (vacancies or holes) are integrated out and the resulting effective action at finite temperature is expanded up to the fourth order in the hopping term as proposed in reference [F.L. Braghin, A. Ferraz, E.A. Kochetov, Phys. Rev. B 78, 115109 (2008)] and, in a square lattice, the fourth order term is shown to have the structure of an extended gauge invariant J-Q model for localized spins. Two cases for which the resulting model is non trivial are analysed and they correspond basically to (1) holes hopping between two sub-lattices and (2) a time-dependent solution for the spinon variables in the square lattice. Whereas the first of these cases yields, at the leading order, an effective antiferromagnetic Heisenberg coupling for localized spins and the second one may lead either to ferromagnetic or antiferromagnetic effective coupling. In the second case, the ordering should appear rather in finite size domains and, although charge variables were integrated out, a subtle imbalance between charge degrees of freedom and spins should be at work.     

Effective Hubbard model for Zn-doped CuO2 plane

In the framework of the cell-perturbation method for the original p-d model an effective two-band Hubbard model for the CuO₂ plane with Zn impurities is derived. Zn impurities are modelled by Wannir oxygen one-hole states at vacant Cu sites. The model is based on the results of band structure calculations carried out within the local-density approximation. Further reduction to an extended t-J model shows a large ferromagnetic superexchange interaction between the Cu spin with the nearest virtual oxygen spin in the Zn cell. Received 17 November 1998     

New Lagrangians for Bosonic m-branes with vanishing cosmological constant

A class of conformally invariant σ model actions in 2n dimensions is shown to be classically equivalent to the Nambu-Goto action for an extended object, an m-brane (m+1=2n), embedded in a higher dimensional space-time (d⪖m+1). when m is even, a (2n + 1)-dimensional σ model action is also constructed, which is classically equivalent to the Nambu-Goto action, but in this case there is no conformal invariance. In both cases the cosmological constant can be set to zero.     

Coherent motion of a hole in a two-dimensional quantum antiferromagnet

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional quantum antiferromagnet is discussed. The system is described by two model Hamiltonians, thet-J model and thet-t-J model, which have been used frequently to discuss strong electron-correlation effects present in high-T _c superconductors. The calculations are based on the introduction of a new wave function which is constructed by use of equations derived by Shraiman and Siggia. The different mechanisms for the coherent propagation, which are due to the spin fluctuation and the hopping terms of the Hamiltonian, are treated on the same footing. As a result of the inclusion of an effective hopping mechanism along spiral paths-first discussed by Trugman-the minimum of the band is somewhat changed compared to results recently obtained in the literature. For large values of the ratiot/J an inversion of the whole dispersion relation occurs. The overall shapes of the dispersion within both models are found to agree quite well, though for small values oft/J the bandwidth within thet-J model becomes significantly smaller than that of thet-t-J model.     

Perovskites in high dimensions

We study the (D+1) band Hubbard model on generalizedD-dimensional perovskite structures. We show that in the limit of high dimensions the possible scaling behaviour is uniquely determined via the bandstructure and that the model without direct oxygen-oxygen hopping necessarily scales to the cluster limit. A 1/dimension expansion then leads to at-J like Hamiltonian and the Zhang-Rice analysis becomes rigorous. The large dimension fixed point, in general, still remains the cluster model even when a hopping term between n.n. oxygensites is included. Only for a unique ratio of the oxygen onsite energies to the oxygen-oxygen hopping amplitude is a new fixed point possible, corresponding to a heavy-Fermion Hamiltonian.     

Spin in the worldline path integral in 2 + 1 dimensions

We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x(τ), the spacetime paths. We then show that the functional integral automatically imposes the constraint , while there is a spin action, which agrees with the one one should expect for a spin- field.     

QCD equation of state for heavy ion collisions

In this work, we calculate the equation of state(EoS) of quark gluon-plasma(QGP) using the CornwallJackiw-Tomboulis(CJT) effective action. We get the quark propagator by using the rank-1 separable model within the framework of the Dyson-Schwinger equations(DSEs). The results from CJT effective action are compared with lattice QCD data. We find that, when μ is small, our results generally fit the lattice QCD data when TT_c,but show deviations at and below T_c. It can be concluded that the EoS of CJT is reliable when TT_c. Then,by adopting the hydrodynamic code UVH2+1, we compare the CJT results of the multiplicity and elliptic flow v2 with the PHENIX data and the results from the original EoS in UVH2+1. While the CJT results of multiplicities generally match the original UVH2+1 results and fit the experimental data, the CJT results of v2 are slightly larger than the original UVH2+1 results for centralities smaller than 40% and smaller than the original UVH2+1 results for higher centralities.     

Self-dual tensors and gravitational anomalies in 4n + 2 dimensions

Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n + 2 dimensions. The manifest classical invariance is achieved using a newly developed method based on a scalar auxiliary field and two new bosonic local symmetries. The resulting anomalies coincide with the ones predicted by the index theorem. In the two-dimensional case, moreover, we perform an exact covariant computation of the effective action for a chiral boson (a scalar) which is seen to coincide with the effective action for a two-dimensional complex Weyl fermion. All these results support the quantum reliability of the new, at the classical level manifestly invariant, method.