Spin stiffness of strongly correlated doped quantum antiferromagnet on 2-dimensional lattices and it's connection with effective exchange constant for a semi- itinerant system
The generalized spin stiffness constant for a doped quantum antiferromagnet has been investigated both analytically and numerically as a function of doping concentration at zero temperature, based on the strongly correlated t-J model on two-dimensional square lattice. The nature of the theoretical dependence of the stiffness constant on doping shows a striking similarity with that of the effective exchange constant, obtained from the combination of other theoretical and experimental techniques in the low doping region. This correspondence once again establishes that spin stiffness can very well play the role of an effective exchange constant even in the strongly correlated semi-itinerant systems. Our theoretical plot of the stiffness constant against doping concentration in the whole doping region exhibits the various characteristic features like a possible crossover in the higher doping regions and persistence of short range ordering even for very high doping with the complete vanishing of spin stiffness occurring only close to 100% doping. Our results receive very good support from various other theoretical approaches and also brings out a few limitations of some of them. Our detailed analysis highlights the crucial importance of the study of spin stiffness for the proper understanding of magnetic correlations in a semi-itinerant magnetic system described by the strongly correlated t-J model. Moreover, our basic formalism can also be utilized for determination of the effective exchange constant and magnetic correlations for itinerant magnetic systems, in general in a novel way.
The generalized spin stiffness constant for a doped quantum antiferromagnet has been investigated both analytically and numerically as a function of doping concentration at zero temperature, based on the strongly correlated t-J model on two-dimensional square lattice. The nature of the theoretical dependence of the stiffness constant on doping shows a striking similarity with that of the effective exchange constant, obtained from the combination of other theoretical and experimental techniques in the low doping region. This correspondence once again establishes that spin stiffness can very well play the role of an effective exchange constant even in the strongly correlated semi-itinerant systems. Our theoretical plot of the stiffness constant against doping concentration in the whole doping region exhibits the various characteristic features like a possible crossover in the higher doping regions and persistence of short range ordering even for very high doping with the complete vanishing of spin stiffness occurring only close to 100% doping. Our results receive very good support from various other theoretical approaches and also brings out a few limitations of some of them. Our detailed analysis highlights the crucial importance of the study of spin stiffness for the proper understanding of magnetic correlations in a semi-itinerant magnetic system described by the strongly correlated t-J model. Moreover, our basic formalism can also be utilized for determination of the effective exchange constant and magnetic correlations for itinerant magnetic systems, in general in a novel way.
The magnetic correlation in one-dimensional doped quantum Heisenberg antiferromagnets is investigated on the basis of the single band t-J model at zero temperature in the strong correlation limit. An analytical expression for the generalized spin stiffness constant corresponding to this model is derived and then stiffness constant is numerically studied as a function of doping concentration. The presence of a maximum in the plot of this theoretically obtained total stiffness constant as a function of doping concentration, occurring at a finite doping, suggests the emergence of a tendency to form a new magnetic ordering of itinerant nature in the system in the low doping region and it's disappearance as the doping is increased further. This prediction of ours is quite novel and may be directly tested by independent experiments in future. Our results for spin stiffness constant are compared with those for the effective exchange constant extracted from the available experimental results obtained so far from the chains of YBa2Cu3O6+x at low temperature and they show very similar behaviour as a function of doping concentration. This firmly establishes the role of spin stiffness constant as effective exchange constant for strongly correlated semi-itinerant systems in one-dimension. Our results in general receive good support from those based on other theoretical approaches.
Expressions for the generalized charge stiffness constant at zero temperature are derived corresponding to low-dimensional hole-doped quantum antiferromagnets, describable by the t–J-like models, with a view to understanding fermionic pairing possibilities and charge couplings in itinerant antiferromagnetic systems. A detailed comparison between spin and charge correlations and couplings are presented for the strong and weak coupling limits in one (1D) and two (2D) dimensions. The result highlights that the charge and spin couplings show very similar behaviour in the over-doped region in both dimensions, whereas they show a completely different trend in the lower doping regimes. A qualitative equivalence of the generalized charge stiffness constant with the effective Drude weight and Coulomb interaction is established based on the comparison with other theoretical and experimental results. The fall in charge stiffness with increase in doping then implies a reduction in magnitude of the effective Coulomb repulsion between the mobile carriers. This leads to an enhanced possibility of fermionic pairing with an increase in doping concentration, in the possible presence of some other attraction-producing mechanism from a source outside the t–J-like models. Moreover, under certain conditions in the optimal doping region, the t–J-like models themselves are able to produce an attractive interaction for pairing.
The spin response functions for a doped strongly correlated quantum Heisenberg antiferromagnet, in the form of a t – J model, on low-dimensional lattices have been explored. In particular, the spin stiffness constant and the spin diffusion coefficient have been calculated as functions of doping concentration by different approaches for this model on a chain and on a square lattice. The occurrences of various possible magnetic phases, namely with long range and short range orders, and also a novel paramagnetic phase, have been predicted at zero temperature. Our conclusions regarding the phase diagram agree remarkably well with those from other recent theoretical approaches. Our results are discussed in the light of experimental results from the cuprates.
The purpose of this work is the derivation of an effective field theory for the low-energy magnetic modes of the t-J model on a two-dimensional square lattice and for small values of doping, which is of relevance to the physics of high-temperature superconductors. In particular, we address the possibility of low-energy excitations that obey fractional spin and statistics. For temperatures where kBT is considerably smaller than the magnetic exchange coupling J and for low values of doping, the system is close to an antiferromagnetically ordered Néel state and the spin correlation length takes values significantly larger than the lattice constant a, such that a field theoretic analysis is justified. The effective model is obtained by means of a gradient expansion around the antiferromagnetically ordered reference state. Dimensional analysis shows that in (2+1) dimensions only terms up to order O(a2) in the effective action are relevant to the behaviour at large scales, whereas O(a3)-terms are marginal and higher order terms are irrelevant. Even though marginal, the O(a3)-contributions may drastically influence the properties of excitations, as they might feature a term of topological nature which endows field histories with a statistical phase factor. In fact, all field histories can be characterized as mappings from compactified spacetime, the three-sphere S3, to the order parameter space S2 and thus fall into different homotopy classes. The topological invariant characterizing these homotopy classes is given by the Hopf invariant. Consequently, if the Hopf invariant emerges in the effective field theory, the spin and statistics of low-energy excitations fractionalize. The analysis is based on a path integral representation of the t-J model which was obtained recently by means of Dirac quantization. After introducing a staggered quantization axis, the single occupancy constraint which is inherent to the t-J model can be taken into account exactly. We perform a long-wavelength, low-frequency gradient expansion of the effective action and integrate over the fermionic degrees of freedom as well as the fast-fluctuating bosonic modes. Since our derivation is based on a microscopic model, we obtain an effective action where the doping dependence of the coupling constants is made explicit.
We analyze the density dependence of the spin stiffnesses and the stability of magnetic order with respect to quantum fluctuations in the two-dimensional Hubbard model close to half-filling. The stiffnesses are computed from the spin susceptibility obtained from a random-phase approximation in a magnetically ordered state. For a sizable next-to-nearest-neighbor hopping amplitude and a moderate Hubbard interaction, the mean-field ground state is a Néel antiferromagnet in the electron-doped regime at and above half-filling and a planar circular spiral state in the hole-doped regime below half-filling. Upon electron doping, the Néel stiffness decreases smoothly and not very steeply. By contrast, the in-plane and out-of-plane stiffnesses in the spiral state drop abruptly at half-filling. The out-of-plane stiffness even drops to zero and then increases again very slowly upon increasing hole doping. At finite temperatures, the Néel-to-spiral transition is shifted into the hole-doped regime, the stiffnesses are continuous functions of the density, and they vanish at the transition. For small hole doping, the spin stiffnesses describe the quantum fluctuations only in a small momentum range, which shrinks to zero upon approaching half-filling. Using the above results, we show that the quantum ground state of the lightly electron-doped Hubbard model remains Néel ordered, while quantum fluctuations probably destroy the spiral long-range order in the hole-doped regime, giving rise to a quantum disordered state with a spin gap.
The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wave function and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wave function of the strongly correlated solid. Exchange, correlation, and magnetic-field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from n doping to p doping in GaAs/Alx${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor \ensuremath{\nu}\ensuremath{\sim}1/5 to \ensuremath{\nu}\ensuremath{\sim}1/3. This lends strong support to the claim that the observed reentrant insulating phases around \ensuremath{\nu}=1/5 for n-doped and around \ensuremath{\nu}=1/3 for p-doped high-mobility samples are primarily caused by electron-electron interaction effects. We discuss the possible implications of our theoretical results for some recent experiments carried out in the quantum Hall regime in search of the electron solid.