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Register a new userDynamic Exponent of t-J and t-J-W Model
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Added by
Hirokazu Tsunetsugu
Publication date
1998
fields
Physics
and research's language is
English
Authors
Hirokazu Tsunetsugu ISSP
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Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, $W$. For the ordinary t-J model with $W$=0, the scaling of the Drude weight $D propto delta^2$ for small doping concentration $delta$ is obtained, which indicates anomalous dynamic exponent $z$=4 of the Mott transition. When $W$ is switched on, the dynamic exponent recovers its conventional value $z$=2. This corresponds to an incoherent-to-coherent transition associated with the switching of the two-particle transfer.
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We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for single hole in t-J model coupled to optical phonons. The systematic-error free diagrammatic Monte Carlo is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonons variables, while magnetic variables are subjected to non-crossing approximation. We obtain that at electron-phonon coupling constants relevant for high Tc cuprates the polaron undergoes self-trapping crossover to strong coupling limit and theoretical ARPES demonstrate features observed in experiment: a broad peak in the bottom of the spectra has momentum dependence which coincides with that of hole in pure t-J model.
We present a systematic study of the phase diagram of the $t{-}t^prime{-}J$ model by using the Greens function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetic and d-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of $t^prime=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism, that survives up to $delta_c sim 0.10$ for $J/t=0.2$ and $delta_c sim 0.13$ for $J/t=0.4$. The presence of a finite $t^prime/t<0$ induces a strong suppression of both magnetic (with $delta_c lesssim 0.03$, for $J/t=0.2$ and $t^prime/t=-0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $delta sim 0.25$, where strong size effects are present.
Determination of the parameter regime in which two holes in the t-J model form a bound state represents a long standing open problem in the field of strongly correlated systems. By applying and systematically improving the exact diagonalization method defined over a limited functional space (EDLFS), we show that the average distance between two holes scales as $langle d rangle sim 2 (J/t)^{-1/4}$ for J/t < 0.15, therefore providing strong evidence that two holes in the t-J model form the bound state for any nonzero J/t. However, the symmetry of such bound pair in the ground state is p-wave. This state is consistent with phase separation at finite hole filling, as observed in a recent study [Maska et al, Phys. Rev. B 85, 245113 (2012)].
In the $t-J$ model, the electron fractionalization is unique due to the non-perturbative phase string effect. We formulated a lattice field theory taking this effect into full account. Basing on this field theory, we introduced a pair of Wilson loops which constitute a complete set of order parameters determining the phase diagram in the underdoped regime. We also established a general composition rule for electric transport expressing the electric conductivity in terms of the spinon and the holon conductivities. The general theory is applied to studies of the quantum phase diagram. We found that the antiferromagnetic and the superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and {it vice versa} in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined and the system is electrically insulating.
The ground state of a hole-doped t-t-J ladder with four legs favors a striped charge distribution. Spin excitation from the striped ground state is known to exhibit incommensurate spin excitation near q=(pi,pi) along the leg direction (qx direction). However, an outward dispersion from the incommensurate position toward q=(0,pi) is strong in intensity, inconsistent with inelastic neutron scattering (INS) experiment in hole-doped cuprates. Motivated by this inconsistency, we use the t-t-J model with m x n=96 lattice sites by changing lattice geometry from four-leg (24x4) to rectangle (12x8) shape and investigate the dynamical spin structure factor by using the dynamical density matrix renormalization group. We find that the outward dispersion has weak spectral weights in the 12x8 lattice, accompanied with the decrease of excitation energy close to q=(pi,pi), being consistent with the INS data. In the 12x8 lattice, weakening of incommensurate spin correlation is realized even in the presence of the striped charge distribution. For further investigation of geometry related spin dynamics, we focus on direction dependent spin excitation reported by recent resonant inelastic x-ray scattering (RIXS) for cuprate superconductors and obtain a consistent result with RIXS by examining an 8x8 t-t-J square lattice.
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