The report discusses the slave-fermion representations of the t-J model and describes another representation, in which fermions and bosons are completely commuting and in which the properties of fermions are directly related to the properties of physical holes. For a study of the system in the new representation at half-filling, interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.
The report discusses the slave-fermion representations of the t-J model and describes another representation, in which fermions and bosons are completely commuting and in which the properties of fermions are directly related to the properties of physical holes. For a study of the system in the new representation at half-filling, interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.
We consider a single hole in the t-J model where the Heisenberg and the hole-hopping terms are expanded in powers of the spin-deviation operators. The lowest order corresponds to the linear spin-wave approximation and leads to an effective Hamiltonian studied earlier by means of self-consistent perturbation theory. In this work we shall include all terms generating up to two-loop diagrams in the perturbative expansion of the single-hole Green's function. The hard-core constraints are partially respected and the overall effect gives a renormalization factor of 1.158 to the hopping parameter t. The vertex that describes the process where a spin wave is absorbed and emitted at the same time by the hole is far more important than others. We find that the numerical solutions of Dyson's equation including all two-loop diagrams lower considerably the single-hole ground-state energies over the previous one-loop results and our results on the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in better agreement with those obtained by exact diagonalization in the physical regime (small J/t). Our method can provide numerical solutions to the hole Green's function on very large lattices. We find that with the inclusion of the two-loop diagrams the spectral function retains all its features found in the one-loop calculation and the bandwidth, the quasiparticle residues, and the ``string'' excitations feel very small corrections.
This report discusses the slave-fermion representations of the $t\ensuremath{-}J$ model and describes another representation in which fermions and bosons are completely commuting. For a study of the system in the new representation at half-filling, the interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.
We present a bond-operator theory (BOT) for analytical consideration of the
t-
J model and its extensions with longer-rage hopping terms. This technique is based on previously suggested representation of electron operators via localized spins 1/2 and spinless Fermi-operators of mobile holons which requires no constraint between them. We introduce a representation of operators of spins, holons, and electrons in (extended) unit cell containing several lattice sites via a zoo of Bose- and Fermi-operators acting in the Hilbert space of all quantum states of the whole unit cell. BOT provides a regular expansion of physical quantities in powers of
1/n using conventional diagrammatic technique, where
n≥1 is the maximum number of introduced quasiparticles (bosons and fermions) which can occupy a unit cell. The suggested representation reproduces commutation algebra of all operators at any
n>0 and allows to consider both magnetically ordered and disordered phases. Some elementary excitations described in the BOT by separate bosons or fermions appear in common approaches as bound states of conventional quasiparticles. In particular, there are two-hole bound states (Cooper pairs of two holes) which are described within the BOT by separate bosons. We discuss in detail properties of the
t-
J model on the square lattice with no more than two holes (polarons). Although the expansion parameter
1/n is not small in the physically meaningful case of
n=1, we obtain a good quantitative agreement with previous numerical findings at
n=1 even in the first order in
1/n after taking into account a few simple diagrams. Self-consistent calculations in the first order in
1/n bring our results to a very good quantitative agreement with previous numerical findings of the ground state energy, staggered magnetization, and spectra of magnons, polarons, and lowest-energy two-hole bound states.
The Holstein-Primakoff boson representation of quantum spins and associated large-
S expansion have been the standard framework for describing the spin wave excitations in magnetically order phases of quantum spin systems. However, we will show that the omission of projection operators and normal-ordering in this representation can produce incorrect magnon hamiltonians for finite
S. We will present the exact normal-ordered forms of the finite-
S projection operators and projected Holstein-Primakoff boson representations of spin and quadrupole operators, which can produce exact two-magnon interaction terms under ferromagnetic or fully polarized states. We will also discuss the difficulties of applying this projected representation to antiferromagnetic spin wave theory.