Slave Fermion Research Articles

Slave fermion interpretation of the pseudogap in doped Mott insulators

Slave fermion interpretation of the pseudogap in doped Mott insulators

Dynamic charge Kondo effect and a slave fermion approach to the Mott transition

Mott transition plays a key role in strongly correlated physics but its nature is not yet fully understood. Motivated by recent development of Schwinger boson approach for the Kondo lattice, we propose in this work a novel slave fermion algorithm to study the Mott transition. Upon local approximation, our method yields a phase diagram with a zero-temperature continuous (Mott) metal-insulator transition at finite Coulomb interaction $U$ for the half-filled one-band Hubbard model on a square lattice, and the resistivity exhibits a critical scaling around the quantum Widom line. We argue that the Mott transition may be associated with a dynamic charge Kondo effect of local degenerate doublon and holon states, causing sharp resonances on the doublon/holon and electron spectra. The transition is pushed to $U=0$ once intersite antiferromagnetic correlations are included, in agreement with exact numerical calculations. Our approach captures some essential features of the Mott transition and offers an alternative angle to view this important problem. It can be extended to study other correlated electron models with more complicated local interactions.

Topological Phase Transitions in Strongly Correlated Systems: Application to Co3Sn2S2

The topological transition in the strongly correlated half-metallic ferromagnetic compound Co$_3$Sn$_2$S$_2$ from Weyl semimetal (including chiral massless fermions) to a non-magnetic state is treated. This transition goes with a change in topological invariant, and is accompanied by a non-topological transition from saturated ferromagnetic to paramagnetic state, the minority Fermi surface being transformed from ghost (hidden) to real. A corresponding description is given in terms of slave fermion representation for the effective narrow-band Hubbard model. The system Co$_3$Sn$_2$S$_2$ provides a bright example of coexistence of non-trivial topology and strong low-dimensional ferromagnetism. A comparison is performed with other compounds where frustrations result in formation of a correlated paramagnetic state.

Slave fermion formalism for the tetrahedral spin chain

We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.

The slave-fermion approach of spin fluctuations in ferromagnet metals

In this work we propose a method to treat the spin fluctuations in itinerant ferromagnets. It is able to do calculation with a convergent series. The slave fermion method is applied to separate the charge (denoted by fermions) and spin (denoted by bosons) degrees of freedom. The spin operators are then replaced by the Schwinger boson fields. This way, the interaction term in the model can be reduced to a very simple form and can be teated without difficulty. Finally the equations of motion are derived in order to obtain the forms of Green's functions of fermions and bosons. The result is applied to the calculation of resistivity as a function temperature.

High-energy anomalies in covalent high-Tc cuprates with large Hubbard Ud on copper

A large Ud theory is constructed for the metallic state of high-Tc cuprates. The Emery three-band model, extended with Ox–Oy hopping tpp, and with Ud→∞, is mapped on slave fermions. The Dyson time-dependent diagrammatic theory in terms of the Cu–O hopping tpd, starting from the nondegenerate unperturbed ground state, is translationally and asymptotically locally gauge invariant. The small parameter of the theory is the average hole occupation of Cu sites nd. The lowest order of the theory generates the single particle propagators of the hybridized pdp- and dpd-fermions with the exact covalent three band structure. The leading many-body effect is band narrowing, accompanied by Landau-like damping of the single particle propagation, due to incoherent local charge Cu–O fluctuations. The corresponding continuum is found below and above the Fermi level.

Pseudofermion ferromagnetism in the Kondo lattices: a mean-field approach

Ground state ferromagnetism of the Kondo lattices is investigated within slave fermion approach by Coleman and Andrei within a mean-field approximation in the effective hybridization model. Conditions for formation of both saturated (half-metallic) and non-saturated magnetic state are obtained for various lattices. A description in terms of universal functions which depend only on bare electron density of states (DOS) is presented. A crucial role of the energy dependence of the bare DOS (especially, of DOS peaks) for the small-moment ferromagnetism formation is demonstrated.

Mesoscopic fluctuations in the Fermi-liquid regime of the Kondo problem

We consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Mesoscopic fluctuations of both the quasiparticle energy levels and the corresponding wavefunctions are large in this case. These mesoscopic fluctuations make the traditional approach to Fermi-liquids impracticable, as it assumes the existence of a limited number of relevant parameters. We show here how this difficulty can be overcome and discuss the relationship between the resulting Fermi-liquid description “à la Nozières” and the mean field slave fermion approximation.

Long-wavelength spin-effective actions for the infinite U Hubbard model

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.

Quantum critical behavior in three-dimensional one-band Hubbard model at half-filling

A one-band Hubbard model with hopping parameter t and Coulomb repulsion U is considered at half-filling. By means of the Schwinger bosons and slave fermions representation of the electron operators and integrating out the spin–singlet Fermi fields an effective Heisenberg model with antiferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Accounting adequately for the magnon–magnon interaction the Néel temperature is calculated. When the ratio tU is small enough (tU≤0.09) the effective model describes a system of localized electrons. Increasing the ratio increases the density of doubly occupied states which in turn decreases the effective spin and Néel temperature. The phase diagram in the plane of temperature TNU and parameter tU is presented. The quantum critical point (TN=0) is reached at tU=0.9. The magnons in the paramagnetic phase are studied and the contribution of the magnons’ fluctuations to the heat capacity is calculated. At the Néel temperature the heat capacity has a peak which is suppressed when the system approaches a quantum critical point. It is important to stress that, at half-filling, the ground state, determined by fermions, is antiferromagnetic. The magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.

SU(2) slave fermion solution of the Kitaev honeycomb lattice model

We apply the SU(2) slave fermion formalism to the Kitaev honeycomb lattice model. We show that both the Toric Code phase (the A phase) and the gapless phase of this model (the B phase) can be identified with p-wave superconducting phases of the slave fermions, with nodal lines which, respectively, do not or do intersect the Fermi surface. The non-Abelian Ising anyon phase is a $p+ip$ superconducting phase which occurs when the B phase is subjected to a gap-opening magnetic field. We also discuss the transitions between these phases in this language.

Stability of Nagaoka phase, spin effective action and delocalized free holes

The Hubbard model in the limit of infinite $U$ is investigated within a projected slave fermion representation and following a previous work of the author and collaborators \cite{BFK}. The stability of the Nagaoka's phase with respect to a non vanishing concentration of holes ($\delta_h$) is analyzed by envisaging the existence of a spin effective action for itinerant magnetism of the Hubbard model. It is considered that,as the hole doping increases away from the half filled insulating limit, free holes are expected to be more delocalized. Depending on treatment for the hopping: a ferromagnetic or anti-ferromagnetic ordering might arise and the Nagaoka's phase might have some stability with respect to $\delta_h \neq 0$.

Low-energy properties of the ferromagnetic metallic phase in manganites: Slave-fermion approach to the quantum double-exchange model

We study the low-energy properties of the one-orbital quantum double-exchange model by using the slave fermion formulation. We construct a mean-field theory which gives a simple explanation for the magnetic and thermodynamic properties of the ferromagnetic metallic phase in manganites at low energy. The resulting electron spectral function and tunneling density of states show an incoherent asymmetric peak with weak temperature dependence, in addition to a quasiparticle peak. We also show that the gauge fluctuations in the ferromagnetic metallic phase are completely screened due to the Anderson-Higgs mechanism. Therefore, the mean-field state is robust against gauge fluctuations and exhibits spin-charge separation at low energy.

Slave-particle approach to the finite-temperature properties of ultracold Bose gases in optical lattices

By using slave particle (slave boson and slave fermion) technique on the Bose-Hubbard model, we study the finite temperature properties of ultracold Bose gases in optical lattices. The phase diagrams at finite temperature are depicted by including different types of slave particles and the effect of the finite types of slave particles is estimated. The superfluid density is evaluated using the Landau second order phase transition theory. The atom density, excitation spectrum and dispersion curve are also computed at various temperatures, and how the Mott-insulator evolves as the temperature increases is demonstrated. For most quantities to be calculated, we find that there are no qualitatively differences in using the slave boson or the slave fermion approaches. However, when studying the stability of the mean field state, we find that in contrast to the slave fermion approach, the slave boson mean field state is not stable. Although the slave boson mean field theory gives a qualitatively correct phase boundary, it corresponds to a local maximum of Landau free energy and can not describe the second order phase transition because the coefficient $a_4$ of the fourth order term is always negative in the free energy expansion.

Phase diagram of ultracold atoms in optical lattices: Comparative study of slave fermion and slave boson approaches to Bose-Hubbard model

We perform a comparative study of the finite temperature behavior of ultracold Bose atoms in optical lattices by the slave fermion and the slave boson approaches to the Bose-Hubbard model. The phase diagram of the system is presented. Although both approaches are equivalent without approximations, the mean field theory based on the slave fermion technique is quantitatively more appropriate. Conceptually, the slave fermion approach automatically excludes the double occupancy of two identical fermions on the same lattice site. By comparing to known results in limiting cases, we find the slave fermion approach better than the slave boson approach. For example, in the non-interacting limit, the critical temperature of the superfluid-normal liquid transition calculated by the slave fermion approach is closer to the well-known ideal Bose gas result. At zero-temperature limit of the critical interaction, strength from the slave fermion approach is also closer to that from the direct calculation using a zero-temperature mean field theory.

Spectral behavior of the electronic states of bilayer cuprate systems using a slave fermion approach

The spectral function for electrons in the normal state of a bilayer cuprate is calculated by employing a slave fermion approach. The electron correlations in the ${\mathrm{CuO}}_{2}$ layers in these cuprates are described by a t-J model, and the electronic coupling between the two ${\mathrm{CuO}}_{2}$ layers within the same unit cell is introduced via a hopping matrix element ${(t}_{\ensuremath{\perp}})$ and an exchange interaction ${(J}_{\ensuremath{\perp}}).$ The spectral function is calculated for different values of the hole concentration, temperature, and anisotropy at various values of the momentum ${(k}_{x}{,k}_{y}).$ It is found that the bilayer coupling ${(t}_{\ensuremath{\perp}})$ significantly affects the behavior of the spectral function. The spectral function around the momentum value (\ensuremath{\pi}, 0) for a coupled bilayer cuprate shows a peak much sharper than that for a system of uncoupled layers. Our calculation also suggests a splitting of electronic states of the bilayer cuprates along the (\ensuremath{\pi}, 0) direction for the heavily overdoped regime. Calculations of the imaginary part of the self-energy ${\ensuremath{\Sigma}}_{1}^{\ensuremath{''}}(k,\ensuremath{\omega})$ for a bilayer system have also been presented. It is found that ${\ensuremath{\Sigma}}_{1}^{\ensuremath{''}}(k,\ensuremath{\omega})$ depends strongly on the momentum and shows a ${\ensuremath{\omega}}^{\ensuremath{\alpha}}$ dependence on energy with $1.2<\ensuremath{\alpha}<1.5$ for values of the parameters t and J considered in the present calculations.

Atomic model of supersymmetric Hubbard operators

We apply the recently proposed susy Hubbard operators to an atomic model. In the limiting case of free spins, we derive exact results for the entropy which are compared with a mean field + gaussian corrections description. We show how these results can be extended to the case of charge fluctuations and calculate exact results for the partition function, free energy and heat capacity of an atomic model for some simple examples. Wavefunctions of possible states are listed. We compare the accuracy of large N expansions of the susy spin operators with those obtained using `Schwinger bosons' and `Abrikosov pseudo-fermions'. For the atomic model, we compare results of slave boson, slave fermion, and susy Hubbard operator approximations in the physically interesting but uncontrolled limiting case of N->2. For a mixed representation of spins we estimate the accuracy of large N expansions of the atomic model. In the single box limit, we find that the lowest energy saddle-point solution reduces to simply either slave bosons or slave fermions, while for higher boxes this is not the case. The highest energy saddle-point solution has the interesting feature that it admits a small region of a mixed representation, which bears a superficial resemblance to that seen experimentally close to an antiferromagnetic quantum critical point.

Slave fermions and the Anderson lattice—ferromagnetism for low electron count in one and two dimensions

We apply the slave-fermion representation of strongly correlated electrons to the spin-12 infinite-U Anderson lattice near quarter-filling. At the mean-field level we find that one conduction band hybridizes with the local states while the other remains uncoupled. When the Fermi level lies in the up-spin hybridization gap this phase is a partially saturated ferromagnet. In one and two dimensions we find that the spin-wave constant vanishes beyond a certain critical filling. We investigate the hybridization and f-level dependence of this critical electron count for the full range of valence and compare with numerical studies in one and two dimensions.

Supersymmetric approach to the infinite U Hubbard model

Using a supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single U(1)×SU(1|1) gauge theory, we discuss the physics of the infinite U Hubbard model. By looking for solutions to the Hamiltonian in which the spins can exist as both condensed ordered moments and as mobile charged carriers, we examine the possibility of a Nagaoka ferromagnetic phase at finite doping with a quantum critical point into the paramagnetic phase.

Supersymmetric Hubbard operators

We develop a supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single $U (1)\times SU (1| 1)$ gauge theory, a group with larger symmetry than the product of two $U (1)$ gauge groups. These representations of the Hubbard operator can be used to incorporate strong Hund's interactions in multi-electron atoms as a constraint. We show how this method can be combined with the $SP (N)$ group to yield a locally supersymmetric large-N formulation of the $t-J$ model.