Z. D. Wang

Publication List Details

Period

1998 - 2008

Number

99

Co-Authors

Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms (2008)

Zhu, Shi-Liang, Zhang, Dan-Wei, Wang, Z. D.

We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to dislocation in comparison with the...

Impurity states in antiferromagnetic Iron Arsenides (2008)

Han, Q., Wang, Z. D.

We explore theoretically impurity states in the antiferromagnetic spin-density wave state of the iron arsenide. Two types of impurity models are employed: one has only the intraband scattering while...

Imbalanced superfluid state in an annular disk (2008)

Ye, Fei, Chen, Yan, Wang, Z. D., Zhang, F. C.

The imbalanced superfluid state with an s-wave pairing of spin-1/2 fermions in an annular disk is numerically studied by solving the Bogoliubov-de-Gennes equation at zero temperature. Annular disks...

Evolution equation of entanglement for general bipartite systems (2008)

Li, Zong-Guo, Fei, S. M., Wang, Z. D., Liu, W. M.

We explore how entanglement of a general bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement for general...

Electronic structure and exotic exchange splitting in spin-density-wave states of BaFe$_2$As$_2$ (2008)

Yang, L. X., Zhang, Y., Ou, H. W., Zhao, J. F., Shen, D. W., Zhou, B., ...

The magnetic properties in the parent compounds are often intimately related to the microscopic mechanism of superconductivity. Here we report the first direct measurements on the electronic...

Origin of entanglement in a class of multi-qubit mixed states without multipartite tangles (2008)

Bai, Yan-Kui, Ye, Ming-Yong, Wang, Z. D.

Based on a purification scenario, we analyze the origin of entanglement in a class of multi-qubit mixed states that are entangled but do not have two-, and genuine three-, four-, ..., N-qubit...

Quantum computation in decoherence-free subspace with superconducting devices (2008)

Xue, Zheng-Yuan, Zhu, Shi-Liang, Wang, Z. D.

We propose a scheme to implement quantum computation in decoherence-free subspace with superconducting devices inside a cavity by unconventional geometric manipulation. Universal single-qubit gates...

Quantum state redistribution based on a generalized decoupling (2008)

Ye, Ming-Yong, Bai, Yan-Kui, Wang, Z. D.

We develop a simple protocol for a one-shot version of quantum state redistribution, which is the most general two-terminal source coding problem. The protocol is simplified from a combination of...

Spin Fluctuations, Interband Coupling, and Unconventional Pairing in Iron-based Superconductors (2008)

Yao, Zi-Jian, Li, Jian-Xin, Wang, Z. D.

Based on the fluctuation-exchange (FLEX) approach and an effective two-band model, we explore spin fluctuations and unconventional superconducting pairing in Fe-based layer superconductors. It is...

An additive and operational entanglement measure: conditional entanglement of mutual information (2008)

Yang, Dong, Horodecki, Michal, Wang, Z. D.

Based on the monogamy of entanglement, we develop the technique of quantum conditioning to build an {\it additive} entanglement measure: the conditional entanglement of mutual information. Its {\it...

Practically secure quantum bit commitment based on quantum seals (2008)

He, Guang Ping, Wang, Z. D.

The relationship between the quantum bit commitment (QBC) and quantum seal (QS) is studied. It is elaborated that QBC and QS are not equivalent, but QS protocols satisfying a stronger unconditional...

Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms (2008)

Shao, L. B., Zhu, Shi-Liang, Sheng, L., Xing, D. Y., Wang, Z. D.

We design an ingenious scheme to realize the Haldane's quantum Hall model without Landau level by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to...

A Generic Two-band Model for Unconventional Superconductivity and Spin-Density-Wave Order in Electron and Hole Doped Iron-Based Superconductors (2008)

Han, Q., Chen, Y., Wang, Z. D.

Based on experimental data on the newly synthesized iron-based superconductors and the relevant band structure calculations, we propose a minimal two-band BCS-type Hamiltonian with the interband...

Operator fidelity susceptibility: an indicator of quantum criticality (2008)

Wang, Xiaoguang, Sun, Zhe, Wang, Z. D.

We introduce the operator fidelity and propose to use its susceptibility for characterizing the sensitivity of quantum systems to perturbations. Two typical models are addressed: one is the...

Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity (2008)

Chen, Gang, Wang, Xiaoguang, Wang, Z. D.

A new extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A...

Quantum secret sharing based on Smolin states alone (2007)

He, Guang Ping, Wang, Z. D., Bai, Yan-Kui

It was indicated [Yu 2007 Phys. Rev. A 75 066301] that a previous proposed quantum secret sharing (QSS) protocol based on Smolin states [Augusiak 2006 Phys. Rev. A 73 012318] is insecure against an...

Exploring Exotic Superfluidity of Polarized Ultracold Fermions in Optical Lattices (2007)

Chen, Y., Wang, Z. D., Zhang, F. C., Ting, C. S.

We explore theoretically the novel superfluidity of harmonically-trapped polarized ultracold fermionic atoms in a two-dimensional (2D) optical lattice by solving the Bogoliubov-de Gennes equations....

Physical implementation of topologically decoherence-protected superconducting qubits (2007)

Xue, Zheng-Yuan, Wang, Z. D., Zhu, Shi-Liang

We propose a scenario to physically implement a kind of topologically decoherence-protected qubit using superconducting devices coupled to a micro-wave cavity mode with unconventional geometric...

Multipartite entanglement in four-qubit cluster-class states (2007)

Bai, Yan-Kui, Wang, Z. D.

Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite...

Detecting unambiguously non-Abelian geometric phases with trapped ions (2007)

Zhang, Xin-Ding, Wang, Z. D., Hu, Liang-Bin, Zhang, Zhi-Ming, Zhu, Shi-Liang

We propose for the first time an experimentally feasible scheme to disclose the noncommutative effects induced by a light-induced non-Abelian gauge structure with trapped ions. Under an appropriate...

Band structure renormalization and weak pseudogap behavior in Na_{0.33}CoO_2: Fluctuation exchange study based on a single band model (2007)

Yao, Zi-Jian, Li, Jian-Xin, Wang, Z. D.

Based on a single band Hubbard model and the fluctuation exchange approximation, the effective mass and the energy band renormalization in Na$_{0.33}$CoO$_2$ is elaborated. The renormalization is...

Spatial reflection and renormalization group flow of quantum many-body systems with matrix product state representation (2007)

Cen, Li-Xiang, Wang, Z. D.

The property of quantum many-body systems under spatial reflection and the relevant physics of renormalization group (RG) procedure are revealed. By virtue of the matrix product state (MPS)...

Tuning Kinetic Magnetism of Strongly Correlated Electrons via Staggered Flux (2007)

Wang, Yi-Fei, Gong, Chang-De, Wang, Z. D.

We explore the kinetic magnetism of the infinite-$U$ repulsive Hubbard models at low hole densities on various lattices with nearest-neighbor hopping integrals modulated by a staggered magnetic flux...

Phenomenological theory of spin excitations in La- and Y-based cuprates (2007)

Zhou, T., Wang, Z. D.

Motivated by recent inelastic neutron scattering (INS) experiments on La-based cuprates and based on the fermiology theories, we study the spin susceptibility for La-based (e.g.,...

Unconditionally secure single qubit quantum secret sharing (2007)

He, Guang Ping, Wang, Z. D.

Analyzing carefully an experimentally feasible non-entangled single qubit quantum secret sharing protocol and its modified version [Phys. Rev. Lett. 95, 230505 (2005); ibid. 98, 028902 (2007)], it is...

Simple unconventional geometric scenario of one-way quantum computation with superconducting qubits inside a cavity (2007)

Xue, Zheng-Yuan, Wang, Z. D.

We propose a simple unconventional geometric scenario to achieve a kind of nontrivial multi-qubit operations with superconducting charge qubits placed in a microwave cavity. The proposed quantum...

Multipartite quantum correlation and entanglement in four-qubit pure states (2007)

Bai, Yan-Kui, Yang, Dong, Wang, Z. D.

Based on the quantitative complementarity relations, we analyze thoroughly the properties of multipartite quantum correlations and entanglement in four-qubit pure states. We find that, unlike the...

Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath (2007)

Quan, H. T., Wang, Z. D., Sun, C. P.

We explore a dynamic signature of quantum phase transition (QPT) in an isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a central qubit coupled to it. We evaluate exactly...

Conditional Entanglement (2007)

Yang, Dong, Horodecki, Michal, Wang, Z. D.

Based on the ideas of {\it quantum extension} and {\it quantum conditioning}, we propose a generic approach to construct a new kind of entanglement measures called {\it conditional entanglement}. The...

Is the dispersion anomaly of the electron spectrum induced by the charge-density-wave in high-$T_c$ superconductors? (2006)

Zhou, T., Wang, Z. D.

We propose that the presence of a rotationally symmetric charge density wave (CDW) with the modulation of 4-lattice constant in high-$T_c$ superconductors is essentially responsible for an anomalous...

Doping dependance of the spin resonance peak in bilayer high-$T_c$ superconductors (2006)

Zhou, T., Wang, Z. D., Li, Jian-Xin

Motivated by a recent experiment on the bilayer Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_y$ superconductor and based on a bilayer $t-J$ model, we calculate the spin susceptibility at different doping...

Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators (2006)

Shao, L. B., Wang, Z. D., Xing, D. Y.

We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a...

Implementation of adiabatic Abelian geometric gates with superconducting phase qubits (2006)

Peng, Z. H., Chu, H. F., Wang, Z. D., Zheng, D. N.

We have developed an adiabatic Abelian geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase-qubit systems. The fidelity...

Theory of optical conductivity in detwinned YBa$_2$Cu$_3$O$_{y}$ (2006)

Zhou, T., Li, Jian-Xin, Wang, Z. D.

We study theoretically the chain and in-plane optical conductivities of detwinned YBa$_2$Cu$_3$O$_{y}$. We elaborate that the chain is superconducting for $y>6.67$ while insulating for $y

Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions (2006)

Zhang, Xin-Ding, Zhang, Q., Wang, Z. D.

We propose a feasible scheme to achieve holonomic quantum computation in a decoherence-free subspace (DFS) with trapped ions. By the application of appropriate bichromatic laser fields on the...

Spin-Orbital Entanglement and Phase Diagram of Spin-orbital Chain with $SU(2) \times SU(2)$ Symmetry (2006)

Chen, Yan, Wang, Z. D., Li, Y. Q., Zhang, F. C.

Spin-orbital entanglement in quantum spin-orbital systems is quantified by a reduced von Neumann entropy, and is calculated for the ground state of a coupled spin-orbital chain with $SU(2)\times...

Detecting a set of entanglement measures in an unknown tripartite quantum state by local operations and classical communication (2006)

Bai, Yan-Kui, Li, Shu-Shen, Zheng, Hou-Zhi, Wang, Z. D.

We propose a more general method for detecting a set of entanglement measures, i.e. negativities, in an \emph{arbitrary} tripartite quantum state by local operations and classical communication. To...

Quantum criticality in a generalized Dicke model (2006)

Li, Yong, Wang, Z. D., Sun, C. P.

We employ a generalized Dicke model to study theoretically the quantum criticality of an extended two-level atomic ensemble interacting with a single-mode quantized light field. Effective...

Thermal Entanglement in Ferrimagnetic Chains (2006)

Wang, Xiaoguang, Wang, Z. D.

A formula to evaluate the entanglement in an one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-1/2 and spin-s...

Scalable solid-state quantum computation in decoherence-free subspaces with trapped ions (2006)

Cen, Li-Xiang, Wang, Z. D., Wang, S. J.

We propose a decoherence-free subspaces (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent Coulomb interaction is exploited, and the universal set of...

Exploring Quantum Phase Transitions with a Novel Sublattice Entanglement Scenario (2005)

Chen, Y., Wang, Z. D., Zhang, F. C.

We introduce a new measure called reduced entropy of sublattice to quantify entanglement in spin, electron and boson systems. By analyzing this quantity, we reveal an intriguing connection between...

On the conservation of spin currents in spin-orbit coupled systems (2005)

Shen, R., Chen, Yan, Wang, Z. D.

Applying the Gordon-decomposition-like technique, the convective spin current (CSC) is extracted from the total angular-momentum current. The CSC describes the transport properties of the electron...

Experimental implementation of high-fidelity unconventional geometric quantum gates using NMR interferometer (2005)

Du, J., Zou, P., Wang, Z. D.

Following a key idea of unconventional geometric quantum computation developed earlier [Phys. Rev. Lett. 91, 197902 (2003)], here we propose a more general scheme in such an intriguing way:...

Geometric nature in adiabatic evolution of dark eigenstates (2005)

Zhu, Shi-Liang, Wang, Z. D.

In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting scheme was proposed to implement a type of conditional quantum phase gates with built-in fault-tolerant feature via...

Unrestricted renormalized mean field theory of strongly correlated electron systems (2005)

Wang, Qiang-Hua, Wang, Z. D., Chen, Yan, Zhang, Fu-Chun

We generalized systematically the renormalized mean field theory in the case of uniform states to the unrestricted case of general inhomogeneous states with competing spin-, charge- and...

Quantum storage and information transfer with superconducting qubits (2005)

Wang, Y. D., Wang, Z. D., Sun, C. P.

We design theoretically a new device to realize the general quantum storage based on dcSQUID charge qubits. The distinct advantages of our scheme are analyzed in comparison with existing storage...

The relationship between two flavors of oblivious transfer at the quantum level (2005)

He, Guang-Ping, Wang, Z. D.

Though all-or-nothing oblivious transfer and one-out-of-two oblivious transfer are equivalent in classical cryptography, we here show that due to the nature of quantum cryptography, a protocol built...

Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators (2005)

Teo, Jeffrey C. Y., Wang, Z. D.

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy...

Nonadiabatic Geometric Quantum Computation Using A Single-loop Scenario (2005)

Zhang, Xin-Ding, Zhu, Shi-Liang, Hu, L., Wang, Z. D.

A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multi-loop approach is used to remove the dynamical phase accumulated in the...

Theoretical understanding of the quasiparticle dispersion in bilayer high-$T_{c}$ superconductors (2005)

Li, Jian-Xin, Zhou, T., Wang, Z. D.

The renormalization of quasiparticle (QP) dispersion in bilayer high-$T_{c}$ cuprates is investigated theoretically by examining respectively the interactions of the QP with spin fluctuations (SF)...

Two dimensional scaling of resistance in flux flow region in $Tl_2Ba_2CaCu_2O_8$ thin films (2004)

Lu, X. F., Wang, Z., Gao, H., Shan, L., Zhang, Y. Z., Lu, R. T., ...

The resistance of $Tl_2Ba_2CaCu_2O_8$ thin films has been measured when the angle between the applied fields and $ab$-plane of the film is changed continuously at various temperatures. Under various...

Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems (2004)

Chen, Yan, Zanardi, Paolo, Wang, Z. D., Zhang, F. C.

Entanglement of the ground states in $XXZ$ and dimerized Heisenberg spin chains as well as in a two-leg spin ladder is analyzed by using the spin-spin concurrence and the entanglement entropy between...

Holonomic Quantum Computation Using Rf-SQUIDs Coupled Through A Microwave Cavity (2004)

Zhang, P., Wang, Z. D., Sun, J. D., Sun, C. P.

We propose a new scheme to realize holonomic quantum computation with rf-SQUID qubits in a microwave cavity. In this scheme associated with the non-Abelian holonomies, the single-qubit gates and a...

Clustering through post inhibitory rebound in synaptically coupled neurons (2004)

Chik, D T W, Coombes, S, Wang, Z D

Post inhibitory rebound is a nonlinear phenomenon present in a variety of nerve cells. Following a period of hyper-polarization this effect allows a neuron to fire a spike or packet of spikes before...

Clustering through post inhibitory rebound in synaptically coupled neurons (2004)

Chik, D T W, Coombes, Stephen, Wang, Z D

Post inhibitory rebound is a nonlinear phenomenon present in a variety of nerve cells. Following a period of hyper-polarization this effect allows a neuron to fire a spike or packet of spikes before...

Geometric quantum computation and multi-qubit entanglement with superconducting charge qubits inside a cavity (2004)

Zhu, Shi-Liang, Wang, Z. D., Zanardi, Paolo

We analyze a new scheme for quantum information processing, with superconducting charge qubits coupled through a cavity mode, in which quantum manipulations are insensitive to the state of the...

Oblivious transfer using quantum entanglement (2003)

He, Guang Ping, Wang, Z. D.

Based on quantum entanglement, an all-or-nothing oblivious transfer protocol is proposed and is proven to be secure. The distinct merit of the present protocol lies in that it is not based on quantum...

The role of the cooperative Jahn-Teller effect in the charge ordered La1-xCaxMnO3 (0.5 (2003)

Zheng, R. K., Li, G., Tang, A. N., Yang, Y., Wang, W., Li, X. G., ...

Based on the magnetoresistance, magnetization, ultrasound, and crystallographic data, we studied the role of the cooperative Jahn-Teller effect in the charge ordered (CO) state for La1-xCaxMnO3. We...

Spin resonance peak in Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O superconductors: A probe of the pairing symmetry (2003)

Li, Jian-Xin, Wang, Z. D.

Motivated by the recent discovery of superconductivity in layered Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O compound, we investigate theoretically the spin dynamics in the superconducting state with three...

Nuclear Spin Relaxation Rate of Disordered $p_x+ip_y$-wave Superconductors (2003)

Han, Q., Wang, Z. D.

Based on an effective Hamiltonian with the binary alloy disorder model defined in the triangular lattice, the impurity scattering effects on the density of states and especially on the spin-lattice...

Unconventional geometric quantum computation (2003)

Wang, Z. D.

We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the...

Vortex State in Na_xCoO_2.yH_2O: p_x\pm ip_y-wave versus d_{x^2-y^2}\pm id_{xy}-wave Pairing (2003)

Han, Qiang, Wang, Z. D., Xia, Tianlong

Based on an effective Hamiltonian specified in the triangular lattice with possible $p_x\pm ip_y$- or $d_{x^2-y^2}\pm id_{xy}$-wave pairing, which has close relevance to the newly discovered...

Impurity and interface bound states in $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ superconductors (2003)

Wang, Qiang-Hua, Wang, Z. D.

Motivated by recent discoveries of novel superconductors such as Na$_x$CoO$_2\cdot y$H$_2$O and Sr$_2$RuO$_4$, we analysize features of quasi-particle scattering due to impurities and interfaces for...

Quantum information processing using Josephson junctions coupled through cavities (2003)

Zhu, Shi-Liang, Wang, Z. D., Yang, Kaiyu

Josephson junctions have been shown to be a promising solid-state system for implementation of quantum computation. The significant two-qubit gates are generally realized by the capacitive coupling...

Universal quantum gates based on both geometric and dynamic phases in quantum dots (2003)

Yang, Kaiyu, Zhu, Shi-Liang, Wang, Z. D.

A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A...

Testing Bell's inequality and measuring the entanglement using superconducting nanocircuits (2003)

He, Guang-Ping, Zhu, Shi-Liang, Wang, Z. D., Li, Hua-Zhong

An experimental scheme is proposed to test Bell's inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated in a sufficient long...

Temperature dependence of Vortex Charges in High Temperature Superconductors (2003)

Chen, Yan, Wang, Z. D., Ting, C. S.

Using a model Hamiltonian with d-wave superconductivity and competing antiferromagnetic (AF) interactions, the temperature (T) dependence of the vortex charge in high T_c superconductors is...

Jahn-Teller effect and stability of the charge-ordered state in La1-xCaxMnO3 (0.5 (2002)

Li, X. G., Zheng, R. K., Li, G., Zhou, H. D., Huang, R. X., Xie, J. Q., ...

The longitudinal ultrasonic sound velocity and attenuation, the resistivity, and lattice parameters were studied as a function of temperature from 30 K to 300 K in La1-xCaxMnO3 (0.5

Geometric phase shift in quantum computation using superconducting nanocircuits: nonadiabatic effects (2002)

Zhu, Shi-Liang, Wang, Z. D.

The nonadiabatic geometric quantum computation may be achieved using coupled low-capacitance Josephson juctions. We show that the nonadiabtic effects as well as the adiabatic condition are very...

Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems (2002)

Zhu, Shi-Liang, Wang, Z. D.

We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase...

Conductance of a quantum point contact in the presence of spin-orbit interaction (2002)

Zhu, Shi-Liang, Wang, Z. D., Hu, Lian

A recursive Green's function technique is developed to calculate the spin-dependent conductance in mesoscopic structures. Using this technique, we study the spin-dependent electronic transport of...

Charge pumping in a quantum wire driven by a series of local time-periodic potentials (2002)

Zhu, Shi-Liang, Wang, Z. D.

We develop a method to calculate electronic transport properties through a mesoscopic scattering region in the presence of a series of time-periodic potentials. Using the method, the quantum charge...

Conductance of a Quantum Point Contact in the presence of a Scanning Probe Microscope Tip (2002)

He, Guang-Ping, Zhu, Shi-Liang, Wang, Z. D.

Using the recursive Green's function technique, we study the coherent electron conductance of a quantum point contact in the presence of a scanning probe microscope tip. Images of the coherent fringe...

Implementation of universal quantum gates based on nonadiabatic geometric phases (2002)

Zhu, Shi-Liang, Wang, Z. D.

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal...

Vortex Charges in High Temperature Superconductors (2002)

Chen, Yan, Wang, Z. D., Zhu, Jian-Xin, Ting, C. S.

Based on an effective model Hamiltonian with competing antiferromagnetic (AF) and d-wave superconductivity (DSC) interactions, the vortex charge in high T_c superconductors is investigated by solving...

Impurity state in the vortex core of d-wave superconductors: Anderson impurity model versus unitary impurity model (2002)

Han, Q., Wang, Z. D.

Using an extended Anderson/Kondo impurity model to describe the magnetic moments around an impurity doped in high-$T_{\text{c}}$ d-wave cuprates and in the framework of the slave-boson meanfield...