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In previous reports (arXiv:0901.2487, arXiv:1007.0745), we introduced a new fermionic variational wavefunction, suitable for interacting multi-species systems and sustaining superfluidity. This disentangled wavefunction contains a new quantum index. Here we introduce a general spin triplet version of this wavefunction.
We propose a new method of solving a class of mean-field (MF) models, which is based on the Maximum Entropy (MaxEnt) principle with additional constraints included. Next, we show equivalence of our method when applied to the Gutzwiller approximation (GA), with the mean-field slave-boson (SB) formalism (on the example of the single-band Hubbard model). This equivalence provides thus an alternative justification of the results obtained within the SB approach which, however, contains ad hoc assumptions to position it in agreement with GA. Our approach implies that all predictions of the MF SB method can be obtained in a simpler, transparent, and controllable manner within GA when supplemented with the statistical-consistency conditions. We call the method as the Statistically-consistent Gutzwiller Approximation (SGA). Explicitly, the present formulation does not require introducing the condensed amplitudes of auxiliary Bose fields, which do not have a direct physical meaning and do not appear in the present formulation. Although the results of SGA are in the present case equivalent to SB, one can improve them further by utilizing more advanced schemes of calculating averages beyond the standard GA. To illustrate our approach, as well as to outline its advantages over alternative treatments of GA, we select the case of almost localized Fermi liquid (ALFL) in two dimensions and analyze it in detail within the tight-binding approximation. We also comment on significance of our method for describing correlated fermions. Namely, the reasoning used here can be applied to the corresponding MF treatment of the multiband Hubbard, the periodic Anderson, the $t-J$, and the $t-J-U$ models. In this manner our method may be applied for strongly correlated electron systems, optical lattices, and other related situations.
The spin-1/2 Heisenberg model on an anisotropic triangular lattice is considered in the mean-field RVB approximation. The analytical estimates for the critical temperatures of the longitudinal s-RVB state (the upper one) and the 2D s-RVB state (the lower one) are obtained which fairly agree with the results of the previous numerical studies on this system. Analytical formulae for the magnetic susceptibility and the magnetic contribution to the specific heat capacity in the longitudinal s-RVB state are obtained which fairly reproduce the results of the numerical experiment concerning these physical quantities.
The interplay between magnetism and superconductivity has been a central issue in unconventional superconductors. While the dynamic magnetism could be the source of electron pairing, the static magnetism is generally believed to compete with superconductivity. In this sense, the observation of Q phase, the coupled spin-density wave order and superconductivity, in the heavy-fermion superconductor CeCoIn5 is very puzzling. Whether this Q phase origins from the novel Fulde-Ferrel-Larkin-Ovchinnikov state is under hot debate. Here we report the resistivity and thermal conductivity study of a newly discovered heavy-fermion superconductor Ce2PdIn8 down to 50 mK. We find an unusual field-induced quantum critical point at the upper critical field Hc2 and unconventional nodal superconductivity in Ce2PdIn8. The jump of thermal conductivity k(H)/T near Hc2 suggests a first-order-like phase transition at low temperatures. These results mimic the features of the Q phase in CeCoIn5, implying that Ce2PdIn8 is another promising compound to investigate the exotic Q phase and FFLO state. The comparison between CeCoIn5 and Ce2PdIn8 may help to clarify the origin of the Q phase.
We review exact approaches and recent results related to the relaxation dynamics and description after relaxation of various one-dimensional lattice systems of hard-core bosons after a sudden quench. We first analyze the integrable case, where the combination of analytical insights and computational techniques enable one to study large system sizes. Thermalization does not occur in this regime. However, after relaxation, observables can be described by a generalization of the Gibbs ensemble. We then utilize full exact diagonalization to study what happens as integrability is broken. We show that thermalization does occur in finite nonintegrable systems provided they are sufficiently far away from the integrable point. We argue that the onset of thermalization can be understood in terms of the eigenstate thermalization hypothesis.
Multi-Species entanglement, defined for a many-particle system as the entanglement between different species of particles, is shown to exist in the thermodynamic limit of the system size going to infinity. This macroscopic entanglement, as it can exhibit singular behavior, is capable of tracking quantum phase transitions. The entanglement between up and down spins has been analytically calculated for the one-dimensional Ising model in a transverse magnetic field. As the coupling strength is varied, the first derivative of the entanglement shows a jump discontinuity and the second derivative diverges near the quantum critical point.
The article is withdrawn and its revised version will be submitted later.
A topological insulator is characterized by spin-momentum locking on its boundary. The spin momentum locking on the surface of a three dimensional topological insulator leads to the existence of a non-trivial Berry's phase which leads to exotic transport phenomena on topological surfaces. Using spin-sensitive probes (Mott polarimetry), we observe the spin-momentum coupling and uncover the chiral nature of surface electrons in TlBiSe2. We demonstrate that the surface electrons in TlBiSe2 collectively carry a quantum Berry's phase of $π$ and a definite chirality ($η$ = -1, left-handed) associated with its spin-texture or vortex-structure on the Fermi surface on both the top and the bottom surfaces. Our experimental results for the first time not only prove the existence of Z2 topological-order in the bulk but also reveal the existence of helical quasiparticle modes on the topological surface. Spin-texture calculations would be reported elsewhere.
We analyze solutions to a superconducting gap equation based on the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping. The Cooper pair potential can be calculated exactly and expressed in terms of elliptic functions. The Fermi surfaces at finite temperature and chemical potential are calculated based on the exact two-body S-matrix of the Hubbard model using the formalism we recently developed, which allows variation of hole doping. The resulting solutions to the gap equation are strongly anisotropic, namely largest in the anti-nodal direction, and zero in the nodal directions of the Brillouin zone. For U/t = 13 and t' /t =-0.3, appropriate to BSCO, and a physically natural choice for the cut-off, our self-contained analytic calculations yield the gap in the anti-nodal direction Delta/t = 0.06 and a maximum Tc/t = 0.04 at hole doping h=0.15. For phenomenological fits to the Fermi surfaces for cuprates, we obtain the comparable value Tc/t = 0.03 at optimal doping, both in good agreement with experiments. The superconducting gap is non-zero for all hole-doping h < 0.35, and increases all the way down to zero doping, suggesting that it evolves into the pseudogap.
The importance of taking into account inter-site $f-f$ hybridization in electron structure calculations for Ce metal and cerium heavy fermion compounds was studied. We demonstrate that for heavy-fermion systems such as cerium compound CeCu$_2$Si$_2$ $f-f$ hybridization can be neglected and Anderson model application is well justified. On another hand for cerium metal $f-f$ hybridization is strong enough to provide the contribution to hybridization function comparable to hybridization between $4f$ and itinerant electrons. We argue that in the case of Ce only the most general Hamiltonian combining Hubbard and Anderson models should be used.
We consider the one-orbital $N$-site repulsive Hubbard model on two kagome-like chains, both of which yield a completely dispersionless (flat) one-electron band. Using exact many-electron ground states in the subspaces with $n\le n_{\max}$ ($n_{\max}\propto N$) electrons, we calculate the square of the total spin in the ground state to discuss magnetic properties of the models. We have found that although for $n<n_{\max}$ the ground states contain fully polarized states, there is no finite region of electron densities $n/{\cal{N}} <1$ (${\cal{N}}=N/3$ or ${\cal{N}}=N/5$) where ground-state ferromagnetism survives for ${\cal{N}}\to\infty$.
A recent letter [H. Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)] reports the first measurements of a pinned mode in a Wigner solid at the (electronic) nu = 1/3 fractional quantum Hall effect (FQHE) filling. The authors suggest that an interpretation of their findings may be found within the interacting composite fermion (ICF) theory. However, to date there is no record reporting crystalline correlations for nu ~ 1/3 obtained from ICF theory, or related theories. We argue that an appropriate interpretation of these findings follows naturally from the rotating-Wigner-molecule approach, which (with inclusion of the rovibrational spectrum of the molecule) encompasses both the crystalline and liquid aspects in the FQHE regime (in particular for nu=1/3, as well as in its neighborhood created by deviations of nu from 1/3, as revealed experimentally).
We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.} [Phys. Rev. Lett. \textbf{85}, 4940 (2000)], which consists of defining a soft ultraviolet regulator in the space of Matsubara frequencies for the renormalized Green's function. Then we proceed to derive analytically and solve numerically integro-differential flow equations for the effective couplings and the quasiparticle weight of the present model, which fully treat the interplay of particle-particle and particle-hole parquet diagrams and the effect of the two-loop self-energy feedback into them. We show that our results correctly reproduce accurate numerical renormalization group data for weak to slightly moderate interactions. These results are in excellent agreement with other functional Wilsonian RG works available in the literature. Since the field-theoretical RG method turns out to be easier to implement at higher loops than the Wilsonian approach, higher-order calculations within the present approach could improve further the results for this model at stronger couplings. We argue that the present RG scheme could thus offer a possible alternative to other functional RG methods to describe electronic correlations within this model.
We have composed the ideas of quantum renormalization group and quantum information by exploring the low energy states dynamic of entanglement resources of a system close to its quantum critical point. We demonstrate the low energy states dynamical quantities of the one dimensional magnetic systems could show the quantum phase transition point and shows the scaling behavior in the vicinity of the transition point. To present our idea, we study the evolution of two spins entanglement in the one-dimensional Ising model in the transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We investigate evolvement of the generation of entanglement with increasing the magnetic field. We have obtained that the derivative of the time at which the entanglement reaches its maximums with respect to the transverse field, diverges at the critical point and its scaling behaviors versus the size of the system are as same as the static ground state entanglement of the the system.
The lecture note consists of four parts. In the first part, we review a 2+1 dimensional lattice model which realizes emergent supersymmetry at a quantum critical point. The second part is devoted to a phenomenon called fractionalization where gauge boson and fractionalized particles emerge as low energy excitations as a result of strong interactions between gauge neutral particles. In the third part, we discuss about stability and low energy effective theory of a critical spin liquid state where stringy excitations emerge in a large N limit. In the last part, we discuss about an attempt to come up with a prescription to derive holographic theory for general quantum field theory.
Barrier planes described by the Ionic Hubbard model and sandwiched between metallic planes on both sides are studied using unrestricted Hartree Fock. For zero onsite correlation, the presence of the metallic interface generates an additional gap in the energy spectrum away from half filling, if the chemically modulated potential in the barrier planes exceed a critical value. There is reentrant behaviour and an insulator-metal-insulator transition as we tune onsite correlation for fixed site potential. The metal is thus able to penetrate the barrier planes due to proximity effect, in a system that is otherwise an insulator throughout.
A Metal-Disordered Mott insulator-Metal heterostructure is studied at half-fiiling using unrestricted Hartree Fock method. The corresponding clean system has been shown to be an insulator for any finite on site correlation. Interestingly we find that introduction of explicit disorder induces a metal-insulator transition at a critical value of disorder. The critical value corresponds to the point at which disorder nullifies the effect of onsite correlation. The wavefunctions are found to delocalize by increasing disorder, rendering the system metallic.
We derive the Bethe-Salpeter (BS) equations for the collective-mode spectrum of superfluid Fermi gases of equal mixture of atomic Fermi gas of two hyperfine states loaded into a moving optical lattice. In a moving lattice the superfluid state is unstable due to spontaneous emission of the short-wavelength rotonlike excitations which appear in the spectrum of the collective modes. It is shown that the spectrum obtained by the BS equations is in an excellent agreement with the collective-mode dispersion calculated by the perturbation approach, while there are some differences between the results obtained by density response function method and by the BS approach. The difference increases with increasing the lattice velocity, which can be seen in the analytical approximations for the dispersion relation in the long-wavelength limit in a weak-coupling regime.