[Show abstract][Hide abstract] ABSTRACT: We present an efficient impurity solver for the dynamical mean-field theory
(DMFT). It is based on the separation of bath degrees of freedom into the low
energy and the high energy parts. The former is solved exactly using exact
diagonalization and the latter is treated approximately using Green's function
equation of motion decoupling approximation. The two parts are combined
coherently under the standard basis operator formalism. The impurity solver is
applied to the Anderson impurity model and, combined with DMFT, to the one-band
Hubbard model. Qualitative agreement is found with other well established
methods. Some promising features and possible improvements of the present
solver are discussed.
[Show abstract][Hide abstract] ABSTRACT: We propose a Monte Carlo algorithm for the free energy calculation based on configuration space sampling. An upward or downward temperature scan can be used to produce F(T). We implement this algorithm for the Ising model on a square lattice and triangular lattice. Comparison with the exact free energy shows an excellent agreement. We analyze the properties of this algorithm and compare it with the Wang-Landau algorithm, which samples in energy space. This method is applicable to general classical statistical models. The possibility of extending it to quantum systems is discussed.
Physical Review E 10/2014; 92(1). DOI:10.1103/PhysRevE.92.013310 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the spin-1/2 J1-J2 Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size L to infinity, we obtain accurate phase boundaries [Formula: see text] (between the Néel antiferromagnetic phase and non-magnetic phase), and [Formula: see text] (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at [Formula: see text] and the first-order one at [Formula: see text]. For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.
[Show abstract][Hide abstract] ABSTRACT: We study the critical behavior of the single-site entanglement entropy S at
the Mott metal-insulator transition in infinite-dimensional Hubbard model. For
this model, the entanglement between a single site and rest of the lattice can
be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the
numerical solution using exact diagonalization and the analytical one using
two-site DMFT gives S-Sc \propto \alpha \log_{2}[(1/2-Dc)/Dc](U-Uc), with Dc
the double occupancy at Uc and \alpha < 0 being different on two sides of the
transition.
Modern Physics Letters B 11/2012; 27(5). DOI:10.1142/S0217984913500346 · 0.75 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Based on the rapid experimental developments of circuit QED, we propose a feasible scheme to simulate a spin-boson model with the superconducting circuits, which can be used to detect quantum Kosterlitz-Thouless (KT) phase transition. We design the spin-boson model by using a superconducting phase qubit coupled with a semi-infinite transmission line, which is regarded as bosonic reservoir with a continuum spectrum. By tuning the bias current or the coupling capacitance, the quantum KT transition can be directly detected through tomography measurement on the states of the phase qubit. We also estimate the experimental parameters using numerical renormalization group method. Comment: 4 pages
[Show abstract][Hide abstract] ABSTRACT: The spin-boson model has nontrivial quantum phase transitions in the
sub-Ohmic regime. For the bath spectra exponent $0 \leqslant s<1/2$, the
bosonic numerical renormalization group (BNRG) study of the exponents $\beta$
and $\delta$ are hampered by the boson state truncation which leads to
artificial interacting exponents instead of the correct Gaussian ones. In this
paper, guided by a mean-field calculation, we study the order parameter
function $m(\tau=\alpha-\alpha_c, \epsilon, \Delta)$ using BNRG. Scaling
analysis with respect to the boson state truncation $N_{b}$, the logarithmic
discretization parameter $\Lambda$, and the tunneling strength $\Delta$ are
carried out. Truncation-induced multiple-power behaviors are observed close to
the critical point, with artificial values of $\beta$ and $\delta$. They cross
over to classical behaviors with exponents $\beta=1/2$ and $\delta=3$ on the
intermediate scales of $\tau$ and $\epsilon$, respectively. We also find
$\tau/\Delta^{1-s}$ and $\epsilon/\Delta$ scalings in the function $m(\tau,
\epsilon, \Delta)$. The role of boson state truncation as a scaling variable in
the BNRG result for $0 \leqslant s<1/2$ is identified and its interplay with
the logarithmic discretization revealed. Relevance to the validity of
quantum-to-classical mapping in other impurity models is discussed.
[Show abstract][Hide abstract] ABSTRACT: We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (CDMFT) combined with continuous time quantum Monte Carlo simulation (CTQMC). A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. We demonstrate that the non-local spatial correlations play a vital role in the Mott transition on the honeycomb lattice. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice. Comment: 4 pages, 6 figures
[Show abstract][Hide abstract] ABSTRACT: The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green’s function onto 2×2 clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ΣX associated with X=(π,0) is shown to develop a collective mode above EF, whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value δc, and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above EF and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that δc≈0.15…0.20 for various system parameters. For electron doping, the collective mode of ΣX(ω) and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below EF. The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.
[Show abstract][Hide abstract] ABSTRACT: The effect of doping in the two-dimensional Hubbard model is studied within finite temperature exact diagonalization combined with cluster dynamical mean field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto 2x2 clusters, a considerably more accurate description of the low frequency properties of the self-energy is achieved than in a pure site picture. The transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest neighbor hopping, and temperature. In particular, the self-energy component Sigma_X associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid behavior as the hole doping decreases below a critical value delta_c. The imaginary part of Sigma_X(omega) then develops a collective mode above E_F, which exhibits a distinct dispersion with doping. Accordingly, the real part of Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing particle-hole asymmetry as the system approaches the Mott transition. This behavior is consistent with the removal of spectral weight from electron states close to E_F and the opening of a pseudogap which increases with decreasing doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various system parameters. For electron doping, the collective mode of Sigma_X(omega) and the concomitant pseudogap are located below the Fermi energy which is consistent the removal of spectral weight from hole states just below E_F. The critical doping which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping. Comment: 18 pages, 21 figures
[Show abstract][Hide abstract] ABSTRACT: The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $\mu/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments. Comment: 11 pages, 8 figures
[Show abstract][Hide abstract] ABSTRACT: The complete strain tensor in the tilted-grown epilayer is studied based on the linear elastic theory. With the boundary constrain conditions, the tilt angle of an epilayer can be obtained from the minimization of the strain energy. In this way we can also describe the distortion of crystal cells in the epilayer. In this Letter, as an application of our theory, we focus on the growth of the MnAs epilayer on the GaAs(001) substrate. It is shown that the lattice mismatch strain between the MnAs epilayer and the GaAs substrate can be relaxed by two mechanisms. On the one hand, by forming the lattice coincidence construction at the interface, the type A growth can be realized. On the other hand, by tilting the epilayer by about 30° with respect to the substrate, the type B growth is favored. The competition between the two mechanisms is near an equilibrium for this specific system, and depending on the growth conditions, it may lead to either an A type growth or a B type growth. Our theoretical results agree well with the reported experimental observations.
Physics Letters A 07/2007; 367(4):373-378. DOI:10.1016/j.physleta.2007.03.013 · 1.68 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study a mesoscopic ring with an inline quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with omega(s) spectral density, can suppress tunneling through the dot, resulting in a quantum phase transition from an unpolarized to a polarized phase. We show that robust signatures of such a transition can be found in the response of the persistent current in the ring to the external flux as well as to the bias between the dot and the arm. Particular attention is paid to the experimentally relevant cases of Ohmic (s = 1) and sub-Ohmic (s = 1/2) noise.
[Show abstract][Hide abstract] ABSTRACT: We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
[Show abstract][Hide abstract] ABSTRACT: The variational cluster approximation (VCA) proposed by M. Potthoff et al. Phys. Rev. Lett. 91 206402 (2003) is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.
Physical Review B 04/2005; 72(11). DOI:10.1103/PhysRevB.72.115104 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate electron transfer processes in donor-acceptor systems with a coupling of the electronic degrees of freedom to a common bosonic bath. The model allows to study many-particle effects and the influence of the local Coulomb interaction U between electrons on donor and acceptor sites. Using the non-perturbative numerical renormalization group approach we find distinct differences between the electron transfer characteristics in the single- and two-particle subspaces. We calculate the critical electron-boson coupling alpha_c as a function of $U$ and show results for density-density correlation functions in the whole parameter space. The possibility of many-particle (bipolaronic) and Coulomb-assisted transfer is discussed.
[Show abstract][Hide abstract] ABSTRACT: The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that the naive mapping fails for the sub-Ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional, variantomega(s). Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.
[Show abstract][Hide abstract] ABSTRACT: We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and sub-Ohmic cases. We present various results for static as well as dynamic quantities and discuss details of the numerical implementation, e.g., the discretization of a bosonic bath with arbitrary continuous spectral density, the suitable choice of a finite basis in the bosonic Hilbert space, and questions of convergence w.r.t. truncation parameters. The method is shown to provide high-accuracy data over the whole range of model parameters and temperatures, which are in agreement with exact results and other numerical data from the literature. Comment: 23 pages, 21 figures; three references and one figure added
[Show abstract][Hide abstract] ABSTRACT: We study the extended Hubbard model with both on-site (U) and nearest neighbor (V) Coulomb repulsion using the exact diagonalization method within the dynamical mean field theory. For a fixed U (U=2.0), the T-n phase-diagrams are obtained for V=1.4 and V=1.2, at which the ground states of n=1/2 system is charge-ordered and charge-disordered, respectively. In both cases, robust charge order is found at finite temperature and in an extended filling regime around n=1/2. The order parameter changes non-monotonously with temperature. For V=1.4, phase separation between charge-ordered and charge-disordered phases is observed in the low temperature and n < 0.5 regime. It is described by an "S"-shaped structure of the n-/mu curve. For V=1.2, the ground state is charge-disordered, and a reentrant charge-ordering transition is observed for 0.42 < n < 0.68. Relevance of our results to experiments for doped manganites is discussed. Comment: 9 pages, 7 figures, submitted to Phys. Rev. B
Physical Review B 03/2004; 70(8). DOI:10.1103/PhysRevB.70.085118 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at s=1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.