Effective Low-energy Hamiltonian Research Articles

Berry phases and pairing symmetry in Holstein-Hubbard polaron systems

We study the tunneling dynamics of dopant-induced hole polarons which are self-localized by electron-phonon coupling in a two-dimensional antiferro- magnet. Our treatment is based on a path integral formulation of the adia- batic approximation, combined with many-body tight-binding, instanton, con- strained lattice dynamics, and many-body exact diagonalization techniques. Our results are mainly based on the Holstein-$tJ$ and, for comparison, on the Holstein-Hubbard model. We also study effects of 2nd neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian which takes the form of a fermion tight-binding model with occupancy dependent, predominant- ly 2nd and 3rd neighbor tunneling matrix elements, excluded double occupan- cy, and an effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the 1st neighbor charge interaction and by Berry phase factors which determine the signs of effective polaron tunneling ma- trix elements. In the two-polaron case, these phase factors lead to polaron pair wave functions of either $d_{x^2-y^2}$-wave symmetry or p-wave symme- try with zero and nonzero total pair momentum, respectively. Implications for the doping dependent isotope effect, pseudo-gap and Tc of a superconduc- ting polaron pair condensate are discussed/compared to observed in cuprates.

Magnetization properties of some quantum spin ladders

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second order terms give corrections to the XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.

Charmless decays of the B-meson in perturbative QCD

Using the perturbative QCD method and Chau's six-quark-graph scheme, we report a theoretical calculation of exclusive nonleptonic decays of the B meson into two light pseodoscalar mesons in the context of the low-energy effective Hamiltonian. The contributions from both tree-level and one-loop diagrams are taken into account. Under the approximation of neglecting light quark and light meson masses, we find that (i) within perturbative QCD there is no singularity which exists in the computation of spacelike penguin diagrams when the BSW model is used; (ii) the contributions from spacelike-type ( W-annihilation, W-exchange, spacelike penguin and penguin-annihilation) graphs are strongly suppressed relative to those from timelike-type (external W-emission, internal W-emission and timelike penguin) ones; (iii) our results are well below the experimental upper limits but lower than the BSW ones.

Low energy effective Hamiltonian for the XXZ spin chain

Coupling constants for the most relevant terms in the low energy effective Hamiltonian of the XXZ spin chain are derived. Using this result we study the low energy (low temperature, weak magnetic field) thermodynamics, finite size effects and subleading long distance asymptotics of correlation functions.

Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment

We consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with a surrounding spin environment, such as nuclear spins. Our aim is to give a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then study the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a macroscopic spin, using exact diagonalization techniques. We find that the low energy central spin effective Hamiltonian gives very accurate results (with increasing accuracy for large S), provided the typical coupling energies between the giant spin and the microscopic spins are not too large, and provided temperature and external field are sufficiently low. The essential limitation to the applicability of the low-energy effective Hamiltonian is just the semiclassical WKB approximation itself, which inevitably fails for very small S. Our results thus justify previous use of this effective Hamiltonian in calculations of the effects of nuclear spins on the dynamics of nanomagnetic systems.

Plaquette basis for the study of Heisenberg ladders

We employ a plaquette basis-generated by coupling the four spins in a $2\times2$ lattice to a well-defined total angular momentum-for the study of Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the Hamiltonian in this basis are evaluated using standard techniques in angular-momentum (Racah) algebra. We show by exact diagonalization of small ($2\times4$ and $2\times6$) systems that in excess of 90% of the ground-state probability is contained in a very small number of basis states. These few basis states can be used to define a severely truncated basis which we use to approximate low-lying exact eigenstates. We show how, in this low-energy basis, the isotropic spin-1/2 Heisenberg ladder can be mapped onto an anisotropic spin-1 ladder for which the coupling along the rungs is much stronger than the coupling between the rungs. The mapping thereby generates two distinct energy scales which greatly facilitates understanding the dynamics of the original spin-1/2 ladder. Moreover, we use these insights to define an effective low-energy Hamiltonian in accordance to the newly developed COntractor REnormalization group (CORE) method. We show how a simple range-2 CORE approximation to the effective Hamiltonian to be used with our truncated basis reproduces the low-energy spectrum of the exact $2\times6$ theory at the $\alt 1%$ level.

CP Violation and the Role of Electroweak Penguins in Nonleptonic B Decays

The phenomenon of CP violation in the B system and strategies for extracting CKM phases are reviewed. We focus both on general aspects and on some recent developments including CP-violating asymmetries in Bd decays, the Bs system in light of a possible width difference ΔΓs, charged B decays, and SU(3) relations among certain transition amplitudes. In order to describe the relevant nonleptonic B decays, low energy effective Hamiltonians calculated beyond the leading logarithmic approximation are used. Special emphasis is given to the role of electroweak penguin operators in such transitions. These effects are analyzed both within a general framework and more specifically in view of the theoretical cleanliness of methods to determine CKM phases. Strategies for obtaining insights into the world of electroweak penguins are discussed.

Monte Carlo Studies for Strong Correlations in Hubbard-Type Models

ABSTRACTThe tight-binding model with repulsive Hubbard interactions represents an ideal prototype for the study of strong correlations. While exact numerical methods have been used with some success, they are typically limited by the size of the clusters that can be investigated or by the temperatures that can be reached. Variational methods, on the other hand, often require considerable advance knowledge of ground-state properties. The method presented here alleviates this problem by augmenting the variational approach with a scheme similar to Lanczos iterations thus bridging the gap between exact diagonalization and variational approaches. For the t-J model, the low-energy effective Hamiltonian of the Hubbard model, material properties like broken translational invariance or superconducting correlations are then investigated and a region of stability of a superconducting phase is found.

Plasmon modes and correlation functions in quantum wires and Hall bars.

We present microscopic derivations of the one-dimensional low-energy boson effective Hamiltonians of quantum wire and quantum Hall bar systems. The quantum Hall system is distinguished by its spatial separation of oppositely directed electrons. We discuss qualitative differences in the plasmon collective-mode dispersions and the ground-state correlation functions of the two systems that are consequences of this difference. The slowly decaying quasisolid correlations expected in a quantum wire are strongly suppressed in quantum Hall bar systems. \textcopyright{} 1996 The American Physical Society.

Composite quasiparticle formation and the low-energy effective Hamiltonians for the one- and two-dimensional Hubbard model.

We investigate the effect of hole doping on the strong-coupling Hubbard model at half-filling in spatial dimensions $D\ge 1$. We start with an antiferromagnetic mean-field description of the insulating state, and show that doping creates solitons in the antiferromagnetic background. In one dimension, the soliton is topological, spinless, and decoupled from the background antiferromagnetic fluctuations at low energies. In two dimensions and above, the soliton is non-topological, has spin quantum number 1/2, and is strongly coupled to the antiferromagnetic fluctuations. We derive the effective action governing the quasiparticle motion, study the properties of a single carrier, and comment on a possible description at finite concentration.

Two-Channel Kondo Model as a Fixed Point of Local Electron-Phonon Coupling System

It is shown on the basis of the multiplicative renormalization-group method of two-loop order that the low-energy effective Hamiltonian of a strongly coupled local electron-phonon system is mapped to the two-channel Kondo model. A phonon is treated as an Einstein oscillator with restricted Hilbert space such that up to one-phonon process is taken into account. By eliminating the high energy process of conduction electrons, it is shown that a certain class of couplings between ion vibrations and conduction electrons is selectively grown up. As a result the system is reduced to the two-channel Kondo model. The crossover temperature $T_{\rm K}$ and the renormalized phonon frequency $\Delta^{x}$ are expressed in terms of the mass ratio $m/M$, $m$ and $M$ being the mass of electron and ion, and the electron-phonon coupling $g/D$, $D$ being half the bandwidth of conduction electrons. The anomalous behaviors associated with this renormalization can be mesuarable if the condition $T_{\rm K}>\Delta^{x}$ is fulfilled. It is demonstrated that such condition is satisfied when $g/D$ is sufficiently large but in a realistic range.

Umklapp processes for electrons and their renormalization-group flow.

We study umklapp couplings and their renormalization-group flow for electrons in a two-dimensional lattice. It is shown that the effective low-energy Hamiltonian involves not only forward scattering, but also considerable nonforward umklapp scattering, when the electrons fill a substantial fraction of the valence band. The behavior of these couplings under the renormalization group is studied in the loop expansion. It is shown that they remain marginal. We conclude with the possible consequences of this on properties of such electronic systems and their Fermi-liquid theory. \textcopyright{} 1996 The American Physical Society.

Tau polarization asymmetry in B-->Xs tau + tau -

Rare {ital B} decays provide an opportunity to probe for new physics beyond the standard model. In this paper, we propose to measure the {tau} polarization in the inclusive decay {ital B}{r_arrow}{ital X}{sub {ital s}}{tau}{sup +}{tau}{sup {minus}} and discuss how it can be used, in conjunction with other observables, to completely determine the parameters of the flavor-changing low-energy effective Hamiltonian. Both the standard model and several new physics scenarios are examined. This process has a large enough branching fraction, {approximately}few{times}10{sup {minus}7}, such that sufficient statistics will eventually be provided by the {ital B} factories currently under construction. {copyright} {ital 1996 The American Physical Society.}

Spacelike penguin diagram effects in B-->PP decays.

The space-like penguin contributions to branching ratios and CP asymmetries in charmless decays of $B$ to two pseudoscalar mesons are studied using the next-to-leading order low energy effective Hamiltonian. Both the gluonic penguin and the electroweak penguin diagrams are considered. We find that the effects are significant.

Connection between low energy effective Hamiltonians and energy level statistics.

We study the level statistics of a non-integrable one dimensional interacting fermionic system characterized by the GOE distribution. We calculate numerically on a finite size system the level spacing distribution $P(s)$ and the Dyson-Mehta $\Delta_3$ correlation. We observe that its low energy spectrum follows rather the Poisson distribution, characteristic of an integrable system, consistent with the fact that the low energy excitations of this system are described by the Luttinger model. We propose this Random Matrix Theory analysis as a probe for the existence and integrability of low energy effective Hamiltonians for strongly correlated systems.

CP-violating asymmetries in penguin-inducedB-meson decays beyond the leading logarithmic approximation

We investigate CP-violating phenomena both in semi-inclusive and exclusive penguin-inducedB-meson decays by using low energy effective Hamiltonians for |ΔB|=1, ΔC=ΔU=0 transitions including leading and next-to-leading order OCD corrections. In particular, we discuss the renormalization scheme dependences arising beyond the leading order and their explicit cancellation for the physical transition amplitudes. In order to estimate the hadronic matrix elements needed for the exclusive penguin modes, we apply both the Bauer, Stech, Wirbel model and the meson model of Brodsky and Lepage. Numerical results are presented for semi-inclusive\(b \to q'\bar qq(q',q \in \{ d,s\} )\) modes and the exclusive decaysB−→K−K0,\(B^ - \to \pi ^ - \bar K^0 \), and\(B_d^0 \to K^0 \bar K^0 \).

Strong-coupling descriptions of high-temperature superconductors: electronic attraction from a repulsive potential

The authors consider the effect of the nearest-neighbour copper-oxygen repulsion, V, when coupled to the charge transfer resonances Cu2+ to Cu3+ and Cu2+ to Cu+ in the high-temperature cuprate superconductors. This is done by deriving effective low-energy Hamiltonians correct to second order in the copper-oxygen hybridization. Only hole doping is considered. When Cu2+ to Cu3+ fluctuations dominate the authors derive an effective one-band model of 'Zhang-Rice' singlets with a nearest-neighbour repulsion between these singlets. When Cu2+ to Cu+ fluctuations dominate they find rich and complex behaviour. If 0<<V/ Delta <or=1/2 (where Delta is the 'bare' copper-oxygen charge transfer gap) the authors show that clusters of charge are more stable than isolated charges. On the other hand, if 0 <or= V/ Delta << 1/2 the Hamiltonian contains both weak attractive and repulsive two-body potentials. Calculations on clusters indicate that the attractive potentials have the same correlations as the more dominant 'single-particle' terms suggesting the possibility 's'-wave pairing.

Position-dependent effective mass for inhomogeneous semiconductors.

A systematic approach is adopted to extract an effective low-energy Hamiltonian for crystals with a slowly varying inhomogeneity, resolving several controversies. It is shown that the effective mass m(R) is, in general, position dependent, and enters the kinetic energy operator as -\ensuremath{\nabla}[m${(\mathrm{R})}^{\mathrm{\ensuremath{-}}1}$]\ensuremath{\nabla}/2. The advantage of using a basis set that exactly diagonalizes the Hamiltonian in the homogeneous limit is emphasized.

Universally coupled extraZ bosons from extended technicolor models

We show that in extended technicolor models there are several neutralZ bosons whose couplings to fermions are independent of family. TheseZ bosons are therefore additional to that of the standard model and induce corrections to the low energy effective Hamiltonian. These corrections are calculated in the most general model which includes technileptons (introduced to give mass to leptons).