Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators

Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. In this paper, the spin-spin correlation function of the antiferromagnetic spin-1/2 chain is calculated numerically in the presence of a next nearest neighbor coupling J2 for chains of up to 32 sites. By varying the coupling strength J2 we can control the effect of the marginal operator, and our results unambiguously confirm the field theory predictions. The critical value at which the marginal operator vanishes has been determined to be at J2 = 0.241167 +/- 0.000005J.Comment: revised paper with extended data-analysis. 5 pages, using revtex with 4 embedded figures (included with macro). A complete postscript file with all figures + text (5 pages) is available from http://FY.CHALMERS.SE/~eggert/marginal.ps or by request from [email protected]

d dimensional SO(d)-Higgs Models with Instanton and Sphaleron: d=2,3

The Abelian Higgs model and the Georgi-Glashow model in 2 and 3 Euclidean dimensions respectively, support both finite size instantons and sphalerons. The instantons are the familiar Nielsen-Oleson vortices and the 't Hooft-Polyakov monopole solutions respectively. We have constructed the sphaleron solutions and calculated the Chern-Simons charges N_cs for sphalerons of both models and have constructed two types of noncontractible loops between topologically distinct vacuua. In the 3 dimensional model, the sphaleron and the vacuua have zero magnetic and electric flux while the configurations on the loops have non vanishing magnetic flux.Comment: 24 pages, 3 figures, LaTe

Nucleation at finite temperature beyond the superminispace model

The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O(3) nonlinear $\sigma$-model, the transition is seen to be only of the first order.Comment: 15 pages, 3 figure

Periodic Bounce for Nucleation Rate at Finite Temperature in Minisuperspace Models

The periodic bounce configurations responsible for quantum tunneling are obtained explicitly and are extended to the finite energy case for minisuperspace models of the Universe. As a common feature of the tunneling models at finite energy considered here we observe that the period of the bounce increases with energy monotonically. The periodic bounces do not have bifurcations and make no contribution to the nucleation rate except the one with zero energy. The sharp first order phase transition from quantum tunneling to thermal activation is verified with the general criterions.Comment: 17 pages, 5 postscript figures include

Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory

Magnetic impurities coupled to both fermionic and bosonic baths or to a fermionic bath with pseudogap density of states, described by the Fermi-Bose Kondo and pseudogap Kondo models, display non-trivial intermediate coupling fixed points associated with critical local-moment fluctuations and local non-Fermi liquid behavior. Based on renormalization group together with a renormalized perturbation expansion around the free-impurity limit, we calculate various impurity properties in the vicinity of those intermediate-coupling fixed points. In particular, we compute the conduction electron T matrix, the impurity susceptibility, and the residual impurity entropy, and relate our findings to certain scenarios of local quantum criticality in strongly correlated lattice models.Comment: 16 pages, 5 figs; (v2) large-N results for entropy of Bose-Kondo model added; (v3) final version as publishe

Asymptotically exact solution of a local copper-oxide model

We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities.Comment: 11 pages, 1 postcript figure is appended as self-extracting archive, Revtex 2.0, ICTP preprint 199

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

Quantum-Classical Phase Transition of Escape rate in Biaxial Spin Particles

The escape rates of the biaxial single domain spin particles with and without an applied magnetic field are investigated. Using the strict potential field description of spin systems developed by Ulyanov and Zaslavskii we obtain new effective Hamiltonians which are considered to be in exact spin-coordinate correspondence unlike the well studied effective Hamiltonians with the approximate correspondence. The sharp first-order transition is found in both cases. The phase diagram of the transitions depending on the anisotropy constant and the external field is also given.Comment: 15 pages, 8 figure

Cellular Dynamical Mean Field Approach to Strongly Correlated Systems

We propose a cellular version of dynamical-mean field theory which gives a natural generalization of its original single-site construction and is formulated in different sets of variables. We show how non-orthogonality of the tight-binding basis sets enters the problem and prove that the resulting equations lead to manifestly causal self energies.Comment: RevTex, 4 pages, 1 embedded figur

Crossover Phenomena in the One-Dimensional SU(4) Spin-Orbit Model under Magnetic Fields

We study the one-dimensional SU(4) exchange model under magnetic fields, which is the simplest effective Hamiltonian in order to investigate the quantum fluctuations concerned with the orbital degrees of freedom in coupled spin-orbit systems. The Bethe ansatz approaches and numerical calculations using the density matrix renormalization group method are employed. The main concern of the paper is how the system changes from the SU(4) to the SU(2) symmetric limit as the magnetic field is increased. For this model the conformal field theory predicts an usual behavior: there is a jump of the critical exponents just before the SU(2) limit. For a finite-size system, however, the orbital-orbital correlation functions approach continuously to the SU(2) limit after interesting crossover phenomena. The crossover takes place in the magnetization range of 1/3 $\sim$ 1/2 for the system with 72 sites studied in this paper.Comment: 8 pages, 6 Postscript figures, REVTeX, submitted to Phys. Rev.