Excited state TBA and renormalized TCSA in the scaling Potts model

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S-matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.Comment: 39 pages, 5 eps figures. v2: reference added. v3: several misprints corrected, and an important step in the derivation of counter terms (in section 3.4.1) is explained in more detai

Confinement in the q-state Potts model: an RG-TCSA study

In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field induces confinement of the domain wall excitations. For the Ising model (q = 2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q = 3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting "hadron" spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renormalization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approach provides a very accurate description for the mesonic spectrum in all the parameter regime for weak magnetic field, while the low-energy expansion from the Bethe-Salpeter equation is only valid for very weak fields where it gives a slight improvement over the semiclassical results. In addition, we confirm the validity of the recent predictions for the baryon spectrum obtained from solving the quantum mechanical three-body problem.Comment: 22 pages, pdflatex source with pdf figures. Version 2: references added, introduction change

Exercising control over memory consolidation

Exercise can improve human cognition. A mechanistic connection between exercise and cognition has been revealed in several recent studies. Exercise increases cortical excitability and this in turn leads to enhanced memory consolidation. Together these studies dovetail with our growing understanding of memory consolidation and how it is regulated through changes in motor cortical excitability

Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach

We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $k\gg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $\lambda$. Moreover for $\lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.Comment: 30 pages, 19 eps figures, LaTeX2e file. Version 2: manuscript accepted for publication; small changes in text and in one of the figure

On the relation between Phi(1,2) and Phi(1,5) perturbed minimal models

We consider the RSOS S-matrices of the Phi(1,5) perturbed minimal models which have recently been found in the companion paper [hep-th/9604098]. These S-matrices have some interesting properties, in particular, unitarity may be broken in a stronger sense than seen before, while one of the three classes of Phi(1,5) perturbations (to be described) shares the same Thermodynamic Bethe Ansatz as a related Phi(1,2) perturbation. We test these new S-matrices by the standard Truncated Conformal Space method, and further observe that in some cases the BA equations for two particle energy levels may be continued to complex rapidity to describe (a) single particle excitations and (b) complex eigenvalues of the Hamiltonian corresponding to non-unitary S-matrix elements. We make some comments on identities between characters in the two related models following from the fact that the two perturbed theories share the same breather sector.Comment: LaTeX, 23 pages, 12 figures. Substantial revision of introductory section, new discussion of complex eigenvalues and non-unitary S-matrice

SELF-ASSEMBLED HETEROLEPTIC CHIRAL LIGANDS, ASYMMETRIC CATALYST SYSTEMS AND METHODS

A method of synthesizing a heteroleptic, multiple metal containing metallocyclic catalyst, particularly Suited for asymmetric catalysis, comprising combining a plurality of plural functional group-containing, monodentate ligands of complementary chirality, said plural functional groups being tethered to each other by tethers in the presence of a scaffold structural metal Ms or derivative thereof, wherein at least one functional group on each ligand combines to ligate M to form a bidentate, Ms centered ligand scaffold containing the remaining functional groups and combining said bidentate ligand scaffold with a catalytic metal Mc or derivative thereof whereby the remaining functional groups combine to ligate Mc, thereby forming said catalyst