Learning from Julius' star, *, ⋆\star

While collecting some personal memories about Julius Wess, I briefly describe some aspects of my recent work on many particle quantum mechanics and second quantization on noncommutative spaces obtained by twisting, and their connection to him.Comment: Late2e file 13 pages. To appear in the Proceedings of the Workshop "Scientific and Human Legacy of Julius Wess - JW2011", Donji Milanovac (Serbia), August 27-29, 2011, International Journal of Modern Physics: Conference Series. On-line at: http://www.worldscientific.com/toc/ijmpcs/13/0

Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces

We introduce a new class of sine-Gordon models, for which interaction term is present in a region different from the domain over which quadratic part is defined. We develop a novel non-perturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the problem of calculating the amplitude of interference fringes in experiments with two independent low dimensional Bose gases. We calculate full distribution functions of interference amplitude for 1D and 2D gases with nonzero temperatures.Comment: final published versio

Magnetization plateau in the S=1/2 spin ladder with alternating rung exchange

We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} \delta ]$ in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an $XXZ$ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is $\sim \delta$. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as $\delta^{\nu}$, where $\nu =4/5$ in the case of ladder with isotropic antiferromagnetic legs and $\nu =2$ in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields ($H^{\pm}_{c1}$ and $H^{\pm}_{c2}$) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.Comment: 6 pages, 2 figure

Magnetic properties of the spin S=1/2S=1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange %on even and odd sites in the presence of additional modulation of exchange on odd bonds with period three. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective $XXZ$ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped string order into the only one gapless L\"uttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to 1/3 and 2/3 of the saturation value. These phases reveal themselves also in magnetization curve as plateaus at corresponding values of magnetization. As the result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.Comment: 21 pages, 5 figures, Journal of Physics: Condensed Matter, 24, 116002, (2012

Band-Insulator-Metal-Mott-Insulator transition in the half--filled t−t′t-t^{\prime} ionic-Hubbard chain

We investigate the ground state phase diagram of the half-filled $t-t^{\prime}$ repulsive Hubbard model in the presence of a staggered ionic potential $\Delta$, using the continuum-limit bosonization approach. We find, that with increasing on-site-repulsion $U$, depending on the value of the next-nearest-hopping amplitude $t^{\prime}$, the model shows three different versions of the ground state phase diagram. For $t^{\prime} < t^{\prime}_{\ast}$, the ground state phase diagram consists of the following three insulating phases: Band-Insulator at $U<U_{c}$, Ferroelectric Insulator at $U_{c} U_{c}$. For $t^{\prime} > t^{\prime}_{c}$ there is only one transition from a spin gapped metallic phase at $U U_{c}$. Finally, for intermediate values of the next-nearest-hopping amplitude $t^{\prime}_{\ast} < t^{\prime} < t^{\prime}_{c}$ we find that with increasing on-site repulsion, at $U_{c1}$ the model undergoes a second-order commensurate-incommensurate type transition from a band insulator into a metallic state and at larger $U_{c2}$ there is a Kosterlitz-Thouless type transition from a metal into a ferroelectric insulator.Comment: 9 pages 3 figure

From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ

Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique in the {\it antiferroelectric regime}. In terms of the counting function we obtain the usual physical quantities, like the energy and the transfer matrix (eigenvalues). Then, we introduce a double scaling limit which appears to describe the sine-Gordon theory on cylindrical geometry, so generalising famous results in the plane by Luther \cite{LUT} and Johnson et al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to excitations, we derive scattering amplitudes involving solitons/antisolitons first, and bound states later. The latter case comes out as manifestly related to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this nonlinear integral equations framework was contrived to deal with finite geometries, we prove it to be effective for discovering or rediscovering S-matrices. As a particular example, we prove that this unique model furnishes explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe} and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description of unknown integrable field theories.Comment: Article, 41 pages, Late

On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces

We explore some general consequences of a proper, full enforcement of the "twisted Poincare'" covariance of Chaichian et al. [14], Wess [50], Koch et al. [34], Oeckl [41] upon many-particle quantum mechanics and field quantization on a Moyal-Weyl noncommutative space(time). This entails the associated braided tensor product with an involutive braiding (or $\star$-tensor product in the parlance of Aschieri et al. [3,4]) prescription for any coordinates pair of $x,y$ generating two different copies of the space(time); the associated nontrivial commutation relations between them imply that $x-y$ is central and its Poincar\'e transformation properties remain undeformed. As a consequence, in QFT (even with space-time noncommutativity) one can reproduce notions (like space-like separation, time- and normal-ordering, Wightman or Green's functions, etc), impose constraints (Wightman axioms), and construct free or interacting theories which essentially coincide with the undeformed ones, since the only observable quantities involve coordinate differences. In other words, one may thus well realize QM and QFT's where the effect of space(time) noncommutativity amounts to a practically unobservable common noncommutative translation of all reference frames.Comment: Latex file, 24 pages. Final version to appear in PR

The arctic curve of the domain-wall six-vertex model

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of $q$-enumerated (with $0<q\leq 4$) large alternating sign matrices. In particular, as $q\to 0$ the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction

A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory

We make contact between the infinite-dimensional non-local symmetry of the typeIIB superstring on AdS5xS5 worldsheet theory and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the Hamiltonian of a spin chain, and show that it commutes with the g*2 N = 0 limit of the non-abelian charges.Comment: 19 pages, harvma

On second quantization on noncommutative spaces with twisted symmetries

By application of the general twist-induced star-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime in a non-commutative language. The procedure deforms in a coordinated way the spacetime algebra and its symmetries, the wave-mechanical description of a system of n bosons/fermions, the algebra of creation and annihilation operators and also the commutation relations of the latter with functions of spacetime; our key requirement is the mode-decomposition independence of the quantum field. In a conservative view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind. In a non-conservative one, we obtain a covariant framework for QFT on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics. One distinguishing feature is that the field commutation relations remain of the type "field (anti)commutator=a distribution". We illustrate the results by choosing as examples interacting non-relativistic and free relativistic QFT on Moyal space(time)s.Comment: Latex file, 45 pages. I have corrected a small typo present in 3 points of the previous version and in the version published also in JPA (which had occurred via late careless serial replacements, with no consequences on the results of the calculations): $\beta^*=\beta^{-1}$ has been corrected into $\beta^*=S(\beta^{-1})