Excited-state quantum phase transitions in a two-fluid Lipkin model

Background: Composed systems have became of great interest in the framework of the ground state quantum phase transitions (QPTs) and many of their properties have been studied in detail. However, in these systems the study of the so called excited-state quantum phase transitions (ESQPTs) have not received so much attention. Purpose: A quantum analysis of the ESQPTs in the two-fluid Lipkin model is presented in this work. The study is performed through the Hamiltonian diagonalization for selected values of the control parameters in order to cover the most interesting regions of the system phase diagram. [Method:] A Hamiltonian that resembles the consistent-Q Hamiltonian of the interacting boson model (IBM) is diagonalized for selected values of the parameters and properties such as the density of states, the Peres lattices, the nearest-neighbor spacing distribution, and the participation ratio are analyzed. Results: An overview of the spectrum of the two-fluid Lipkin model for selected positions in the phase diagram has been obtained. The location of the excited-state quantum phase transition can be easily singled out with the Peres lattice, with the nearest-neighbor spacing distribution, with Poincar\'e sections or with the participation ratio. Conclusions: This study completes the analysis of QPTs for the two-fluid Lipkin model, extending the previous study to excited states. The ESQPT signatures in composed systems behave in the same way as in single ones, although the evidences of their presence can be sometimes blurred. The Peres lattice turns out to be a convenient tool to look into the position of the ESQPT and to define the concept of phase in the excited states realm

Massive Gauge Axion Fields

A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the non-gauge invariant proposal are established. The supersymmetric version of the gauge invariant model is constructed.Comment: Final version. New references adde

Phase diagram of an extended Agassi model

Background: The Agassi model is an extension of the Lipkin-Meshkov-Glick model that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960's by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.Comment: Accepted for publication in PR

An extended Agassi model: algebraic structure, phase diagram, and large size limit

The Agassi model is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick (LMG) model. In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a $1/j$ analysis, with $j$ proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite$-j$.Comment: Accepted in Physica Scripta. Focus on SSNET 201

Intrinsic structure of two-phonon states in the interacting boson model

A general study of excitations up to two-phonon states is carried out using the intrinsic-state formalism of the Interacting Boson Model (IBM). Spectra and transitions for the different dynamical symmetries are analyzed and the correspondence with states in the laboratory frame is established. The influence of multi-phonon states is discussed. The approach is useful in problems where the complexity of the IBM spectrum renders the analysis in the laboratory frame difficult.Comment: 22 pages, TeX (ReVTeX). 7 eps figures. Submitted to Nucl. Phys.

Magnetic structure and orbital ordering in BaCoO3 from first-principles calculations

Ab initio calculations using the APW+lo method as implemented in the WIEN2k code have been used to describe the electronic structure of the quasi-one-dimensional system BaCoO3. Both, GGA and LDA+U approximations were employed to study different orbital and magnetic orderings. GGA predicts a metallic ground state whereas LDA+U calculations yield an insulating and ferromagnetic ground state (in a low-spin state) with an alternating orbital ordering along the Co-Co chains, consistent with the available experimental data.Comment: 8 pages, 9 figure

Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group

Let $U_n$ denote the group of $n\times n$ unipotent upper-triangular matrices over a fixed finite field \FF_q, and let U_\cP denote the pattern subgroup of $U_n$ corresponding to the poset \cP. This work examines the superclasses and supercharacters, as defined by Diaconis and Isaacs, of the family of normal pattern subgroups of $U_n$. After classifying all such subgroups, we describe an indexing set for their superclasses and supercharacters given by set partitions with some auxiliary data. We go on to establish a canonical bijection between the supercharacters of U_\cP and certain \FF_q-labeled subposets of \cP. This bijection generalizes the correspondence identified by Andr\'e and Yan between the supercharacters of $U_n$ and the \FF_q-labeled set partitions of $\{1,2,...,n\}$. At present, few explicit descriptions appear in the literature of the superclasses and supercharacters of infinite families of algebra groups other than \{U_n : n \in \NN\}. This work signficantly expands the known set of examples in this regard.Comment: 28 page

Topological mass in seven dimensions and dualities in four dimensions

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions.Comment: 7 page