Jordan-Wigner fermionization of quantum spin systems on arbitrary 2D lattices: A mutual Chern-Simons approach

A variety of analytical approaches have been developed for the study of quantum spin systems in two dimensions, the notable ones being spin-waves, slave boson/fermion parton constructions, and for lattices with one-to-one local correspondence of faces and vertices, the 2D Jordan-Wigner (JW) fermionization. Field-theoretically, JW fermionization is implemented through Chern-Simons (CS) flux attachment. For a correct fermionization of lattice quantum spin-$1/2$ magnets, it is necessary that the fermions obey mutual bosonic (anyonic) statistics under exchange - this is not possible to implement on arbitrary 2D lattices if fermionic matter couples only to the lattice gauge fields. Enlarging the gauge degrees of freedom to include the dual lattice allows the construction of consistent mutual Chern-Simons field theories. Here we propose a mutual CS theory where the microscopic (spin) degrees of freedom are represented as lattice fermionic matter additionally coupled to specific combinations of dual lattice gauge fields that depend on the local geometry. We illustrate the use of this method for understanding the properties of a honeycomb Kitaev model subjected to a strong Zeeman field in the $z$-direction. Our CS gauge theory framework provides an understanding why the topological phase is degraded at lower (higher) critical fields for the ferro- (antiferro-) magnetic Kitaev interaction. Additionally, we observe an effectively one-dimensional character of the low-excitations at higher fields in the $z$-direction which we also confirm by spin-wave calculations.Comment: 13 pages, 7 figure

Field tuning Kitaev systems for spin fractionalization and topological order

The honeycomb Kitaev model describes a $Z_2$ spin liquid with topological order and fractionalized excitations consisting of gapped $\pi$-fluxes and free Majorana fermions. Competing interactions, even when not very strong, are known to destabilize the Kitaev spin liquid. Magnetic fields are a convenient parameter for tuning between different phases of the Kitaev systems, and have even been investigated for potentially counteracting the effects of other destabilizing interactions leading to a revival of the topological phase. Here we review the progress in understanding the effects of magnetic fields on some of the perturbed Kitaev systems, particularly on fractionalization and topological order.Comment: 24 pages, 2 figures, For JPCM topical reviews: comments are welcom

Modular Differential Equations with Movable Poles and Admissible RCFT Characters

Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach.Comment: 81 pages, 4 figures, 2 table

Modular differential equations with movable poles and admissible RCFT characters

Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach

On Petri Nets with Hierarchical Special Arcs

We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy of places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also investigate what happens when we have a mix of these special arcs, some of which respect the hierarchy, while others do not. We settle the decidability status of the above four problems for all combinations of hierarchy, inhibitor, reset and transfer arcs, except the termination problem for two combinations. For both these combinations, we show that deciding termination is as hard as deciding the positivity problem on linear recurrence sequences -- a long-standing open problem

Infra Red Spectra of Different Species of Cultivated Oyster Mushrooms Possible Tool for Identifying Bioactive Compounds and Establishing Taxonomic Linkage

Mushrooms are macrofungi that serve as a vegetarian source of protein along with various bio-active molecules of primary health importance. The activity of the bio-active molecules range from antioxidant, immunomodulation, hepatoprotection. Cultivated oyster mushrooms are also rich in these components which may be estimated quantitatively by skill intensive ‘destructive’ chemical techniques. Infra Red spectroscopy provides a non-destructive user friendly technique to quickly assess the presence of bio-active compounds in mushroom species to be used as a quality control measure as this non-destructive tool can be used to segregate mushroom harvest according to availability of bioactive compounds. IR spectra based strain classification and taxa delimitation of mushroom samples are also attempted vis a vis DNA sequence based phylogeny analysis of the same, but no correlation is observed between the two types of phylogeny analysis

A retrospective study of post-operative gall bladder pathology with special reference to incidental carcinoma of the gall bladder

Background:Surgical removal of gall bladder for its diseases is common. However, not much is known about the incidence of incidental carcinoma in such patients in our population. Objective of current study was to analyze the different pathological entities of post-operative gall bladder specimen with particular emphasis on incidental carcinoma.Methods:This retrospective study was carried out at a multi-specialty hospital in eastern India from the pathology records for the period from August 2005 to July 2008. The records were analyzed for gender, age group distribution, and pathological types with different histology.Results:Out of 863 records, chronic cholecystitis 51.2% was the most common histology and malignancy was seen in 2.7% (23/863) both pre-operative and post-operative diagnosis. In the neoplastic group incidental carcinoma was diagnosed in 1.9% (17/23) of casesConclusion:Histopathological examination of gallbladder specimen helps to identify non-neoplastic conditions with its complications and also, for the detection of incidental carcinoma. Thorough sampling of all gallbladder specimens is a must to detect focal neoplastic changes

Primary cutaneous tuberculosis associated with reactive cervical lymphadenopathy: a case report

Tuberculosis (TB) is a mycobacterial infection that most frequently occurs due to infection with Mycobacterium tuberculosis, an acid-fast bacillus. Cutaneous lesions are relatively uncommon manifestations of TB, occurring in only 1 to 2 percent of all infected patients.  Cutaneous tuberculosis can be acquired either exogenously or endogenously .We present here a case of primary cutaneous tuberculosis with reactive cervical lymphadenopathy.  A high index of suspicion is necessary for prompt diagnosis and treatment