scholarly journals Exactly solvable spin chain models corresponding to BDI class of topological superconductors

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
S. A. Jafari ◽  
Farhad Shahbazi
Keyword(s):  
Time Reversal ◽  
Solvable Models ◽  
Topological Superconductors ◽  
Spin Interactions ◽  
Detailed Classification ◽  
Exactly Solvable ◽  
Solvable Extension ◽  
Xy Chain ◽  
Topological Phase Transitions

Abstract We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, n M which are in turn related to an integer winding number, n W . The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions – a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the n W (n M ) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

scholarly journals FRACTIONAL STATISTICS IN SOME EXACTLY SOLVABLE MODELS WITH PT INVARIANT INTERACTIONS

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1875-1882 ◽  
Author(s):  
B. BASU-MALLICK
Keyword(s):  
Time Reversal ◽  
Critical Value ◽  
Real Spectrum ◽  
Reflection Symmetry ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Eigenvalues And Eigenfunctions ◽  
Calogero Model ◽  
Exactly Solvable ◽  
Invariant Interaction

Here we review a method for constructing exact eigenvalues and eigenfunctions of a many-particle quantum system, which is obtained by adding some nonhermitian but PT invariant (i.e., combined parity and time reversal invariant) interaction to the Calogero model. It is shown that such extended Calogero model leads to a real spectrum obeying generalised exclusion statistics. It is also found that the corresponding exchange statistics parameter differs from the exclusion statistics parameter and exhibits a 'reflection symmetry' provided the strength of the PT invariant interaction exceeds a critical value.

scholarly journals CLASSIFICATION OF STATIC AND HOMOGENEOUS SOLUTIONS IN EXACTLY SOLVABLE MODELS OF TWO-DIMENSIONAL DILATON GRAVITY

2003 ◽  
Vol 18 (26) ◽  
pp. 4837-4850 ◽  
Author(s):  
O. B. ZASLAVSKII
Keyword(s):  
Exactly Solvable Models ◽  
Dilaton Field ◽  
Dilaton Gravity ◽  
Solvable Models ◽  
Field Equations ◽  
Homogeneous Solutions ◽  
Conformal Fields ◽  
Exactly Solvable ◽  
Wide Family

We give the full list of types of static (homogeneous) solutions within a wide family of exactly solvable 2D dilaton gravities with backreaction of conformal fields. It includes previously known solutions as particular cases. Several concrete examples are considered for illustration. They contain a black hole and cosmological horizon in thermal equilibrium, extremal and ultraextremal horizons, etc. In particular, we demonstrate that AdS and dS geometries can be exact solutions of semiclassical field equations for a nonconstant dilaton field.

Description and symmetry of aperiodic crystals

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Time Reversal ◽  
Mathematical Concept ◽  
New Materials ◽  
Magnetic Systems ◽  
Atomic Structures ◽  
Modulated Phases ◽  
Quasiperiodic Functions ◽  
Aperiodic Crystals ◽  
Superspace Description

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

scholarly journals Exactly solvable models in arbitrary dimensions

1998 ◽  
Vol 238 (4-5) ◽  
pp. 213-218 ◽  
Author(s):  
Ranjan Kumar Ghosh ◽  
Sumathi Rao
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Exactly Solvable ◽  
Arbitrary Dimensions
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