scholarly journals Exact solution of a cluster model with next-nearest-neighbor interaction

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yuji Yanagihara ◽  
Kazuhiko Minami
Keyword(s):  
Phase Diagram ◽  
Cluster Model ◽  
Nearest Neighbor ◽  
Spin Chains ◽  
Neighbor Interaction ◽  
Conformal Field ◽  
Cubic Equation ◽  
Algebraic Generalization ◽  
Wigner Transformation ◽  
Distribution Of Roots

Abstract A 1D cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a transformation obtained automatically from its interactions, which is an algebraic generalization of the Jordan–Wigner transformation. The gapless condition is expressed as a condition on the roots of a cubic equation, and the phase diagram is obtained exactly. We find that the distribution of roots for this algebraic equation determines the existence of long-range order, and we again obtain the ground-state phase diagram. We also derive the central charges of the corresponding conformal field theory. Finally, we note that our results are universally valid for an infinite number of solvable spin chains whose interactions obey the same algebraic relations.

scholarly journals Phase Diagram ofS=1 XXZ Chain with Next-Nearest-Neighbor Interaction

2005 ◽  
Vol 74 (5) ◽  
pp. 1544-1551 ◽  
Author(s):  
Takahiro Murashima ◽  
Keigo Hijii ◽  
Kiyohide Nomura ◽  
Takashi Tonegawa
Keyword(s):  
Phase Diagram ◽  
Nearest Neighbor ◽  
Neighbor Interaction ◽  
Xxz Chain

scholarly journals Phase diagram ofS=12XXZchain with next-nearest-neighbor interaction

2000 ◽  
Vol 61 (14) ◽  
pp. 9453-9456 ◽  
Author(s):  
Shunsaku Hirata ◽  
Kiyohide Nomura
Keyword(s):  
Phase Diagram ◽  
Nearest Neighbor ◽  
Neighbor Interaction

CORRELATION FUNCTIONS IN QUANTUM SPIN CHAINS AND VERTEX MODELS

2001 ◽  
Vol 16 (11) ◽  
pp. 1875-1887
Author(s):  
VIERI MASTROPIETRO
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Nearest Neighbor ◽  
Quantum Spin ◽  
Spin Chains ◽  
Vertex Model ◽  
Quantum Spin Chains ◽  
Neighbor Interaction ◽  
Vertex Models

Some correlation functions of critical models, like the anisotropic spin chain with nearest and next-to-nearest neighbor interaction, or the eight vertex model, are computed as a corollary of the study of the XYZ model in [2].

scholarly journals The integrable (hyper)eclectic spin chain

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher
Keyword(s):  
Spin Chain ◽  
Nearest Neighbor ◽  
Inverse Scattering Method ◽  
Spin Chains ◽  
Scattering Method ◽  
Yang Mills ◽  
Deformation Parameters ◽  
Dilatation Operator ◽  
The One ◽  
State Spin

Abstract We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills Theory.

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

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