scholarly journals Integrable deformations of the XXZ spin chain

2013 ◽  
Vol 2013 (09) ◽  
pp. P09028 ◽  
Author(s):  
Niklas Beisert ◽  
Lucas Fiévet ◽  
Marius de Leeuw ◽  
Florian Loebbert
AIP Advances ◽  
2015 ◽  
Vol 5 (3) ◽  
pp. 037128 ◽  
Author(s):  
Tathamay Basu ◽  
Niharika Mohapatra ◽  
Kiran Singh ◽  
E. V. Sampathkumaran
Keyword(s):  

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Luis Colmenarez ◽  
David J. Luitz
Keyword(s):  

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher

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.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marius de Leeuw ◽  
Tamás Gombor ◽  
Charlotte Kristjansen ◽  
Georgios Linardopoulos ◽  
Balázs Pozsgay
Keyword(s):  

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Haifeng Qiao ◽  
Yadav P. Kandel ◽  
Kuangyin Deng ◽  
Saeed Fallahi ◽  
Geoffrey C. Gardner ◽  
...  

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Charles B. Thorn

Abstract Although the energy spectrum of the Heisenberg spin chain on a circle defined by$$ H=\frac{1}{4}\sum \limits_{k=1}^M\left({\sigma}_k^x{\sigma}_{k+1}^x+{\sigma}_k^y{\sigma}_{k+1}^y+\Delta {\sigma}_k^z{\sigma}_{k+1}^z\right) $$ H = 1 4 ∑ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether M ∈ 4ℕ + r, where r = −1, 0, 1, 2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M1< M and M − M1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case ∆ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R0. We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for ∆ ≠ 0 is a change in the compactification radius R0→ R∆. As ∆ → −1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.


2013 ◽  
Vol 174 (1) ◽  
pp. 134-153 ◽  
Author(s):  
G. F. Helminck ◽  
A. G. Helminck ◽  
E. A. Panasenko

Sign in / Sign up

Export Citation Format

Share Document