Spin chain overlaps and the twisted Yangian

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.

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1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative

Optical and Quantum Electronics ◽

10.1007/s11082-021-02739-9 ◽

2021 ◽

Vol 53 (2) ◽

Cited By ~ 1

Author(s):

K. Hosseini ◽

L. Kaur ◽

M. Mirzazadeh ◽

H. M. Baskonus

Keyword(s):

Spin Chain ◽

Time Derivative ◽

Soliton Solutions ◽

Chain Model ◽

Heisenberg Ferromagnetic Spin Chain ◽

Spin Chain Model

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A novel class of translationally invariant spin chains with long-range interactions

Journal of High Energy Physics ◽

10.1007/jhep08(2020)099 ◽

2020 ◽

Vol 2020 (8) ◽

Author(s):

B. Basu-Mallick ◽

F. Finkel ◽

A. González-López

Keyword(s):

Long Range ◽

Degrees Of Freedom ◽

Spin Chains ◽

Open Chain ◽

New Class ◽

Spin Interactions ◽

Long Range Interactions ◽

Spin Reversal ◽

Twisted Yangian ◽

Internal Degrees Of Freedom

Abstract We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under “twisted” translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain’s spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

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Erratum: Coherent Multispin Exchange Coupling in a Quantum-Dot Spin Chain [Phys. Rev. X 10 , 031006 (2020)]

Physical Review X ◽

10.1103/physrevx.11.029904 ◽

2021 ◽

Vol 11 (2) ◽

Author(s):

Haifeng Qiao ◽

Yadav P. Kandel ◽

Kuangyin Deng ◽

Saeed Fallahi ◽

Geoffrey C. Gardner ◽

...

Keyword(s):

Quantum Dot ◽

Spin Chain ◽

Exchange Coupling

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Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string

Journal of High Energy Physics ◽

10.1007/jhep02(2021)162 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Charles B. Thorn

Keyword(s):

Energy Spectrum ◽

Excited States ◽

Spin Chain ◽

Discrete Dynamical System ◽

Heisenberg Spin ◽

Free Fermions ◽

Heisenberg Spin Chain ◽

Delta Sigma ◽

Special Cases ◽

Quantized String

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.

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