Topologically protected localised states in spin chains

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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Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains

Physical Review Research ◽

10.1103/physrevresearch.1.033104 ◽

2019 ◽

Vol 1 (3) ◽

Author(s):

Jarrett L. Lancaster ◽

Joseph P. Godoy

Keyword(s):

Power Law ◽

Quantum Spin ◽

Steady States ◽

Spin Chains ◽

Nonequilibrium Steady States ◽

Quantum Spin Chains

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Slow Propagation in Some Disordered Quantum Spin Chains

Journal of Statistical Physics ◽

10.1007/s10955-020-02681-2 ◽

2021 ◽

Vol 182 (1) ◽

Author(s):

Bruno Nachtergaele ◽

Jake Reschke

Keyword(s):

Quantum Spin ◽

Spin Chains ◽

Quantum Spin Chains ◽

Slow Propagation

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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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