Off-shell Bethe vectors are constructed via Yangian double currents and verified to satisfy defining properties previously used for on-shell vectors in ggo-invariant models.
Bethe Vectors in Quantum Integrable Models with Classical Symmetries
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abstract
The first goal of this paper is to give a precise and simple definition for off-shell Bethe vectors in a generic $g$-invariant integrable model for $g=gl_n$, $o_{2n+1}$, $sp_{2n}$ and $o_{2n}$. We prove from our definition that the off-shell Bethe vectors indeed become on-shell when the Bethe equations are obeyed. Then, we show that some properties for these off-shell Bethe vectors, such as the action formulas of monodromy entries on these vectors, their rectangular recurrence relations and their coproduct formula, are a consequence of our definition.
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A deterministic algorithm prepares arbitrary multi-qudit states in a definite-weight subspace via Gray-code ordering of multiset permutations, reducing preparation to controlled 2-qudit Gray rotations, and is demonstrated on Bethe states of the SU(3) Heisenberg model and SU(d) Dicke states.
Serre relations in Yangian doubles are reformulated as quadratic commutation relations between composed currents for classical Lie algebras.
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Yangian Doubles and off-Shell Bethe Vectors
Off-shell Bethe vectors are constructed via Yangian double currents and verified to satisfy defining properties previously used for on-shell vectors in ggo-invariant models.
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Preparing multi-qudit states in a definite-weight subspace
A deterministic algorithm prepares arbitrary multi-qudit states in a definite-weight subspace via Gray-code ordering of multiset permutations, reducing preparation to controlled 2-qudit Gray rotations, and is demonstrated on Bethe states of the SU(3) Heisenberg model and SU(d) Dicke states.
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Serre Relations in Yangian Doubles
Serre relations in Yangian doubles are reformulated as quadratic commutation relations between composed currents for classical Lie algebras.