5 research outputs found
Hybrid Proofs of the \u3cem\u3eq\u3c/em\u3e-Binomial Theorem and Other Identities
We give hybrid proofs of the q-binomial theorem and other identities. The proofs are hybrid in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version.
We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan.
Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities
Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
We study the symmetry resolved entanglement entropies in gapped integrable
lattice models. We use the corner transfer matrix to investigate two
prototypical gapped systems with a U(1) symmetry: the complex harmonic chain
and the XXZ spin-chain. While the former is a free bosonic system, the latter
is genuinely interacting. We focus on a subsystem being half of an infinitely
long chain. In both models, we obtain exact expressions for the charged moments
and for the symmetry resolved entropies. While for the spin chain we found
exact equipartition of entanglement (i.e. all the symmetry resolved entropies
are the same), this is not the case for the harmonic system where equipartition
is effectively recovered only in some limits. Exploiting the gaussianity of the
harmonic chain, we also develop an exact correlation matrix approach to the
symmetry resolved entanglement that allows us to test numerically our analytic
results.Comment: 45 pages, 10 figures, version
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Hybrid Proofs of the q-Binomial Theorem and other identities
We give "hybrid" proofs of the q-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan. Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities
HYBRID PROOFS OF THE q-BINOMIAL THEOREM AND OTHER IDENTITIES
We give “hybrid” proofs of the q-binomial theorem and other identities. The proofs are “hybrid ” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan. Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities