Overlaps between eigenstates of the XXZ spin-1/2 chain and a class of simple product states

Pozsgay, Balázs

doi:10.1088/1742-5468/2014/06/p06011

Cited by 99 publications

(188 citation statements)

References 45 publications

(96 reference statements)

Supporting

Mentioning

183

Contrasting

Order By: Relevance

“…Recently, some progress has been made in calculating overlaps using the Bethe ansatz [122][123][124]130]. There are now exact formulas for the overlap between a Néel state and any eigenstate in terms of the Bethe roots describing the eigenstate [122-124, 131, 132].…”

Section: The Modelmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

View full text Add to dashboard Cite

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

show abstract

Section: The Modelmentioning

confidence: 99%

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

et al. 2016

View full text Add to dashboard Cite

show abstract

“…However, as stressed already elsewhere [43], since the number of permutations grows like P !, these expressions for the overlaps are not useful for any practical numerical or analytic evaluation.…”

Section: The Xxz Spin Chain and The Algebraic Bethe Ansatzmentioning

confidence: 78%

“…[43]. As a relevant difference, our proof does not use any concept coming from the Boundary Algebraic Bethe Ansatz solution of the classical six-vertex model and it is genuinely based on the solution of the XXZ chain.…”

Section: Discussionmentioning

confidence: 99%

“…[43] using Boundary Bethe Ansatz techniques [73]. Denoting generically with |ψ the two-site shift invariant state, we want to prove the following determinant formula [43] …”

Section: Proof Of Overlaps Determinant Formulasmentioning

confidence: 99%

“…(56) is a simple rewriting in our notations of the overlaps formulas in Ref. [43] for these states. From the structure of Eq.…”

Section: Proof Of Overlaps Determinant Formulasmentioning

confidence: 99%

See 2 more Smart Citations

Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

Piroli¹,

Calabrese²

2014

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We consider the problem of computing the overlaps between the Bethe states of the XXZ spin-1/2 chain and generic states. We derive recursive formulas for the overlaps between some simple product states and off-shell Bethe states within the framework of the Algebraic Bethe Ansatz. These recursive formulas can be used to prove in a simple and straightforward way the recently-obtained results for the overlaps of the Bethe states with the Néel state, the dimer state, and the q-deformed dimer state. However, these recursive formulas are derived for a broader class of states and represent a concrete starting point for the computation of rather general overlaps. Our approach can be easily extended to other one-dimensional Bethe Ansatz integrable models.

show abstract