Form factors of the finite quantum<i>XY</i>-chain

Iorgov, N. Z.

doi:10.1088/1751-8113/44/33/335005

Cited by 15 publications

(30 citation statements)

References 49 publications

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“…. , q K NS , which are known explicitly from previous studies [32][33][34]. In the following we always consider the thermodynamic limit N → ∞, where the sums over momenta can be turned into integrals and the expressions for the form factors are summarized in Appendix A.…”

Section: Magnetization Dynamicsmentioning

confidence: 99%

Front dynamics in the XY chain after local excitations

Eisler

Maislinger

2020

SciPost Phys.

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We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.

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Section: Magnetization Dynamicsmentioning

confidence: 99%

Front dynamics in the XY chain after local excitations

Eisler

Maislinger

2020

SciPost Phys.

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“…Ising spin matrix elements between the eigenvectors of V ′ should therefore coincide with the form factors of σ x between the eigenstates of XY hamiltonian, which were found in [14] by the method of separation of variables.…”

Section: Remark 21mentioning

confidence: 77%

“…The presented approach seems to be quite natural and straightforward. It is likely to be applicable to other free-fermion lattice models, such as those considered in [14,18,29].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Ising Correlations and Elliptic Determinants

Iorgov¹,

Lisovyy²

2011

J Stat Phys

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Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors -matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation operator. Free-fermion structure of the model implies that any multiparticle form factor is given by the pfaffian of a matrix constructed from the two-particle ones. Crossed two-particle form factors can be obtained by inverting a block of the matrix of linear transformation induced on fermions by the spin conjugation. We show that the corresponding matrix is of elliptic Cauchy type and use this observation to solve the inversion problem explicitly. Non-crossed two-particle form factors are then obtained using theta functional interpolation formulas. This gives a new simple proof of the factorized formulas for periodic Ising form factors, conjectured by A. Bugrij and one of the authors.

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“…Eqs. (25)(26)(27)(28)) in the large-N limit. Indeed, in Appendix B, we derive the following crucial identities relating low-lying eigenstates of the Frustrated Ring spin glass benchmark with those of its ferromagnetic counterpart H:…”

Section: Analysis Of Flux Qubit Noise At the Annealing Bottleneckmentioning

confidence: 99%

Noise amplification at spin-glass bottlenecks of quantum annealing: A solvable model

et al. 2020

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To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits N in the limit that N → ∞. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground-state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.

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Form factors of the finite quantumXY-chain

Cited by 15 publications

References 49 publications

Front dynamics in the XY chain after local excitations

Front dynamics in the XY chain after local excitations

Ising Correlations and Elliptic Determinants

Noise amplification at spin-glass bottlenecks of quantum annealing: A solvable model

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