### Abstract

We study the time evolution of an integrable many-particle system, described by the q-boson Hamiltonian in the limit of strong bosonic interactions q→. It is shown that, for a particular class of pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the q -boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the generalized Gibbs ensemble for homogeneous initial Fock states.

Original language | English |
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Article number | 053107 |

Journal | Journal of statistical mechanics - theory and experiment |

Volume | 2016 |

Issue number | 5 |

DOIs | |

Publication status | Published - 19 May 2016 |

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### Keywords

- integrable spin chains (vertex models)
- quantum integrability (Bethe Ansatz)
- quantum quenches
- solvable lattice models

### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics
- Statistics, Probability and Uncertainty

### Cite this

**Real-time dynamics in a strongly interacting bosonic hopping model : Global quenches and mapping to the XX chain.** / Pozsgay, Balázs; Eisler, Viktor.

Research output: Contribution to journal › Article › Research › peer-review

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TY - JOUR

T1 - Real-time dynamics in a strongly interacting bosonic hopping model

T2 - Global quenches and mapping to the XX chain

AU - Pozsgay, Balázs

AU - Eisler, Viktor

PY - 2016/5/19

Y1 - 2016/5/19

N2 - We study the time evolution of an integrable many-particle system, described by the q-boson Hamiltonian in the limit of strong bosonic interactions q→. It is shown that, for a particular class of pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the q -boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the generalized Gibbs ensemble for homogeneous initial Fock states.

AB - We study the time evolution of an integrable many-particle system, described by the q-boson Hamiltonian in the limit of strong bosonic interactions q→. It is shown that, for a particular class of pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the q -boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the generalized Gibbs ensemble for homogeneous initial Fock states.

KW - integrable spin chains (vertex models)

KW - quantum integrability (Bethe Ansatz)

KW - quantum quenches

KW - solvable lattice models

UR - http://www.scopus.com/inward/record.url?scp=84970024486&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2016/05/053107

DO - 10.1088/1742-5468/2016/05/053107

M3 - Article

VL - 2016

JO - Journal of statistical mechanics - theory and experiment

JF - Journal of statistical mechanics - theory and experiment

SN - 1742-5468

IS - 5

M1 - 053107

ER -