Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models

• URL: http://arxiv.org/abs/2302.09271v1
• Date: Sat, 18 Feb 2023 09:37:45 GMT
• Title: Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models
• Authors: Tommaso Roscilde, Tommaso Comparin and Fabio Mezzacapo
• Abstract summary: Non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians. We show that the dynamics of the OAT model can be closely reproduced by systems with power-lawdecaying interactions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space; and it is central to the understanding of the many-body entangled states that can be generated by state-of-the-art quantum simulators. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians, initialized in a state which breaks the U(1) symmetry -- the paradigmatic example being the evolution of the so-called one-axis-twisting (OAT) model, featuring infinite-range interactions between spins. In this work we show that the dynamics of the OAT model can be closely reproduced by systems with power-law-decaying interactions, thanks to an effective separation between the zero-momentum degrees of freedom, associated with the so-called Anderson tower of states, and reconstructing a OAT model; and finite-momentum ones, associated with spin-wave excitations. This mechanism explains quantitatively the recent numerical observation of spin squeezing and Schr\"odinger-cat generation in the dynamics of dipolar Hamiltonians; and it paves the way for the extension of this observation to a much larger class of models of immediate relevance for quantum simulations.

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