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Open AccessArticle

Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

Institut für Theroretische Physik, Universität Regensburg, 93040 Regensburg, Germany
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Condens. Matter 2020, 5(2), 26; https://doi.org/10.3390/condmat5020026
Received: 6 March 2020 / Revised: 2 April 2020 / Accepted: 2 April 2020 / Published: 4 April 2020
(This article belongs to the Special Issue Many Body Quantum Chaos)
We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit. View Full-Text
Keywords: phase transitions; semiclassical approximation; Dirac bosons; mean field analysis; adiabatic separation phase transitions; semiclassical approximation; Dirac bosons; mean field analysis; adiabatic separation
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Nitsch, M.; Geiger, B.; Richter, K.; Urbina, J.-D. Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System. Condens. Matter 2020, 5, 26.

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