Abstract
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.
Highlights
The methods and ideas of quantum chaos [1,2] provided deep insights into the way classical information conspires with hin a subtle manner
We explored a relativistic extension of the attractive Lieb-Liniger model, by considering both particles with linear dispersion and spin degree of freedom
Our objective was to check the existence of a relativistic analogue of the well-known quantum phase transition [26] displayed by the original non-relativistic model, where the attractive potential drives a transition of the ground state from a homogeneous state into an inhomogeneous one due to the critical appearance of a bright soliton, as thoroughly study by means of semiclassical methods in [21]
Summary
The methods and ideas of quantum chaos [1,2] provided deep insights into the way classical information conspires with hin a subtle manner. A natural arena for testing this idea is the attractive Lieb-Liniger model [22] describing one-dimensional bosons attractively interacting through short-range forces and, in particular, its low-energy effective description that was experimentally realized [23,24] The reason for this is that this system displays a quantum phase transition [25,26,27,28] and admits a proper semiclassical derivation of a well-defined and controlled classical limit in the form of mean-field equations, allowing for direct application of semiclassical techniques [21].
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