Geometry-induced entanglement in a mass-imbalanced few-fermion system

Abstract

Many-body systems undergoing quantum phase transitions reveal substantial growth of non-classical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy. Here we show, that very similar features may be observed in one-dimensional systems of a few strongly interacting atoms when the structural transitions between different spatial orderings are driven by a varying shape of an external potential. When the appropriate adaptation of the finite-size scaling approach is performed in the vicinity of the transition point, fewfermion systems display a characteristic power-law invariance of divergent quantities. arXiv:1909.08949v2 [cond-mat.quant-gas]

Few strongly interacting fermions of different mass driven in the vicinity of a critical point

“…Contrary, in the harmonic potential (λ = 1), the lighter component is split and located on the edges while the heavier one remains in the center. Following this observation, it was shown that the system undergoes some sort of critical transition when one adiabatically changes parameter λ from 0 to 1 [17,18]. It turned out that the transition has properties quite similar to that known from typical quantum phase transition, e.g.…”

“…It means that a role of the thermodynamic limit is played by a limit of infinite repulsions [17]. The analogy to typical quantum phase transitions was supported further in [18] by confirming that quantum correlations between different parties of the system, quantified by appropriate entanglement entropies, are also power-law divergent in the transition point [19][20][21].…”

“…In this work, we have explored the dynamical properties of the interacting system of a few fermions driven through the critical transition by time-varying external potential. In contrast to previous studies [17,18], we focused on diabatic transition in which the system can be dynamically excited to other many-body states. By detailed investigation of temporal many-body spectra, we argued that a whole driving process can be welldescribed in significantly reduced Hilbert space spanned by only a few of the lowest many-body states.…”

“…On the quantum level, it means, that a considered many-body system may continuously switch between substantially different ground states when it is driven through its critical point. One of such possibilities was found recently for two-component one-dimensional systems of a few strongly interacting fermions [17,18]. It was argued, that in the vicinity of infinite inter-component repulsions, along with changing shape of external confinement, the many-body ground state undergoes a critical transition between two different spatial orderings.…”

“…The case of adiabatic transition (τ → ∞) can be easily reconstructed from detailed studies on the groundstate properties of the system [18]. It is known that in this case, the entropy rapidly increases near the critical shape of the trap, signaling a strong enhancement of inter-component correlations.…”