Effects of Spontaneous Symmetry Break in the Origin of Non-analytic Behavior of Entanglement at Quantum Phase Transitions

Abstract

We present an example where spontaneous symmetry breaking (SSB) may affect not only the behavior of the entanglement at Quantum Phase Transitions (QPT), but also the origin of its non-analyticity. In particular, in the XXZ model, we study the non-analyticities in the concurrence between two spins, which was claimed to be accidental since it had its origin in the optimization involved in the concurrence definition. We show that when one takes into account the effect of the SSB, even though the values of the entanglement measure does not change, the origin of the non-analytical behavior changes. The non-analytical behavior is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the SSB not observed before. We also show that the value of entanglement between one site and the rest of the chain changes after taking into account the SSB.

Entanglement scaling at first order quantum phase transitions

“…For instance, in the spin-1/2 XXZ chain, at the 1QPT between the ferromagnetic and critical phase, the concurrence is a function of the energy at the critical point and it remains continuous in the thermodynamic limit while its first derivative is discontinuous [19,20]. For the same transition, it has been shown that a symmetry breaking in the ferromagnetic phase also modifies the origin of the non-analytic behavior of the concurrence [21]. In [22], a three-body local Hamiltonian model was presented in which the pairwise concurrence is non analytical in the absence of any QPT [22].…”

“…In the spin-1/2 XXZ model, for example, there is a continuous C and a discontinuous derivative along the 1QPT between the ferromagnetic and critical phase [19]. For the same transition, it has been shown that a symmetry breaking in the ferromagnetic phase also modifies the origin of the non-analytic behavior of the concurrence [20]. Also, a non-analytic C in the absence of a QPT for a model with three body interactions has been reported in [21].…”

Entanglement and dynamical phase transition in a spin-orbit-coupled Bose-Einstein condensate

“…As one of the most intriguing features of quantum mechanics, quantum entanglement has been regarded as a key resource to detect and understand properties of complex many-body systems. For instance, recently a great deal of effort has been devoted to establishing a deep understanding about quantum phase transitions (QPTs) via the examination of their entanglement behaviors [1][2][3][4][5][6][7][8][9][10][11]. Quantum phase transition is defined as a transition between distinct ground states of quantum many-body systems when a controlled parameter in the Hamiltonian crosses a critical point [12].…”