Abstract
We investigate the quantum phase transition of the Su-Schrieffer-Heeger (SSH) model by inspecting the two-site entanglements in the ground state. It is shown that the topological phase transition of the SSH model is signified by a nonanalyticity of local entanglement, which becomes discontinuous for finite even system sizes, and that this nonanalyticity has a topological origin. Such a peculiar singularity has a universal nature in one-dimensional topological phase transitions of noninteracting fermions. We make this clearer by pointing out that an analogous quantity in the Kitaev chain exhibiting the identical nonanalyticity is the local electron density. As a byproduct, we show that there exists a different type of phase transition, whereby the pattern of the two-site entanglements undergoes a sudden change. This transition is characterised solely by quantum information theory and does not accompany the closure of the spectral gap. We analyse the scaling behaviours of the entanglement in the vicinities of the transition points.
Highlights
Modern understanding of quantum phase transition has been significantly enriched by incorporating the concept of entanglement[7, 8, 11,12,13,14,15,16,17]
The aim of this paper is to investigate the quantum phase transition of one-dimensional topological models in terms of the two-site entanglements, namely, the concurrences, in the ground state[18]
As we have addressed in Introduction, this singularity is not originated from the nonanalyticity of the ground-state wave function and the transition is not a quantum phase transition in the conventional sense
Summary
Modern understanding of quantum phase transition has been significantly enriched by incorporating the concept of entanglement[7, 8, 11,12,13,14,15,16,17]. We first derive an analytic formula for the concurrence between any two sites and show that in the thermodynamic limit, the first derivative of the concurrence between adjacent sites with respect to λ diverges logarithmically at the critical point λ0 = 0, the exact form of which is derived This result is similar to the case of the symmetry-breaking quantum phase transition in the Heisenberg spin chain[11, 12]. Due to the topological origin, there exists an interesting difference: for finite even N, the concurrence is discontinuous at λ = λ0 with a gap inversely proportional to N, while it remains analytic for odd N This feature contrasts with the case of symmetry-breaking quantum phase transitions wherein the nonanalyticity appears only in the thermodynamic limit. We show that for the Kitaev chain[4], the local electron density is an analogous quantity exhibiting the identical nonanalyticity at the critical point: its first derivative, i.e., the local compressibility, diverges logarithmically in the thermodynamic limit and it is discontinuous for finite even system sizes
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
