# Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang–Baxter system

Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang–Baxter system In this paper, we investigate the ground-state fidelity and fidelity susceptibility in the many-body Yang–Baxter system and analyze their connections with quantum phase transition. The Yang–Baxter system was perturbed by a twist of $$e^{i\varphi }$$ e i φ at each bond, where the parameter $$\varphi$$ φ originates from the q-deformation of the braiding operator U with $$q = e^{-i\varphi }$$ q = e - i φ (Jimbo in Yang–Baxter equations in integrable systems, World Scientific, Singapore, 1990), and $$\varphi$$ φ has a physical significance of magnetic flux (Badurek et al. in Phys. Rev. D 14:1177, 1976). We test the ground-state fidelity related by a small parameter variation $$\varphi$$ φ which is a different term from the one used for driving the system toward a quantum phase transition. It shows that ground-state fidelity develops a sharp drop at the transition. The drop gets sharper as system size N increases. It has been verified that a sufficiently small value of $$\varphi$$ φ used has no effect on the location of the critical point, but affects the value of $$F(g_{c},\varphi )$$ F ( g c , φ ) . The smaller the twist $$\varphi$$ φ , the more the value of $$F(g_{c},\varphi )$$ F ( g c , φ ) is close to 0. In order to avoid the effect of the finite value of $$\varphi$$ φ , we also calculate the fidelity susceptibility. Our results demonstrate that in the Yang–Baxter system, the quantum phase transition can be well characterized by the ground-state fidelity and fidelity susceptibility in a special way. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang–Baxter system

, Volume 16 (1) – Dec 18, 2016
9 pages

/lp/springer_journal/quantum-phase-transition-quantum-fidelity-and-fidelity-susceptibility-8Vh9QLgTsB
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1487-5
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we investigate the ground-state fidelity and fidelity susceptibility in the many-body Yang–Baxter system and analyze their connections with quantum phase transition. The Yang–Baxter system was perturbed by a twist of $$e^{i\varphi }$$ e i φ at each bond, where the parameter $$\varphi$$ φ originates from the q-deformation of the braiding operator U with $$q = e^{-i\varphi }$$ q = e - i φ (Jimbo in Yang–Baxter equations in integrable systems, World Scientific, Singapore, 1990), and $$\varphi$$ φ has a physical significance of magnetic flux (Badurek et al. in Phys. Rev. D 14:1177, 1976). We test the ground-state fidelity related by a small parameter variation $$\varphi$$ φ which is a different term from the one used for driving the system toward a quantum phase transition. It shows that ground-state fidelity develops a sharp drop at the transition. The drop gets sharper as system size N increases. It has been verified that a sufficiently small value of $$\varphi$$ φ used has no effect on the location of the critical point, but affects the value of $$F(g_{c},\varphi )$$ F ( g c , φ ) . The smaller the twist $$\varphi$$ φ , the more the value of $$F(g_{c},\varphi )$$ F ( g c , φ ) is close to 0. In order to avoid the effect of the finite value of $$\varphi$$ φ , we also calculate the fidelity susceptibility. Our results demonstrate that in the Yang–Baxter system, the quantum phase transition can be well characterized by the ground-state fidelity and fidelity susceptibility in a special way.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 18, 2016

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