Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field Yoshihiro Nishiyama a Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan
Received 23 May 2020 / Received in final form 18 July 2020 / Accepted 29 July 2020 Published online 14 September 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field H = iθT /2 with the “topological” angle θ and temperature T was investigated numerically. In order to treat such a complex-valued statistical weight, we employed the transfer-matrix method. As a probe to detect the order–disorder phase transition, we resort to an extended version of the fidelity F , which makes sense even for such a non-Hermitian transfer matrix. As a preliminary survey, for an intermediate value of θ, (θ) (θ) we investigated the phase transition via the fidelity susceptibility χF . The fidelity susceptibility χF exhibits a notable signature for the criticality as compared to the ordinary quantifiers such as the magnetic susceptibility. Thereby, we analyze the end-point singularity of the order–disorder phase boundary at θ = π. (θ) We cast the χF data into the crossover-scaling formula with δθ = π − θ scaled carefully. Our result for the crossover exponent φ seems to differ from the mean-field and square-lattice values, suggesting that the lattice structure renders subtle influences as to the multi-criticality at θ = π.
1 Introduction The concept of fidelity has been developed in the field of the quantum dynamics [1–4]. The fidelity F is given by the overlap F = |hθ|θ + ∆θi| between the ground states, |θi and |θ + ∆θi, with the proximate interaction parameters, θ and θ + ∆θ, respectively; see references [5–7] for a review. Meanwhile, it turned out that it detects the quantum phase transitions rather sensitively [8–14]. Actu2 F |∆θ=0 (N : ally, the fidelity susceptibility χF = − N1 ∂∆θ number of lattice points) exhibits a pronounced signature for the criticality as compared to the ordinary quantifiers such as the magnetic susceptibility [15]. Additionally, the fidelity susceptibility does not rely on any presumptions as to the order parameter concerned [16], and it is less influenced by the finite-size artifacts [11]. As would be apparent from the definition, the fidelity F = |hθ|θ + ∆θi| fits the numerical diagonalization method, which admits the ground-state vector |θi explicitly. However, it has to be mentioned that the fidelity is accessible via the quantum Monte Carlo method [15–18] and the experimental observations [19–21] as well. In this paper, by the agency of the fidelity, we investigate the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field. To cope with the complexvalued statistical weight, we employed the transfer-matrix method [22,23] through resorting to the extended versio
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