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Register a new userFidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field
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Added by
Yoshihiro Nishiyama
Publication date
2020
fields
Physics
and research's language is
English
Authors
Yoshihiro Nishiyama
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The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field $H=itheta T /2$ with the topological angle $theta$ 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 $theta$, we investigated the phase transition via the fidelity susceptibility $chi_F^{(theta)}$. The fidelity susceptibility $chi_F^{(theta)}$ 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 $theta=pi$. We cast the $chi_F^{(theta)}$ data into the crossover-scaling formula with $delta theta = pi-theta$ scaled carefully. Our result for the crossover exponent $phi$ 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 $theta=pi$.
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The square-lattice Ising antiferromagnet subjected to the imaginary magnetic field $H=i theta T /2 $ with the topological angle $theta$ and temperature $T$ was investigated by means of the transfer-matrix method. Here, as a probe to detect the order-disorder phase transition, we adopt an extended version of the fidelity susceptibility $chi_F^{(theta)}$, which makes sense even for such a non-hermitian transfer matrix. As a preliminary survey, for an intermediate value of $theta$, we examined the finite-size-scaling behavior of $chi_F^{(theta)}$, and found a pronounced signature for the criticality; note that the magnetic susceptibility exhibits a weak (logarithmic) singularity at the Neel temperature. Thereby, we turn to the analysis of the power-law singularity of the phase boundary at $theta=pi$. With $theta-pi$ scaled properly, the $chi_F^{(theta)}$ data are cast into the crossover scaling formula, indicating that the phase boundary is shaped concavely. Such a feature makes a marked contrast to that of the mean-field theory.
We study the fidelity susceptibility in the two-dimensional(2D) transverse field Ising model and the 2D XXZ model numerically. It is found that in both models, the fidelity susceptibility as a function of the driving parameter diverges at the critical points. The validity of the fidelity susceptibility to signal for the quantum phase transition is thus verified in these two models. We also compare the scaling behavior of the extremum of the fidelity susceptibility to that of the second derivative of the ground state energy. From those results, the theoretical argument that fidelity susceptibility is a more sensitive seeker for a second order quantum phase transition is also testified in the two models.
We have made substantial advances in elucidating the properties of the susceptibility of the square lattice Ising model. We discuss its analyticity properties, certain closed form expressions for subsets of the coefficients, and give an algorithm of complexity O(N^6) to determine its first N coefficients. As a result, we have generated and analyzed series with more than 300 terms in both the high- and low-temperature regime. We quantify the effect of irrelevant variables to the scaling-amplitude functions. In particular, we find and quantify the breakdown of simple scaling, in the absence of irrelevant scaling fields, arising first at order |T-T_c|^{9/4}, though high-low temperature symmetry is still preserved. At terms of order |T-T_c|^{17/4} and beyond, this symmetry is no longer present. The short-distance terms are shown to have the form (T-T_c)^p(log|T-T_c|)^q with p ge q^2. Conjectured exact expressions for some correlation functions and series coefficients in terms of elliptic theta functions also foreshadow future developments.
We use numerical transfer-matrix methods, together with finite-size scaling and conformal invariance concepts, to discuss critical properties of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with couplings which are antiferromagnetic along at least one lattice axis, in a uniform external field. We focus mainly on the shape of the phase diagram in field-temperature parameter space; in order to do so, both the order and universality class of the underlying phase transition are examined. Our results indicate that, in one particular case studied, the critical line has a horizontal section (i.e. at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the reentrant features predicted in earlier studies.
We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr{e} model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr{e} model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr{e} model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in near future.
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