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Register a new userImaginary-field-driven phase transition for the $2$D Ising antiferromagnet: A fidelity-susceptibility approach
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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 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.
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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 $theta=pi$.
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.
The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied both to the ground-state and non-zero temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-$1/2$ XXZ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.
We studied the dynamic response and stochastic resonance of kinetic Ising spin system (ISS), subject to the joint external field of weak sinusoidal modulation and stochastic white-noise, through solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows the occurrence of characteristic stochastic resonance as well as nonequilibrium dynamic phase transition (NDPT) when the frequency and amplitude h0 of driving field, the temperature t of the system and noise intensity D attain a specific accordance in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to zero and unit dynamic order parameter. We also figured out the NDPT boundary surface of the system which separates the dynamic paramagnetic and dynamic ferromagnetic phase in the 3D parameter space of h0~t~D. An intriguing dynamical ferromagnetic phase with an intermediate order parameter at 0.66 was revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. Our primary result indicates that the intermediate order dynamical ferromagnetic phase is dynamic metastable in nature and owns a peculiar characteristic in its stability and response to external driving field when compared with fully order dynamic ferromagnetic phase.
We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.
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