The critical properties of the one-dimensional transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility is used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J2, we calculated the fidelity susceptibility as a function of the transverse field (Bx) and the strength of the longitudinal field (Bz). The phase diagram in the (Bx,Bz)-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For Bx < 1, we observed an antiferromagnetic phase for small values of Bz and a paramagnetic phase for large values of Bz. For Bx > 1 and low Bz, we found a disordered phase that undergoes a phase transition to a paramagnetic phase for large values of Bz.
The inner product between the ground-state eigenvectors with proximate interaction parameters, namely, the fidelity, plays a significant role in the quantum dynamics. In this paper, the critical behaviors of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum (transverse-field) Ising model are investigated by means of the numerical diagonalization method; the former susceptibility has been investigated rather extensively. The critical exponents for these fidelity susceptibilities are estimated as α^{(t)}_F=0.752(24) and α^{(h)}_F=1.81(13), respectively. These i…
Comparison of the ferromagnetic Blume-Emery-Griffiths model and the AF spin-1 longitudinal Ising model at low temperature
我们推导出了在外加纵向磁场作用下一维Blume-Emery-Griffiths（BEG）模型和一维交错模型的Helmholtz自由能（HFE）.我们详细讨论了该模型的铁磁版本的热力学行为，该模型在低温下的磁化强度的$z$分量中表现出与磁场相关的平台。我们还研究了它的比热和熵的行为，每个网站，在有限的温度。计算了铁磁BEG模型相图中不同相的分界线上基态的简并度，扩展了[S.M. de Souza和M.T. Magazz，J. of Mag. and Mag. Mat. {354}（2014）205]。我们探讨了在$T=0$相图的平等，与$\frac{K}{|J|} = -2$的铁磁BEG模型和自旋1 AF伊辛模型的$\frac{D}{|J|} > \frac{1}{2}$的影响。
We study quasi-particle dynamics in a quasi-periodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasi-particle spreading under a field chosen randomly from binary values $\pm h$ at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasi-particle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvecto…
We investigate the operator growth dynamics of the transverse field Ising spin chain in one dimension as varying the strength of the longitudinal field. An operator in the Heisenberg picture spreads in the extended Hilbert space. Recently, it has been proposed that the spreading dynamics has a universal feature signaling chaoticity of underlying quantum dynamics. We demonstrate numerically that the operator growth dynamics in the presence of the longitudinal field follows the universal scaling law for one-dimensional chaotic systems. We also find that the operator growth dynamics satisfies a c…
Motivated by the compound ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider the Ising chain with random couplings and in the presence of simultaneous random transverse and longitudinal fields, and study its low-energy properties at zero temperature by the strong disorder renormalization group approach. In the absence of longitudinal fields, the system exhibits a quantum-ordered and a quantum-disordered phase separated by a critical point of infinite disorder. When the longitudinal random field is switched on, the ordered phase vanishes and the trajectories of the renormalization group are attr…
We show that the Temperley-Lieb algebra is constructed from the generators of the transverse-field Ising-type bond algebra. It is also shown that, when we take the representation of the generators to the one-dimensional transverse-field Ising model, then the Temperley-Lieb algebra constructed on three consecutive bond generators becomes the XXZ model. Furthermore, we obtain several integrable spin systems from other representations for the bond generators.
We study the out-of-time-order correlation (OTOC) of the Floquet transverse Ising model and use it to verify the phase diagram of the system. First, we present the exact analytical solution of the transverse magnetization OTOC using the Jorden-Wigner transformation. We calculate the speed of correlation propagation and analyze the behavior of the revival time with the separation between the observables. In order to get the phase structure of the Floquet transverse Ising system, we use the longitudinal magnetization OTOC as it is known to serve as an order parameter of the system. We show the p…
Quantum many-body scar (QMBS) and quantum integrability(QI) have been recognized as two distinct mechanisms for the breakdown of eigenstate thermalization hypothesis(ETH) in an isolated system. In this work, we reveal a smooth route to connect these two ETH-breaking mechanisms in the Ising chain with transverse and longitudinal fields. Specifically, starting from an initial Ising anti-ferromagnetic state, we find that the dynamical system undergoes a smooth non-thermal crossover from QMBS to QI by changing the Ising coupling($J$) and longitudinal field($h$) simultaneously while keeping their r…
The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in $d$-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective non-integrable model with $d\geq2$ as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for non-equi…
On the coupling constant bounds implying area decay of Wilson loop for Z2 lattice gauge theories with Wilson action Boltzmann factor given by bond variables described by transverse Ising model
