In random quantum magnets, like the random transverse Ising chain, the low energy excitations are localized in rare regions and there are only weak correlations between them. It is a fascinating question whether these correlations are completely irrelevant in the sense of the renormalization group. To answer this question, we calculate the distribution of the excitation energy of the random transverse Ising chain in the disordered Griffiths phase with high numerical precision by the strong disorder renormalization group method and - for shorter chains - by free-fermion techniques. Asymptotically, the two methods give identical results, which are well fitted by the Fréchet limit law of the extremes of independent and identically distributed random numbers. Given the finite size corrections, the two numerical methods give very similar results, but they differ from the correction term for uncorrelated random variables. This fact shows that the weak correlations between low-energy excitations in random quantum magnets are not entirely irrelevant.
The critical behavior of the random transverse-field Ising model in finite dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in $d=1,2$ and $3$ dimensions. At the critical point an algebraic decay of the form $\sim r^{-η_t}$ is found, with a decay exponent being approximately $η_t \approx 2+2d$. In $d=1$ the r…
Assessment of the RE(OH)3 Ising-like Magnetic Materials as Possible Candidates for the Study of Transverse-Field-Induced Quantum Phase Transitions
LiHo $_x$ Y $_{1-x}$ F $_4$ Ising磁性材料经受垂直于Ho $^{3+}$ Ising方向的磁场$B_x$，在过去的二十年中已经显示出许多非常有趣的热力学和磁性现象。不幸的是，除了可以由横向场伊辛模型描述的LiHo $_x$ Y $_{1-x}$ F $_4$之外的其他磁性材料的可用性仍然非常有限。正是在这种情况下，我们在这里使用平均场理论来研究的适用性Ho（OH）$_{3}$，Dy（OH）$_{3}$和Tb（OH）$_3$绝缘六方偶极类伊辛铁磁体的研究量子相变所引起的磁场，$B_x$，施加垂直于伊辛自旋方向。从我们的计算，我们估计的临界横向场，$B_{x}^{c}$，破坏铁磁秩序在零温度下为$B_{x}^{c}=$ 4.35 T，$B_{x}^{c}=$ 5.03 T和$B_{x}^{c}=$ 54.81 T的Ho（OH）$_{3}$，Dy（OH）$_{3}$和Tb（OH）$_{3}$，分别。计算结果表明，Ho（OH）$_{3}$和Dy（OH）$_{3}$以及它们的Y $^{3+}$抗磁稀释变体Ho $_{x}$ Y $_{1-x}$（OH）$_{3}$和Dy $_{x}$ Y $_{1-x}$（OH）$_{3}$是研究硬轴（类伊辛）磁性材料中横向场诱导量子涨落效应的潜在有趣体系.
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…
Recently, Heim, Ronnow, Isakov and Troyer [Science 348 (2015) 215] have reported that Monte Carlo simulations for the Ising spin glass model on the square lattice in the physically relevant continuous-imaginary-time limit do not show superiority of quantum annealing (QA) using transverse field against classical annealing (CA). Although the QA schedule that they had used has been using conventionally, however the QA schedule mathematically has no guarantee that the used schedule is the best QA schedule for performance of optimization. We propose a new QA schedule for studying transverse-field-b…
We investigate the transverse field Ising model subject to a two-step periodic driving protocol and quasiperiodic modulation of the Ising couplings. Analytical results on the phase boundaries associated with Majorana edge modes and numerical results on the localization of single-particle excitations are presented. The implication of a region with fully localized domain-wall-like excitations in the parameter space is eigenstate order and exact spectral pairing of Floquet eigenstates, based on which we conclude the existence of time crystals. We also examine various correlation functions of the …
Based on a relationship with continuous-time random walks discovered by Iglói, Turban, and Rieger [Phys. Rev. E {\bf 59}, 1465 (1999)], we derive exact lower and upper bounds on the lowest energy gap of open transverse-field Ising chains, which are explicit in the parameters and are generally valid for arbitrary sets of possibly random couplings and fields. In the homogeneous chain and in the random chain with uncorrelated parameters, both the lower and upper bounds are found to show the same finite-size scaling in the ferromagnetic phase and at the critical point, demonstrating the ability of…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories (paths). A key feature, novel in the context of similar algorithms, is the explicit separation of the classical and quantum parts of the distributions. Numerical simulations show accurate results in comparison with the sampled solution of the cavity equations, the exact diagonalization of the Hamiltonian (when possible) and other approximate inference methods in …
Random transverse and longitudinal field Ising chains
Szeged University（塞格德大学）；HUN-REN Wigner Research Centre for Physics, Institute for Solid State Physics and Optics（匈牙利研究与教育网络维格纳物理研究中心固体物理与光学研究所）；Northwestern University（西北大学）
It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant space in the infinite volume limit. The weak Fortuin-Kasteleyn-Ginibre property in this model and the Ghirlanda-Guerra identities in artificial models in a path integral representation based on the Lie-Trotter-Suzuki formula enable us to extend Chatterjee's proof for the random field Ising model to the quantum model.
