The physics of three simple solvable quantum models is reviewed in some detail: the spin 1/2 XX chain (and the related dilute spinless Fermi gas), the Ising chain in a transverse field, and the large N limit of the O(N) quantum rotor model. A unified scaling description is presented, and the many common features among the models are highlighted. The crossovers in these systems are the simplest ...

We propose the implementation of a digital quantum simulation of spin chains coupled to bosonic field modes in superconducting circuits. Gates with high fidelities allows one to simulate a variety of Ising magnetic pairing interactions with transverse field, Tavis-Cummings interaction between spins and a bosonic mode, and a spin model with three-body terms. We analyze the feasibility of the imp...

We investigate the quantum phase transition in the random transverse-field Ising model under the influence of Ohmic dissipation. To this end, we numerically implement a strong-disorder renormalization-group scheme. We find that Ohmic dissipation destroys the quantum critical point and the associated quantum Griffiths phase by smearing. Our results quantitatively confirm a recent theory [Phys. R...

A Green’s function formalism is used to calculate the spectrum of excitations of two neighboring impurities implanted in a semi-infinite ferromagnetic. The equations of motion for the Green’s functions are determined in the framework of the Ising model in a transverse field and results are given for the effect of the exchange coupling, position and orientation of the impurities on the spectra o...

Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of increasing the temperature and the transverse field on the wetting and layering transitions is outlined. —...

We introduce an operator fidelity and propose to use its susceptibility for characterizing the sensitivity of quantum systems to perturbations. Two typical models are addressed: One is the transverse Ising model exhibiting a quantum phase transition, and the other is the one-dimensional Heisenberg spin chain with next-nearest-neighbor interactions, which has the degeneracy. It is revealed that ...

We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with...

The conventional Quantum Adiabatic Algorithm(QAA) encounters problem of exponential closing gaps when applied to a restrictred class of MAX 2-SAT problem. This exponential closing gap is exactly caused by the phase transition in random transverse Ising spin model predicted by Fisher et.al. [1, 2]. We propose some strategy that will hopefully avoid this exponential closing gap, promising a polyn...

We study the quantum phase transition in the one-dimensional Ising model at zero temperature. As the strength g of the transverse field is changed, the system undergoes a quantum phase transition from an ordered to a disordered phase, characterized by spontaneous magnetization in the z-direction. We apply the standard technique of finite-size scaling in statistical mechanics to detect the natur...

We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with the interface width. After quenching to a homogeneous critical system, the entropy grows logarithmically in time in the XX model, but quadratically in the tr...