Transverse Ising Chain (Pure System)

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Robin B. Stinchcombe

A phenomenological scaling method is used to obtain exact renormalisation-group transformations for pure and bond-diluted transverse Ising chains at zero temperature. An exact discussion is given of basic critical properties of the two systems, and the exponents characterising the quantum and percolative critical behaviour of the correlation length of the dilute chain are found to be nu lambda = nu rho =1.

Sei Suzuki, Hiroki Oshiyama, Naokazu Shibata

We study quantum annealing of pure and random transverse Ising chains that are coupled to boson baths, using a novel numerical method based on the combination of the quasi-adiabatic propagation path integral (QUAPI) and the matrix product state (MPS) formalisms. We present numerical results on systems up to 64 spins and conclude that the baths disturb quantum annealing of pure and random Ising chains. The numerical method to compute the reduced density matrix is described in detail.

Cécile Monthus

The Dyson hierarchical version of the quantum Ising chain with Long-Ranged power-law ferromagnetic couplings J ( r ) ∝ r −1− σ and pure or random transverse fields is studied via real-space renormalization. For the pure case, the critical exponents are explicitly obtained as a function of the parameter σ , and are compared with previous results of other approaches. For the random case, the RG rules are numerically applied and the critical behaviors are compared with previous strong disorder renormalization results.