2017/06/30 by Sudip Mukherjee, Atanu Rajak, Bikas K. Chakrabarti +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Ergodic theory #Hamiltonian (control theory) #Mathematical analysis #Mathematics #Physics #Quantum #Quantum algorithm #Quantum annealing #Quantum mechanics #Scaling #Spin glass #Spin model #Statistical physics #Theoretical and Computational Physics #Thermodynamic limit #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.97.022146
published as Phys. Rev. E 97, 022146 (2018) · 6 Pages, 10 figures
arxiv created 2018/02/28 · openalex publication_date 2018/02/28 · arxiv updated 2018/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.