Numerical simulations of condensed matter: From eigensolvers to quantum spin glass

S. S. Makler, E. V. Anda

Sheng Feng

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite momenta, which was recently proposed to avoid the difficulties of a zero momentum quantity, for capturing the spin glass phase transition. Unfortunately, this new indicator is fairly noisy, so a large pool of samples at low temperature and small external field are needed to generate results with a sufficiently small statistical error for analysis. We thus implement the Monte Carlo method using graphics processing units to drastically speed up the simulation. We confirm previous findings that conventional indicators for the spin glass transition, including the Binder ratio and the correlation length do not show any indication of a transition for rather low temperatures. However, the ratio of spin glass susceptibilities does show crossing behavior, albeit a systematic analysis is beyond the reach of the present data. This reveals the difficulty with current numerical methods and computing capability in studying this problem. One of the fundamental challenges of theoretical condensed matter physics is the accurate solution of quantum impurity models. By taking expansion in the hybridization about an exactly solved local limit, one can formulate a quantum impurity solver. We implement the hybridization expansion quantum impurity solver on Intel Xeon Phi accelerators, and aim to apply this approach on the Dynamic Hubbard Models.

J.D. Doll, James E. Gubernatis

R. Harris, Yuki Sato, A. J. Berkley +28 more

Understanding magnetic phases in quantum mechanical systems is one of the essential goals in condensed matter physics, and the advent of prototype quantum simulation hardware has provided new tools for experimentally probing such systems. We report on the experimental realization of a quantum simulation of interacting Ising spins on three-dimensional cubic lattices up to dimensions 8 × 8 × 8 on a D-Wave processor (D-Wave Systems, Burnaby, Canada). The ability to control and read out the state of individual spins provides direct access to several order parameters, which we used to determine the lattice's magnetic phases as well as critical disorder and one of its universal exponents. By tuning the degree of disorder and effective transverse magnetic field, we observed phase transitions between a paramagnetic, an antiferromagnetic, and a spin-glass phase.

Yoshihiko Nonomura, Kiyoshi Katō, Hitoshi Asakawa +3 more

Eduard J. Braun

Frustration, bond disorder, and long-range interactions can produce novel, highly nontrivial phases of matter. This thesis investigates a bond-disordered, dipolar-interacting XY spin model, studied through both numerical simulations and experiments on a Rydberg quantum simulator. Three major results are achieved: (i) We analyze energetic-magnetic hysteresis in two disorder configurations, and find pronounced hysteresis in the strongly disordered configuration for low energies. This is a first experimental evidence of energetic-magnetic hysteresis in putative isolated glasses. (ii) We develop an extension of the generalized Kibble-Zurek mechanism for reverse quenches, which allows to characterize putative spin glass quantum phase transitions by global magnetization measurements. We validate this extension numerically exactly for one-dimensional systems, and subsequently experimentally extract a critical exponent consistent with spin glass critical exponents measured in other systems. This is a first tentative experimental evidence of a spin glass phase in an isolated dipolar interacting spin system. (iii) We studied time reversal on a Rydberg quantum simulator and showed numerically that, in bond-disordered power-law interacting models, time-reversal–based protocols reveal a localization mechanism distinct from conventional many-body localization at finite sizes.