스핀 글라스

노트

말뭉치

1. A diverse collection of condensed matter systems, such as ferroelectrics (11) and magnetic spin glasses (12), can be described by the TFIM.
2. Spin glasses are frustrated magnetic systems and a hallmark of their “glassiness” is the presence of a rugged energy landscape with many local minima.
3. A phenomenological theory of the ordered phase of short-range quantum Ising spin glass is developed in terms of droplet excitations, and presented in detail.
4. The magnetic disorder of spin glass compared to a ferromagnet is analogous to the positional disorder of glass (left) compared to quartz (right).
5. The term "glass" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass, e.g., a window glass.
6. It is the time dependence which distinguishes spin glasses from other magnetic systems.
7. Upon reaching T c , the sample becomes a spin glass and further cooling results in little change in magnetization.
8. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems.
9. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem.
10. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem.
11. An algorithm which is essentially a quantum walk on a spin glass, although presented using different terminology, has been analysed by Hastings (2019).
12. The spin glass, a network of frustrated spins with random bonds, exhibits a low temperature, non-ergodic phase with all spins frozen in a complex metastable state.
13. The spin glass and MBL phases have qualitative similarities; both are characterized by a breakdown of the ergodic behavior on which the foundations of statistical mechanics rest.
14. Both models show that the spin glass phase is accompanied by MBL, but that the MBL phase persists beyond the limit of the glass phase into paramagnetic phases.
15. In this phase the eigenstates are delocalized, the ETH is obeyed, and there is no spin glass order.
16. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins.
17. Several thermodynamic quantities are calculated numerically as well as spin self-interaction and spin glass order parameter for spin S=1/2.
18. Detailed discussion on quantum spin glasses and its application in solving combinatorial optimization problems is required for better understanding of quantum annealing concepts.
19. Fulfilling this requirement, the book highlights recent development in quantum spin glasses including Nishimori line, replica method and quantum annealing methods along with the essential principles.
20. Classical spin models from ferromagnetic spin systems to spin glasses 3.
21. The Ising spin glass model in a transverse field has a zero temperature phase transition driven solely by quantum fluctuations.
22. At the Conference on “Complex Quantum Systems out of Equilibrium” in Murcia, Spain I presented my latest work with Dmitry Abanin on the relation between MBL and spin glasses.
23. We show that a third, intermediate, state can emerge in a long-range one-dimensional spin glass under the applica- tion of a transverse field.
24. At small applied fields and low temperatures the spin glass order remains, as characterized by the Edwards-Anderson order parameter.
25. The ”quantum spin glass” is therefore neither ergodic, nor many-body localized.
26. In its simplest form, the emergent hierarchical order in spin glasses is mimicked by Derrida’s hierarchical models, which I will briefly review.
27. The main aim of this talk then concerns the fate of the spin glass phase under the addition of a constant perpendicular magnetic field.
28. The underlying principle of erasure of hierarchical spin glass order will be discussed.
29. In this talk I will discuss the possibility of many-body localization (MBL) in a model of quantum spin glass, namely, the quantum Sherrington-Kirkpatrick (SK) model.
30. Yet, the model captures the essential properties of the spin glass: its qualitative features directly apply to much more general models, including Sherrington-Kirkpatrick.
31. Solving spin glass models is a complex, often NP-hard, task.
32. A comparison with recent theoretical and experimental data in spin glass is made.
33. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases.
34. As a result, spin glass (6⇓⇓–9), charge glass (or charge-cluster glass) (10, 11), and superconducting vortex liquid/glass (12) all occur in the x-H-T phase diagram near the SIT.
35. The region is located within the thermodynamic spin glass phase.
36. These earlier works point to the necessity to examine a finite-connectivity quantum spin glass, in search of MBL.
37. In this section, we apply the previously described methods to the transverse-field Ising spin glass Hamiltonian (2.1).
38. Here, we immediately face an issue: the computation of the forward approximation is obstructed by the fact that the spin glass term has highly degenerate energy levels.