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日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Physical Review B

Annual review of condensed matter physics

Journal of Statistical Mechanics: theory and experiment

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10--20 times speedup.

Self-learning Monte Carlo method

United States. Department of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering. (award DE-SC0010526)

http://dspace.mit.edu/openaccess-disseminate/1721.1/106311

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl_{3} and Na_{2}IrO_{3}, having an effective S=1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe_{3}, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds.

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S = 3 / 2

We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub ``cumulative update'', to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.

Self-learning Monte Carlo method and cumulative update in fermion systems

Recent work has used a U(1) gauge theory to describe the physics of Fermi pockets in the presence of fluctuating spin density wave order. We generalize this theory to an arbitrary band structure and ordering wave vector. The transition to the large Fermi-surface state, without pockets induced by local spin density wave order, is described by embedding the U(1) gauge theory in a SU(2) gauge theory. The phase diagram of the SU(2) gauge theory shows that the onset of spin density wave order in the Fermi liquid occurs either directly, in the framework discussed by Hertz, or via intermediate non-Fermi-liquid phases with Fermi surfaces of fractionalized excitations. We discuss application of our results to the phase diagram of the cuprates.

/pdf/fluctuating-spin-density-waves-in-metals-54rqunrwlu.pdf

Yang Qi

Papers

Self-learning Monte Carlo method

Self-learning Monte Carlo method

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S = 3 / 2

Self-learning Monte Carlo method and cumulative update in fermion systems

Fluctuating spin density waves in metals