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Register a new userSpectroscopic Properties of Polarons in Strongly Correlated Systems by Exact Diagrammatic Monte Carlo Method
مؤثرات السپكتروسكوبية للبولارون في النظم المرتبطة بشدة بواسطة طريقة مونتي كارلو الرسمية الدقيقة
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Added by
Andrei Mishchenko S
Publication date
2007
fields
Physics
and research's language is
English
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نقدم في هذا المقال التقدم الحديث في فهم الحالات الأساسية والمثيرة للإشعاع الذي يرتبط بالإلكترون والفونون باستخدام طرق جديدة من الحساب الذهني الأحادي والتحسين الأحصائي، التي تتيح حساب الدالة الخضراء الماتسوباري في الأوقات الخيالية والاستمرار التحليلي بدون تشخيص إلى الترددات الحقيقية. نقدم نتائج عددية دقيقة حول خصائص الحالة الأساسية، ودالة اللايمان وموازنة الإشعاع البصري للنظم المرتبطة بشدة مختلفة: البولارون الفروليخ، والإكسيتون البولارون الراشبا-بيكار، والبولارون الجان-تلر الخاص، والإكسيتون، والثقب المتفاعل مع الفونون في النموذج t-J.
We present recent advances in understanding of the ground and excited states of the electron-phonon coupled systems obtained by novel methods of Diagrammatic Monte Carlo and Stochastic Optimization, which enable the approximation-free calculation of Matsubara Green function in imaginary times and perform unbiased analytic continuation to real frequencies. We present exact numeric results on the ground state properties, Lehmann spectral function and optical conductivity of different strongly correlated systems: Frohlich polaron, Rashba-Pekar exciton-polaron, pseudo Jahn-Teller polaron, exciton, and interacting with phonons hole in the t-J model.
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The diagrammatic Monte Carlo (Diag-MC) method is a numerical technique which samples the entire diagrammatic series of the Greens function in quantum many-body systems. In this work, we incorporate the flat histogram principle in the diagrammatic Monte method and we term the improved version Flat Histogram Diagrammatic Monte Carlo method. We demonstrate the superiority of the method over the standard Diag-MC in extracting the long-imaginary-time behavior of the Greens function, without incorporating any a priori knowledge about this function, by applying the technique to the polaron problem
We present a simple trick that allows to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models. With our approach one achieves superior performance compared to Diagrammatic Monte Carlo, while rendering the algorithmic part dramatically simpler. As we consider the sum of all connected diagrams at once, we allow for cancellations between diagrams with different signs, alleviating the sign problem. Moreover, the complexity of the calculation grows exponentially with the order of the expansion, which should be constrasted with the factorial growth of the standard diagrammatic technique. We illustrate the efficiency of the technique for the two-dimensional Fermi-Hubbard model.
A powerful perspective in understanding non-equilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, not much else is known about the refined characters of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagation out-of-equilibrium, from the view of entanglement Hamiltonian. As a prototypical example, we study quantum quench dynamics of a one-dimensional Bose-Hubbard model by means of time-dependent density-matrix renormalization group simulation. Before reaching equilibration, it is found that a current operator emerges in entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, entanglement temperature of steady state is spatially independent, which provides an intuitive trait of equilibrium. We demonstrate that these features are consistent with predictions from conformal field theory. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from perspective of entanglement Hamiltonian.
We discuss the Auxiliary Field Quantum Monte Carlo (AFQMC) method applied to dilute neutron matter at finite temperatures. We formulate the discrete Hubbard-Stratonovich transformation for the interaction with finite effective range which is free from the sign problem. The AFQMC results are compared with those obtained from exact diagonalization for a toy model. Preliminary calculations of energy and chemical potential as a function of temperature are presented.
We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as the trial state, but a more rapid convergence can be obtained using a good variational state. As an alternative to first carrying out a time consuming variational Monte Carlo calculation, we show that a very good trial state can be generated in an iterative fashion in the course of the simulation itself. We also show how the properties of the valence bond basis enable calculations of quantities that are difficult to obtain with the standard basis of Sz eigenstates. In particular, we discuss quantities involving finite-momentum states in the triplet sector, such as the dispersion relation and the spectral weight of the lowest triplet.
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