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首页> 外文期刊>Physical review >Ohmic two-state system from the perspective of the interacting resonant level model: Thermodynamics and transient dynamics
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Ohmic two-state system from the perspective of the interacting resonant level model: Thermodynamics and transient dynamics

机译：从相互作用的共振能级模型的角度看欧姆二态系统：热力学和瞬态动力学

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摘要

We investigate the thermodynamics and transient dynamics of the (unbiased) Ohmic two-state system by exploiting the equivalence of this model to the interacting resonant level model. For the thermodynamics, we show, by using the numerical renormalization group (NRG) method, how the universal specific heat and susceptibility curves evolve with increasing dissipation strength α from those of an isolated two-level system at vanishingly small dissipation strength, with the characteristic activatedlike behavior in this limit, to those of the isotropic Kondo model in the limit α → 1~-. At any finite α > 0, and for sufficiently low temperature, the behavior of the thermodynamics is that of a gapless renormalized Fermi liquid. Our results compare well with available Bethe ansatz calculations at rational values of a, but go beyond these, since our NRG calculations, via the interacting resonant level model, can be carried out efficiently and accurately for arbitrary dissipation strengths 0 ≤ α < 1~-. We verify the dramatic renormalization of the low-energy thermodynamic scale T_0 with increasing α, finding excellent agreement between NRG and density matrix renormalization group (DMRG) approaches. For the zero-temperature transient dynamics of the two-level system, P(t) = <σ_z-(t)), with initial-state preparation P(t ≤ 0) = +1, we apply the time-dependent extension of the NRG (TDNRG) to the interacting resonant level model, and compare the results obtained with those from the noninteracting-blip approximation (NIBA), the functional renormalization group (FRG), and the time-dependent density matrix renormalization group (TD-DMRG). We demonstrate excellent agreement on short to intermediate time scales between TDNRG and TD-DMRG for 0 ≲ α ≲ 0.9 for P(t), and between TDNRG and FRG in the vicinity of α = 1/2. Furthermore, we quantify the error in the NIBA for a range of a, finding significant errors in the latter even for 0.1 ≤ α ≤ 0.4. We also briefly discuss why the long-time errors in the present formulation of the TDNRG prevent an investigation of the crossover between coherent and incoherent dynamics. Our results for P(t) at short to intermediate times could act as useful benchmarks for the development of new techniques to simulate the transient dynamics of spin-boson problems.
机译：我们通过利用该模型与相互作用的共振能级模型的等价关系，研究（无偏）欧姆二态系统的热力学和瞬态动力学。对于热力学，我们展示了通过使用数值重归一化组（NRG）方法，通用的比热和磁化率曲线如何随着耗散强度α的增加而从孤立的两级系统的消散强度逐渐减小的情况下随着特性强度的变化而演化，其特性在该极限下的激活样行为，类似于在α→1〜-极限下的各向同性近藤模型。在任何有限的α> 0且对于足够低的温度下，热力学行为都是无间隙的重归一化费米液体的行为。我们的结果与在a的合理值下可用的Bethe ansatz计算结果很好地相比较，但是超出了这些范围，因为我们的NRG计算可以通过相互作用的共振能级模型有效且准确地针对任意耗散强度0≤α<1〜-进行。 。我们验证了随着α的增加，低能热力学标度T_0发生了显着的重新归一化，发现NRG和密度矩阵重新归一化组（DMRG）方法之间具有极好的一致性。对于两级系统的零温度瞬态动力学，P（t）= <σ_z-（t）），在初始状态准备下P（t≤0）= +1，我们应用了随时间变化的将NRG（TDNRG）转换为相互作用的共振能级模型，并将获得的结果与非相互作用斑点逼近（NIBA），功能重归一化组（FRG）和随时间变化的密度矩阵重归一化组（TD-DMRG）进行比较）。我们证明了在TDNRG和TD-DMRG之间对于P（t）为0≲α≲0.9，以及在TDNRG和FRG之间在α= 1/2附近的短至中间时间尺度具有极好的一致性。此外，我们量化了NIBA在a范围内的误差，即使在0.1≤α≤0.4的情况下，在后者中也发现了明显的误差。我们还简要讨论了为什么TDNRG当前公式中的长期错误会阻止对相干动力学和非相干动力学之间的交叉进行研究。我们在短时间到中间时间的P（t）结果可以作为开发模拟自旋玻色子问题瞬态动力学的新技术的有用基准。

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  • 来源
    《Physical review》 |2016年第16期|165130.1-165130.24|共24页
  • 作者

    H. T. M. Nghiem; D. M. Kennes; C. Klockner; V. Meden; T. A. Costi;

  • 作者单位

    Peter Gruenberg Institut and Institute for Advanced Simulation, Research Centre Jiilich, D-52425 Juelich, Germany;

    Institut fiir Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany;

    Institut fiir Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany;

    Institut fiir Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany,Peter Griinberg Institut, Research Centre Jiilich, D-52425 Jiilich, Germany;

    Peter Gruenberg Institut and Institute for Advanced Simulation, Research Centre Jiilich, D-52425 Juelich, Germany;

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