Ohmic two-state system from the perspective of the interacting resonant level model: Thermodynamics and transient dynamics

Abstract

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 activated-like 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 α, 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 T0 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) = σz(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 α, 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.

Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment

“…We follow the approach of Ref. 60 and evaluate I 0 (T ) and I 1 (T ) by inserting the discrete form of the spectral function (6) into Eq. (5) to obtain…”

“…This way of calculating I 0 (T ) and I 1 (T ) avoids any additional errors that can arise by first broadening the spectral function in (6) and then using the resulting smooth spectral functions to carry out explicitly the integrations in (5). Moreover, since the expressions for I i=0,1 in Eq.…”

“…The Kondo effect, originally describing the anomalous lowtemperature increase in the resistivity of nonmagnetic metals due to the presence of magnetic impurities 1,2 , is by now a ubiquitous phenomenon in condensed matter physics 3 . It plays a role, for example, in the decoherence of qubits coupled ohmically to an environment [4][5][6] , in transition metal atoms in nanowires 7 , in magnetic adatoms on surfaces [8][9][10][11][12][13] , in semiconductor [14][15][16][17][18] and molecular quantum dots [19][20][21] , in heavy fermions 2,22 and in the Mott transition in strongly correlated materials 23 .…”

Finite-bias transport through the interacting resonant level model coupled to a phonon mode -- a functional renormalization group study

“…However, the logarithmic increase for Γ/D → 0 shows that perturbative (in either U or Γ) methods fail in this so-called scaling limit. Several approaches to avoid this, being either analytical [7][8][9][10][11][12][13] or numerical [11][12][13][14][15] are available.…”

Time-dependent numerical renormalization group method for multiple quenches: Towards exact results for the long-time limit of thermodynamic observables and spectral functions

“…Techniques currently being used to investigate the timedependent dynamics of quantum impurity systems, include functional and real-time renormalization group methods [17][18][19] , flow equation 20,21 , quantum Monte Carlo [22][23][24][25] , and density matrix renormalization group methods [26][27][28] , the hierarchical quantum master equation approach 29,30 , and the time-dependent numerical renormalization group (TDNRG) method [31][32][33][34][35][36][37][38][39][40] . However, no single technique is able to address in a nonperturbative and numerically exact way the timedependent and nonequilibrium dynamics of quantum impurity systems in the interesting low-temperature strong-coupling regime.…”