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The deep sub-Ohmic spin-boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly quenched even in the coherent regime, in which the non-Markovian feature dominates. With this finding we come up with a novel way to implement the unitary equilibration, the essential term of the eigenstate-thermalization hypothesis, through a short-time evolution of the model., 9 pages, 6 figures

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Neel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.

A variety of one-dimensional Ising spin systems, including staggered and parallel magnetic fields, alternating and second neighbor interactions, four-spin coupling, etc., are discussed in terms of renormalization group theory. A continuous range of distinct renormalization groups is constructed in exact closed form, analyzed in detail, and compared with exactly calculated thermodynamic properties. Fixed point linearization yields relevant, irrelevant, and marginal operators. All groups yield identical “critical” behavior (at T = 0) with η = 1, δ = ∞, γ = ν = 2 − α, and with identical linear scaling fields. A generalization of Wegner's analysis to discrete groups yields explicit power series for the nonlinear scaling fields; these are seen to depend on the particular renormalization group and, hence, are physically nonunique. A planar, multiconnected “truncated tetrahedron” model of effective dimensionality log2 3 is analyzed via a dedecoration and star-triangle group revealing highly singular behavior as T → Tc = 0.

We apply the recently developed real space dynamic renormalization group method to the one-dimensional kinetic Ising model. We show how one can develop block spin methods that lead to recursion relations for the space and time dependent correlation functions that correspond to the observables for this system. We point out the importance of carefully choosing the appropriate parameters governing the behavior of individual blocks of spins and the necessity of worrying about the high temperature properties of the temperature recursion relations if one is to obtain the proper exponential decay of correlation functions at large distances away from the critical point at zero temperature. We systematically investigate the accuracy of our approximate recursion relations for various correlation functions by checking them against the known exact results. Our simple methods work surprisingly well over a wide range of temperatures, wavenumbers and frequencies.

We present a formal calculation of the infrared singularity structure of the fermion propagator in QED based on the Faddeev-Kulish asymptotic solution. The Renormalization program is reviewed in the context of the BPHZ subtraction scheme and a refinement of the Renormalization group methods is employed to study the infrared singularities in perturbation theory.

We discuss the method of dimensional renormalization as applied to quantum electrodynamics. Then we give a general method which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes.

An algebric method of the renormalization group equations is proposed in order to study the field theory with multiple coupling constants for Γ i = 0. The method is applied to a non abelian gauge theory with two scalar fields.