The spin-boson model, describing a two-level system coupled to a bath of harmonic oscillators, is a generic model for quantum dissipation, with manifold applications. It has also been studied as a simple example for an impurity quantum phase transition. Here, we present a detailed study of a U(1)-symmetric two-bath spin-boson model, where two different components of an SU(2) spin
21 are coupled to separate dissipative baths. Nontrivial physics arises from the competition of the two dissipation channels, resulting in a variety of phases and quantum phase transitions. We employ a combination of analytical and numerical techniques to determine the properties of both the stable phases and the quantum critical points. In particular, we find a critical intermediate-coupling phase which is bounded by a continuous quantum phase transition which violates the quantum-to-classical correspondence.
Spin-boson models are simple examples of quantum dissipative systems, but also serve as effective models in quantum magnetism and exhibit nontrivial criticality. Recently, they have been established as a platform to study the nontrivial renormalization-group (RG) scenario of fixed-point annihilation, in which two intermediate-coupling RG fixed points collide and generate an extremely slow RG flow near the collision. For the Bose Kondo model, a single
S=1/2 spin where each spin component couples to an independent bosonic bath with power-law spectrum
∝ωs via dissipation strengths
αi,
i∈{x,y,z}, such phenomena occur sequentially for the U(1)-symmetric model at
αz=0 and the SU(2)-symmetric case at
αz=αxy, as the bath exponent
s<1 is tuned. Here we use an exact wormhole quantum Monte Carlo method for retarded interactions to explore how this nontrivial fixed-point structure affects the phase diagram and phase transitions of the anisotropic model. In particular, we show how fixed-point annihilation within a symmetry-enhanced critical manifold leads to (i) a continuous order-to-order transition beyond the Landau paradigm, (ii) a symmetry-enhanced first-order transition, and (iii) pseudocriticality, which can be tuned into each other via the bath exponent
s. We extract critical exponents at the continuous transition, but also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent
s. Moreover, we provide direct numerical evidence for pseudocritical scaling on both sides of the fixed-point collision, which manifests in an extremely slow drift of the correlation-length exponent. We also study the crossover away from the SU(2)-symmetric case and determine the phase boundary of an extended U(1)-symmetric critical phase.
The annihilation of two intermediate-coupling renormalization-group (RG) fixed points is of interest in diverse fields from statistical mechanics to high-energy physics, but has so far only been studied using perturbative techniques. Here we present high-accuracy quantum Monte Carlo results for the SU(2)-symmetric S=1/2 spin-boson (or Bose-Kondo) model. We study the model with a power-law bath spectrum ∝ω^{s} where, in addition to a critical phase predicted by perturbative RG, a stable strong-coupling phase is present. Using a detailed scaling analysis, we provide direct numerical evidence for the collision and annihilation of two RG fixed points at s^{*}=0.6540(2), causing the critical phase to disappear for s<s^{*}. In particular, we uncover a surprising duality between the two fixed points, corresponding to a reflection symmetry of the RG beta function, which we utilize to make analytical predictions at strong coupling which are in excellent agreement with numerics. Our work makes phenomena of fixed-point annihilation accessible to large-scale simulations, and we comment on the consequences for impurity moments in critical magnets.
Quantum criticality that goes beyond the Landau framework of order-parameter fluctuations is playing a central role in elucidating the behavior of strange metals. A prominent case appears in Kondo lattice systems, which have been extensively analysed in terms of an effective Bose-Fermi Kondo model. Here, a spin is simultaneously coupled to conduction electron bands and gapless vector bosons that represent magnetic fluctuations. The Bose-Fermi Kondo model features interacting fixed points of Kondo destruction with such properties as dynamical Planckian (
ℏω/kBT) scaling and loss of quasiparticles. Here we carry out a renormalization-group analysis of the model with spin isotropy and identify pair-wise annihilations of the fixed points as the spectrum of the bosonic bath evolves. Our analysis not only provides an essentially complete understanding of the previous numerical results of an SU(2)-symmetric model, but also reveals a surprising feature of sequential fixed-point annihilation. Our results lay the foundation for the understanding of quantum criticality in spin-isotropic heavy-fermion metals as well as in doped Mott-Hubbard systems.
In quantum critical heavy fermion systems, local moments are coupled to both collective spin fluctuations and conduction electrons. As such, the Bose-Fermi Kondo model, describing the coupling of a local moment to both a bosonic and a fermionic bath, has been of extensive interest. For the model in the presence of SU(2) spin rotational symmetry, questions have been raised about its phase diagram. Here we develop a version of continuous-time Quantum Monte Carlo (CT-QMC) method suitable for addressing this issue; this procedure can reach sufficiently low temperatures while preserving the SU(2) symmetry. Using this method for the Bose-Fermi Anderson model, we clarify the renormalization-group fixed points and the phase diagram for the case with a constant fermionic-bath density of states and a power-law bosonic-bath spectral function
ρb(ω)∝ωs (
0<s<1). We find two types of Kondo destruction QCP, depending on the power-law exponent
s in the bosonic bath spectrum. For
s∗<s<1, both types of QCPs exist and, in the parameter regime accessible by an analytical
ϵ-expansion renormalization-group calculation (here
ϵ=1−s), the CT-QMC result is fully consistent with prior predictions by the latter method. For
s<s∗, there is only one type of QCP. At both type of Kondo destruction QCPs, we find that the exponent of the local spin susceptibility
η obeys the relation
η=ϵ, which has important implications for Kondo destruction QCP in the Kondo lattice problem.
We extend the numerical renormalization-group method to treat Bose-Fermi Kondo models (BFKMs) describing a local moment coupled both to a conduction band and to a dissipative bosonic bath representing, e.g., lattice or spin collective excitations of the environment. We apply the method to the Ising-symmetry BFKM with a structureless band and a bath spectral function $\ensuremath{\eta}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{s}$. The method is valid for all bath exponents
s and all temperatures
T. For
0<s<1, the range of interest in the context of heavy-fermion quantum criticality, an interacting critical point, characterized by hyperscaling of exponents and $\ensuremath{\omega}∕T$ scaling, describes a continuous quantum phase transition between Kondo-screened and localized phases. For Ohmic dissipation
s=1, where the model is relevant to certain dissipative mesoscopic qubit devices, the transition is found to be Kosterlitz-Thouless-like. In both regimes the impurity spectral function for the corresponding Anderson model shows clearly the collapse of the Kondo resonance at the transition. Connection is made to other recent results for the BFKM and the spin-boson model.