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arXiv:2403.02400 · Physical review. B./Physical review. B

Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model

Manuel Weber

Published Dec 10, 2025• 0 citations
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Abstract

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 $\propto ω^s$ via dissipation strengths $α_i$, $i\in\{x,y,z\}$, such phenomena occur sequentially for the U(1)-symmetric model at $α_z=0$ and the SU(2)-symmetric case at $α_z = α_{xy}$, 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.

DOI
10.1103/mtq7-n96c

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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=1/2S=1/2S=1/2 spin where each spin component couples to an independent bosonic bath with power-law spectrum ∝ωs\propto ω^s∝ωs via dissipation strengths αiα_iαi​, i∈{x,y,z}i\in\{x,y,z\}i∈{x,y,z}, such phenomena occur sequentially for the U(1)-symmetric model at αz=0α_z=0αz​=0 and the SU(2)-symmetric case at αz=αxyα_z = α_{xy}αz​=αxy​, as the bath exponent s<1s<1s<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 sss. 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 sss. 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.
The SU(2)-symmetric three-component spin-boson model (also Bose-Kondo model) exhibits different behavior of quantum phase and phase transition from its widely studied single-component counterpart. In this paper we proposed and theoretically studied a model of two separated spins coupled to a common bosonic bath. For our SU(2)-symmetric model, the stable fixed point representing the nonclassical phase and an unstable fixed point corresponding to the transition between the strong-coupling and nonclassical phases can be continuously tuned by the distance between the two spins. Thus the fixed-point collision and annihilation (FPCAA) could be achieved by simply changing the distance. We also studied in detail variations of the values of the two fixed points above as the distance is changed. Our work is essential for realization of FPCAA in such systems and paves the way for studying related physics such as deconfined criticality and quasiuniversality.
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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\rho_{b}(\omega) \propto \omega^{s}ρb​(ω)∝ωs (0<s<10<s<10<s<1). We find two types of Kondo destruction QCP, depending on the power-law exponent sss in the bosonic bath spectrum. For s∗<s<1s^{*}<s<1s∗<s<1, both types of QCPs exist and, in the parameter regime accessible by an analytical ϵ\epsilonϵ-expansion renormalization-group calculation (here ϵ=1−s\epsilon=1-sϵ=1−s), the CT-QMC result is fully consistent with prior predictions by the latter method. For s<s∗s<s^{*}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\etaη obeys the relation η=ϵ\eta=\epsilonη=ϵ, which has important implications for Kondo destruction QCP in the Kondo lattice problem.
We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like ${|\ensuremath{\epsilon}|}^{r}$ at the Fermi energy ($\ensuremath{\epsilon}=0$) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to ${|\ensuremath{\omega}|}^{s}$. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<120<r<\frac{1}{2}0<r<21​ and $\frac{1}{2}\ensuremath{\le}s<1$, and applying the numerical renormalization group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum-critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and $\ensuremath{\omega}/T$ scaling in the dynamics that characterize an interacting critical point. The (r,s)(r,s)(r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum-critical point.
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 12\frac{1}{2}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.