Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Quantum Monte Carlo Study with a Continuous Imaginary Time Cluster Algorithm

Winter, André; Rieger, Heiko; Vojta, Matthias; Bulla, Ralf

doi:10.1103/physrevlett.102.030601

Cited by 161 publications

(274 citation statements)

References 30 publications

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“…(9). Fortunately, in the scaling limit∆ c can also be found analytically, leading to the final prediction, previous seen in NRG and other approaches [11,16,17,20,22,23].…”

Section: Ground State Energy Critical Exponents and Critical Couplingsmentioning

confidence: 71%

“…However, it is now believed that the nonmean-field results found by NRG in 0 < s < 0.5 are incorrect, and arise from the truncation of the number of states N b used to describe each oscillator in the Wilson chain [14,15]. Recent studies of the sub-Ohmic QPT using quantum monte carlo (QMC) [16], sparse polynomial space approach (SPSA) [17], and an extended coherent state technique have indeed found mean-field critical exponents for 0 < s < 0.5 [18].In this article we propose a variational ansatz for the ground state of the sub-Ohmic SBM for 0 < s < 0.5 which does not require any truncation of the environment. This is an important feature, as we shall show that the number of environmental bosons diverges above the transition.…”

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confidence: 99%

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Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

et al. 2011

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The sub-ohmic spin-boson model is known to possess a novel quantum phase transition at zero temperature between a localised and delocalised phase. We present here an analytical theory based on a variational ansatz for the ground state, which describes a continuous localization transition with mean-field exponents for 0 < s < 0.5. Our results for the critical properties show good quantitiative agreement with previous numerical results, and we present a detailed description of all the spin observables as the system passes through the transition. Analysing the ansatz itself, we give an intuitive microscopic description of the transition in terms of the changing correlations between the system and bath, and show that it is always accompanied by a divergence of the lowfrequency boson occupations. The possible relevance of this divergence for some numerical approaches to this problem is discussed and illustrated by looking at the ground state obtained using density matrix renormalisation group methods.The physics of quantum systems in contact with environmental degrees of freedom plays a fundamental role in many areas of physics, chemsitry and biology, including systems as diverse as solid state quantum computers[1, 2], quantum impurities [3], and photosynthetic biomolecules [4][5][6][7][8]. A key theoretical model for the study of system-environment interactions is the spin-boson model (SBM), which consists of a two-level system (TLS) that is linearly coupled to an 'environment' of harmonic oscillators [9,10]. Although this model has been studied extensively, there are still many open problems in SBM physics, most notably those concerning the quantum phase transition (QPT) between delocalised and localised phases that exists in the SBM when the oscillators are characterised by sub-Ohmic spectral densities.The standard quantum-classical mapping predicts that the sub-ohmic SBM should be equivalent to a classical Ising spin chain with long-range interactions, and predicts a continuous magnetic transition with mean-field critical exponents for 0 < s < 0.5. In Ref.[11], a continuous transition in the sub-Ohmic SBM was observed using the numerical renormalisation group (NRG) technique for all values of 0 < s < 1, but the critical properties of the transition were found to be non-mean-field for 0 < s < 0.5. It was suggested that this implied a breakdown of the classical to quantum mapping, and some subsequent work in this and other systems has supported this claim [12,13]. However, it is now believed that the nonmean-field results found by NRG in 0 < s < 0.5 are incorrect, and arise from the truncation of the number of states N b used to describe each oscillator in the Wilson chain [14,15]. Recent studies of the sub-Ohmic QPT using quantum monte carlo (QMC) [16], sparse polynomial space approach (SPSA) [17], and an extended coherent state technique have indeed found mean-field critical exponents for 0 < s < 0.5 [18].In this article we propose a variational ansatz for the ground state of the sub-Ohmic SBM for 0 < s < 0.5 whi...

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“…(9). Fortunately, in the scaling limit∆ c can also be found analytically, leading to the final prediction, previous seen in NRG and other approaches [11,16,17,20,22,23].…”

Section: Ground State Energy Critical Exponents and Critical Couplingsmentioning

confidence: 71%

mentioning

confidence: 99%

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

et al. 2011

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“…Another possibility is that already the quantum critical point of the BFK model cannot be described by a local φ 4 -theory and that the quantum-toclassical mapping relating the two fails for the BFK model. This possibility has been recently discussed for the totally spin-isotropic BFK model as well as the easy-axis BFK model [27,28,29,30,31,32]. As already mentioned, the QCP arises out of the competition between the Kondo effect and magnetic fluctuations.…”

Section: Extended Dmft Quantum Critical Bose-fermi Kondo Models and mentioning

confidence: 95%

“…It therefore seems a prerequisite to choose an approach that correctly captures Kondo screening, including the restoration of SU(2) invariance at the Kondo-screened fixed point. For this reason the easy-axis BFK model is delicate [30,31]. In the following, we will focus on the spin-isotropic BFK model where the restoration of the SU(2) invariance in the Kondo-screened phase is not an issue.…”

Section: Extended Dmft Quantum Critical Bose-fermi Kondo Models and mentioning

confidence: 99%

Critical Kondo destruction and the violation of the quantum-to-classical mapping of quantum criticality

Kirchner

2009

Physica B: Condensed Matter

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Antiferromagnetic heavy fermion metals close to their quantum critical points display a richness in their physical properties unanticipated by the traditional approach to quantum criticality, which describes the critical properties solely in terms of fluctuations of the order parameter. This has led to the question as to how the Kondo effect gets destroyed as the system undergoes a phase change. In one approach to the problem, Kondo lattice systems are studied through a self-consistent Bose-Fermi Kondo model within the Extended Dynamical Mean Field Theory. The quantum phase transition of the Kondo lattice is thus mapped onto that of a sub-Ohmic Bose-Fermi Kondo model. In the present article we address some aspects of the failure of the standard order-parameter functional for the the Kondo-destroying quantum critical point of the Bose-Fermi Kondo model.

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“…Reference 5 applied a cluster Monte-Carlo method at various nonzero values of the short-range cutoff τ 0 , while Ref. 13 used a similar method after taking the limit τ 0 → 0. These works both confirmed an earlier conclusion 14 that the critical points of such long-ranged classical spin chains are interacting for 0 < ǫ < 1 2 and Gaussian for 1 2 < ǫ < 1, consistent with the predictions of the local φ 4 theory.…”

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confidence: 99%

Quantum criticality of the sub-Ohmic spin-boson model

Kirchner

Ingersent

2012

Phys. Rev. B

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We revisit the critical behavior of the sub-ohmic spin-boson model. Analysis of both the leading and subleading terms in the temperature dependence of the inverse static local spin susceptibility at the quantum critical point, calculated using a numerical renormalization-group method, provides evidence that the quantum critical point is interacting in cases where the quantum-to-classical mapping would predict mean-field behavior. The subleading term is shown to be consistent with an ω/T scaling of the local dynamical susceptibility, as is the leading term. The frequency and temperature dependences of the local spin susceptibility in the strong-coupling (delocalized) regime are also presented. We attribute the violation of the quantum-to-classical mapping to a Berry-phase term in a continuum path-integral representation of the model. This effect connects the behavior discussed here with its counterparts in models with continuous spin symmetry.

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Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Quantum Monte Carlo Study with a Continuous Imaginary Time Cluster Algorithm

Cited by 161 publications

References 30 publications

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

Critical Kondo destruction and the violation of the quantum-to-classical mapping of quantum criticality

Quantum criticality of the sub-Ohmic spin-boson model

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