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The traditional approach to quantum criticality describes a quantum system near a zero-temperature transition in terms of a Landau-Ginzburg-Wilson functional of the order parameter in the spatial and (imaginary) temporal directions. Critical quantum fluctuations thus are mapped to classical order parameter fluctuations of an effective D+z dimensional system, where D is the space dimensionality of the quantum system and z-1 is a measure for the anisotropy between space and time. The existence of quantum critical modes beyond the order parameter fluctuations violates such a 'quantum-to-classical' mapping and complicates a classification of quantum phase transitions into universality classes. A typical example is for heavy fermion systems, where quantum criticality can involve critical destruction of the Kondo entanglement[1]. The Bose-Fermi Kondo model (BFKM) occurs as the effective quantum impurity model within the Extended Dynamical Mean Field Theory (EDMFT) for quantum critical heavy fermion compounds. There have been indications [2] that the QCP of BFKM cannot be described in terms of a local O(3)-symmetric φ4-theory as prescribed by the quantum to classical mapping, but the issue remains unsettled. In this presentation we show that the Berry phase term influences the critical properties of a Kondo-destroying quantum phase transition [3]. Such a Berry phase term is a geometrical phase inherent in any spin path integral representation and does not have an immediate classical counterpart. We elucidate its role in the mapping of the quantum critical Bose-Fermi Kondo model (BFKM) onto a classical spin model. In addition, we review how different approaches to this problem deal with the Berry phase and compare the physics the BFKM to the spin-boson model [4]. [1] P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008). [2] L. Zhu, S. Kirchner, Q. Si and A. Georges, Phys. Rev. Lett. 93, 267201 (2004). [3] S. Kirchner and Q. Si, arXiv:0808.2647 (2008) and submitted to Phys. Rev. Lett. [4] M. Vojta, N.-H. Tong and R. Bulla, Phys. Rev. Lett. 94, 070604 (2005), M. Glossop, K. Ingersent, PRL 95, 060702 (2005), A. Winter, H. Rieger, M. Vojta, R. Bulla, arXiv:0807.4716 (2008), S. Kirchner, Q.Si and K. Ingersent, arXiv:0808.0916 and submitted to Phys. Rev. Lett.(2008). |
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