Quantum phase transitions in a resonant-level model with dissipation: Renormalization-group studies (original) (raw)
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Quantum phase transitions in a charge-coupled Bose-Fermi Anderson model
Physical Review B, 2009
We study the competition between Kondo physics and dissipation within an Anderson model of a magnetic impurity level that hybridizes with a metallic host and is also coupled, via the impurity charge, to the displacement of a bosonic bath having a spectral density proportional to ω s. As the impurity-bath coupling increases from zero, the effective Coulomb interaction between two electrons in the impurity level is progressively renormalized from its repulsive bare value until it eventually becomes attractive. For weak hybridization, this renormalization in turn produces a crossover from a conventional, spin-sector Kondo effect to a charge Kondo effect. At particle-hole symmetry, and for sub-Ohmic bath exponents 0 < s < 1, further increase in the impurity-bath coupling results in a continuous, zero-temperature transition to a broken-symmetry phase in which the ground-state impurity occupancyn d acquires an expectation value n d 0 = 1. The response of the impurity occupancy to a locally applied electric potential features the hyperscaling of critical exponents and ω/T scaling that are expected at an interacting critical point. The numerical values of the critical exponents suggest that the transition lies in the same universality class as that of the sub-Ohmic spin-boson model. For the Ohmic case s = 1, the transition is instead of Kosterlitz-Thouless type. Away from particle-hole symmetry, the quantum phase transition is replaced by a smooth crossover, but signatures of the symmetric quantum critical point remain in the physical properties at elevated temperatures and/or frequencies.
Physical Review B, 2010
Based on the recent paper (Phys. Rev. Lett. 102, 216803, (2009)), we study the nonequilibrium occupation number n d and charge susceptibility χ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium Renormalization Group (RG) approach, we calculate nonequilibrium magnetization M and spin susceptibility χ in the effective Kondo model, corresponding to 2n d − 1 and χ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization M as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in M at the transition in equilibrium. In the limit of large bias voltages, we find M and χ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both n d − 1/2 and χ decrease more rapidly to zero with increasing bias voltages.
Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths
Physical Review B, 2007
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2 frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow the flow towards a stable strong-coupling state. Since the low-energy bosons live around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.
Quantum Phase Transition in the Spin Boson Model
Lecture Notes in Physics, 2010
In this paper we give a general introduction to quantum critical phenomena, which we practically illustrate by a detailed study of the low energy properties of the spin boson model (SBM), describing the dynamics of a spin 1/2 impurity (or more generically a two-level system) coupled to a bath of independent harmonic oscillators. We show that the behavior of the model is very sensitive to the bath spectrum, in particular how the properties of the quantum critical point in the SBM are affected by the functional form of the bath Density of States (DoS). To this effect, we review the renormalization group (RG) treatment of the SBM for various bath DoS, based on an unconventional Majorana representation of the spin 1/2 degree of freedom. We also discuss the derivation of Shiba's relation for the sub-ohmic SBM, and explicitely derive an effective action vindicating the quantum to classical mapping.
Renormalization-group approach to the infrared behavior of a zero-temperature Bose system
Physical Review B, 2004
We exploit the renormalization-group approach to establish the exact infrared behavior of an interacting Bose system at zero temperature. The local-gauge symmetry in the broken-symmetry phase is implemented through the associated Ward identities, which reduce the number of independent running couplings to a single one. For this coupling the ǫ-expansion can be controlled to all orders in ǫ (= 3−d). For spatial dimensions 1 < d ≤ 3 the Bogoliubov fixed point is unstable towards a different fixed point characterized by the divergence of the longitudinal correlation function. The Bogoliubov linear spectrum, however, is found to be independent from the critical behavior of this correlation function, being exactly constrained by Ward identities. The new fixed point properly gives a finite value of the coupling among transverse fluctuations, but due to virtual intermediate longitudinal fluctuations the effective coupling affecting the transverse correlation function flows to zero. As a result, no transverse anomalous dimension is present. This treatment allows us to recover known results for the quantum Bose gas in the context of a unifying framework and also to reveal the non-trivial skeleton structure of its perturbation theory.
Quantum phase transitions in Bose–Fermi systems
Annals of Physics, 2011
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Quantum Thermodynamics at Impurity Quantum Phase Transitions
Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory, 2020
The study of quantum thermodynamics, i.e. equilibrium and non-equilibrium thermodynamics of quantum systems, has been applied to various many-body problems, including quantum phase transitions. An important question is whether outof-equilibrium quantities from this emerging field, such as fluctuations of work, exhibit scaling after a sudden quench. In particular, it is very interesting to explore this problem in impurity models where the lack of an obvious symmetry breaking at criticality makes it very challenging to characterize. Here, by considering a spin emulation of the two impurity Kondo model and performing density matrix renor
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We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime where the bosons are in a superfluid ground state, integrate them out, and obtain an effective action for the fermions. We carry out a renormalization group analysis of this effective fermionic action at low temperatures, show that the presence of the spinor bosons may lead to a separation of Fermi surfaces of the spin-up and spin-down fermions, and investigate the parameter range where this phenomenon occurs. We also calculate the susceptibilities corresponding to the possible superfluid instabilities of the fermions and obtain their possible brokensymmetry ground states at low temperatures and weak interactions.
Dissipative quantum Ising model in a cold-atom spin-boson mixture
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Using cold bosonic atoms with two (hyperfine) ground states, we introduce a spin-boson mixture which allows to implement the quantum Ising model in a tunable dissipative environment. The first specie lies in a deep optical lattice with tightly confining wells and forms a spin array; spin-up/down corresponds to occupation by one/no atom at each site. The second specie forms a superfluid reservoir. Different species are coupled coherently via laser transitions and collisions. Whereas the laser coupling mimics a transverse field for the spins, the coupling to the reservoir sound modes induces a ferromagnetic (Ising) coupling as well as dissipation. This gives rise to an order-disorder quantum phase transition where the effect of dissipation can be studied in a controllable manner.