Quantum phase transition in a resonant level coupled to interacting leads

Mebrahtu, Henok; Borzenets, Ivan; Liu, Dong E.; Zheng, Haizhong; Bomze, Yuriy; Smirnov, Alex I.; Baranger, Harold U.; Finkelstein, Gleb

doi:10.1038/nature11265

Cited by 84 publications

(152 citation statements)

References 31 publications

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“…Quantum dot states change when the coupling is increased, and qualitatively new phenomena can arise such as various Kondo effects and possibly even quantum phase transitions (Mebrahtu et al, 2012). Great potential for new experiments arises when the leads are given interesting properties.…”

Section: Discussionmentioning

confidence: 99%

Quantum transport in carbon nanotubes

et al. 2015

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Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike in conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and valley freedom. The interplay between the two is the focus of this review. The energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are explained, together with their consequences for transport measurements through nanotube quantum dots. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behavior. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, open questions for the field are also clearly stated. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a low level.

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Section: Discussionmentioning

confidence: 99%

Quantum transport in carbon nanotubes

et al. 2015

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“…An Ohmic bosonic bath can be engineered through a long transmission line [15,16]. Another setup of interest is a one-dimensional Luttinger liquid [18,19], where a dissipative quantum phase transition were recently observed [62,63]. Cold atom setups [17,64,65] are also viable candidates to simulate an Ohmic bath coupled to a two-level system.…”

Section: Conclusion and Experimental Perspectivesmentioning

confidence: 99%

Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect

et al. 2017

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We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H(sin theta cos phi, sin theta sin phi cos theta) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for alpha < 1. We report a divergence of the Berry curvature at alpha(c) = 1 for magnetic fields aligned along the equator theta = pi/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schrodinger approach we find that, for a fixed field sweep velocity theta(t) = vt, the bath induces a crossover from ( quasi) adiabatic to nonadiabatic dynamical behavior when the spin bath coupling a increases. We also investigate the particular regime H/omega(c) << v/H << 1 with large bath cutoff frequency.c, where the dynamical Chern number vanishes already at alpha = 1/2. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of alpha = 1/2. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium. Disciplines Condensed Matter Physics | Physics CommentsThis article is published as Henriet, Loïc, Antonio Sclocchi, Peter P. Orth, and Karyn Le Hur. "Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect." Physical Review B 95, no. 5 (2017) We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H (sin θ cos φ, sin θ sin φ, cos θ ) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for α < 1. We report a divergence of the Berry curvature at α c = 1 for magnetic fields aligned along the equator θ = π/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs a...

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“…Recent experimental and theoretical studies explore an even richer variety of complex quantum impurities and phase transitions, such as the interplay of the Kondo effect and interimpurity couplings [76][77][78], coupling to superconducting or Dirac fermion baths [79][80][81][82][83], and the effect of multiple levels or multiple channels [84][85][86][87], see Refs. [24,88] for a review.…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 4 Decembmentioning

confidence: 99%

Fidelity Susceptibility Perspective on the Kondo Effect and Impurity Quantum Phase Transitions

2015

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The Kondo effect is a ubiquitous phenomenon appearing at low temperature in quantum confined systems coupled to a continuous bath. Efforts in understanding and controlling it have triggered important developments across several disciplines of condensed matter physics. A recurring pattern in these studies is that the suppression of the Kondo effect often results in intriguing physical phenomena such as impurity quantum phase transitions or non-Fermi-liquid behavior. We show that the fidelity susceptibility is a sensitive indicator for such phenomena because it quantifies the sensitivity of the system's state with respect to its coupling to the bath. We demonstrate the power of the fidelity susceptibility approach by using it to identify the crossover and quantum phase transitions in the one and two impurity Anderson models. The feasibility of measuring fidelity susceptibility in condensed matter as well as ultracold quantum gases experiments opens exciting new routes to diagnose the Kondo problem and impurity quantum phase transitions. [7,8], and boundary conformal field theory [9] to the quantum impurity problems. Experimental interest increased in the late 1990s due to breakthroughs in fabricating artificial nanodevices [10][11][12][13][14][15]. Kondo physics is also directly relevant to dissipative two-state systems [16] and the heavy-fermion compounds [17,18]. There has also been an increasing interest in realizing the Kondo effect in ultracold atomic gases [19][20][21][22]. High controllability of the latter system may offer chances to gain even deeper understandings of the intriguing physics of quantum impurity models.A general description of the quantum impurity problems can be written aŝ HðλÞ ¼Ĥ impurity þĤ bath |fflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflffl ffl}whereĤ 0 describes the quantum impurity together with a continuous bath, and the last term describes the coupling between them. We treat λ as a parameter and aim to characterize the state of the quantum impurity as a function of its coupling to the bath. The Kondo effect originates from the bath's tendency to screen the local moment formed on the quantum impurity. Renormalization group analysis shows that, in the Kondo region, the coupling strength flows to infinity at low energy [4,5], implying that the local moment will eventually get screened at a low enough temperature even with an arbitrarily weak bare impurity-bath coupling strength. There are, however, various physical processes that can compete with the Kondo effect. In the presence of such competitions, the system may undergo an impurity quantum phase transition where a competing state (local moment, charge order, etc.) takes over as the bath-impurity coupling λ decreases. Suppression of the Kondo screening often leads to non-Fermi liquid behavior [23,24]. However, different from the quantum phase transition in bulk systems [25], at such an impurity quantum critical point, only a nonextensive term in the free energy becomes singular. It is not always straightfo...

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Quantum phase transition in a resonant level coupled to interacting leads

Cited by 84 publications

References 31 publications

Quantum transport in carbon nanotubes

Quantum transport in carbon nanotubes

Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect

Fidelity Susceptibility Perspective on the Kondo Effect and Impurity Quantum Phase Transitions

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