[Show abstract][Hide abstract] ABSTRACT: We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin E(alpha,Delta,h), where alpha is the dissipation strength, Delta is the tunneling amplitude between qubit states, and h is the level asymmetry. For 1-alpha>Delta/omegac and (Delta,h)<omegac, we show that the Kondo energy scale TK controls the entanglement between the qubit and the bosonic environment (omegac is a high-energy cutoff). For h<TK, the disentanglement proceeds as (h/TK)2; for h>TK, E vanishes as (TK/h)2-2alpha, up to a logarithmic correction. For a given h, the maximum entanglement occurs at a value of alpha which lies in the crossover regime h approximately TK. We emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise.
[Show abstract][Hide abstract] ABSTRACT: We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.
Annals of Physics 06/2007; 322(6-322):1466-1476. DOI:10.1016/j.aop.2006.08.002 · 2.10 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The extreme variability of observables across the phase diagram of the cuprate high-temperature superconductors has remained a profound mystery, with no convincing explanation for the superconducting dome. Although much attention has been paid to the underdoped regime of the hole-doped cuprates because of its proximity to a complex Mott insulating phase, little attention has been paid to the overdoped regime. Experiments are beginning to reveal that the phenomenology of the overdoped regime is just as puzzling. For example, the electrons appear to form a Landau Fermi liquid, but this interpretation is problematic; any trace of Mott phenomena, as signified by incommensurate antiferromagnetic fluctuations, is absent, and the uniform spin susceptibility shows a ferromagnetic upturn. Here, we show and justify that many of these puzzles can be resolved if we assume that competing ferromagnetic fluctuations are simultaneously present with superconductivity, and the termination of the superconducting dome in the overdoped regime marks a quantum critical point beyond which there should be a genuine ferromagnetic phase at zero temperature. We propose experiments and make predictions to test our theory and suggest that an effort must be mounted to elucidate the nature of the overdoped regime, if the problem of high-temperature superconductivity is to be solved. Our approach places competing order as the root of the complexity of the cuprate phase diagram.
Proceedings of the National Academy of Sciences 04/2007; 104(15):6123-7. DOI:10.1073/pnas.0701265104 · 9.67 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the entanglement between a qubit and its environment by calculating the von Neumann entropy of the spin in the delocalized phase of the spin-boson model. Using a well-known mapping between the spin-boson model with Ohmic dissipation and the anisotropic Kondo model, we obtain exact results for the entanglement entropy E at arbitrary dissipation strength alpha and level asymmetry h. We show that the Kondo energy scale TK controls the entanglement between the qubit and the bosonic environment. For h TK, we find that E=E(h=0)-2e^b/(2-2alpha) gamma[1+1/(2-2alpha)]pi2 gamma[1+alpha/(2-2alpha)] (hTK)^2, where b=alphaalpha+ (1-alpha) (1-alpha). The universal (h/TK)^2 scaling reflects the Fermi liquid nature of the Kondo ground state. In the limit h TK, E vanishes as (TK/h)^2-2alpha, up to a logarithmic correction. We thoroughly explore the phase space (,); for a given h, the maximal entanglement occurs in the crossover regime h ˜TK. We also emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise.
[Show abstract][Hide abstract] ABSTRACT: We revisit the interlayer tunneling theory of high temperature superconductors and formulate it as a mechanism by which the striking systematics of the transition temperature within a given homologous series can be understood. We pay attention not only to the enhancement of pairing, as was originally suggested, but also to the role of competing order parameters that tend to suppress superconductivity, and to the charge imbalance between inequivalent outer and inner CuO2 planes in a unit cell. Calculations based on a generalized Ginzburg-Landau theory yield results that bear robust and remarkable resemblance to experimental observations.
Proceedings of SPIE - The International Society for Optical Engineering 08/2005; DOI:10.1117/12.623139 · 0.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examining exact solutions of models of correlated systems and find that the temperature can be surprisingly high. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, $\rho_{s}(0)$, and the transition temperature, $T_{c}$, of the cuprates are related by $T_{c}\propto\rho_{s}(0)^y$, where the exponent $y$ is different at the two edges of the superconducting dome, signifying the respective QCPs. This relationship can be tested in high quality crystals.
[Show abstract][Hide abstract] ABSTRACT: The transition temperature (Tc) of multi-layer cuprate
superconductors has an unusual dependence on the number of layers (n)
per unit cell: it forms a bell-shaped curve peaked at n=3. An
explanation of this behavior is due to the combined effects of
interlayer tunneling and a competing order, the latter effect being
enhanced for n >=3 by a charge imbalance between the layers. We
explore this proposal further by examining the mean-field theory of a
superconducting order parameter and a competing d-density wave (DDW)
order parameter. We focus on three effects: interlayer DDW coupling,
increased charge imbalance in the five-layer system, and fluctuations of
the superconducting order parameter. We find that (1) the DDW order
parameters in neighboring layers prefer to couple
``anti-ferromagnetically''---and, surprisingly, the coupling vanishes
identically for two layers with order parameters that are
``ferromagnetically'' aligned; (2) both the interlayer DDW coupling and
the increased charge imbalance bring the calculation into better
agreement with the experimental results; and (3) fluctuations can have a
more pronounced effect when they occur in the presence of a competing
order parameter.
[Show abstract][Hide abstract] ABSTRACT: The low temperature scanning tunneling microscopy spectra in the underdoped regime is analyzed from the perspective of coexisting $d$-density wave and d-wave superconducting states. The calculations are carried out in the presence of a low concentration of unitary impurities and within the framework of the fully self-consistent Bogoliubov-de Gennes theory, which allows local modulations of the magnitude of the order parameters in response to the impurities. Our theory captures the essential aspects of the experiments in the underdoped BSCCO at very low temperatures.