Session U12: Strongly Correlated Electron Systems: Quantum Phase Transitions

Quantum phase transition of a magnetic impurity in a dissipative environment

We study the quantum phase transition (QPT) induced by dissipation in the Bose-Fermi Anderson model of a magnetic impurity that hybridizes with a metallic host and is also coupled (via its charge) to a bosonic bath having a spectral density proportional to $\omega^s$. For sub-Ohmic bath exponents $0 < s < 1$, numerical renormalization-group calculations show that upon increasing the coupling to the bosonic bath from zero, there is a crossover from a conventional (spin-sector) Kondo effect to a charge-Kondo effect. Further increase of the bosonic coupling results in a zero-temperature transition to a phase in which charge fluctuations on the impurity site are frozen out. Critical exponents describing the response of the impurity charge to a locally applied electric field are found to obey the hyperscaling relations characteristic of an interacting critical point. The numerical value of these exponents suggests that the QPT lies in the same universality class as that of the sub-Ohmic spin-boson model. Results for the Ohmic case $s=1$ will also be presented.   

Quantum Criticality of the Pseudogapped Kondo Problem: Finite Temperature Scaling and Conformal Invariance

The critical destruction of the Kondo effect is of interest as a potential mechanism for quantum-critical heavy-fermion metals. Here, we study the pseudogapped Kondo model [1], with a conduction-electron density of states proportional to $|\epsilon|^r$, which provides a paradigm for understanding critical local-moment fluctuations. In general, an interacting quantum critical point (QCP), at a finite critical Kondo coupling $J_c$, separates Kondo-screened and free local-moment phases [2]. We focus on finite-$T$ scaling properties in the vicinity of the QCP, obtained using a dynamical large-N method for an SU(N) generalization of the model. Though the bulk lacks conformal invariance for $r>0$, we show that correlation functions assume the form expected of a boundary conformal field theory, implying an enhanced symmetry at the QCP. We also address these and related issues in the N=2 model using a continuous-time quantum Monte Carlo impurity solver [3], which involves a stochastic evaluation of an expansion in the host-impurity hybridization. [1] D. Withoff and E. Fradkin, Phys. Rev. Lett. 64, 1835 (1990) [2] K. Ingersent and Q. Si., Phys. Rev. Lett. 89, 076403 (2002). [3] P. Werner et al., Phys. Rev. Lett. 97, 076405 (2006)   

Quantum-criticality in models of an impurity coupled to fermionic and bosonic baths

Impurity models exhibiting quantum phase transitions (QPTs) have attracted interest in connection with impurities in cuprate superconductors, heavy-fermion quantum criticality, and quantum-dot devices. This talk focuses on three models describing an impurity level coupled both to a band of fermions (either spinful or spinless) with a density of states varying as $|\epsilon|^r$ around the Fermi energy $\epsilon=0$, and to a dissipative bosonic bath having a spectral function $\propto \omega^s$. Each of these models features a QPT between a phase in which the fermionic band dominates the impurity dynamics and a second phase in which the bosons freeze out the impurity degrees of freedom. We study these QPTs using a recently developed numerical renormalization-group technique. Over much of the parameter space spanned by the exponents $r$ and $s$, the QPT in all three models falls into the universality class of the pure-bosonic spin-boson model, with exponents that are independent of $r$. However, for sufficiently strong fermionic pseudogaps (large values of $r$), new universality classes of QPT emerge.   

The Two-Impurity Anderson Model at Quantum Criticality

We propose a realization of the two-impurity Anderson model in a double quantum-dot system. When charge transfer between the dots is suppressed the system exhibits a non-Fermi liquid critical line parameterized by the amount of charge localized on the dots. Employing conformal field theory techniques we identify the critical exponents that govern transport and thermodynamics in the vicinity of the critical line. We also determine the dynamical exponent that sets the time scale for buildup of the non-Fermi liquid state after the system is shifted into the critical region, e.g. by a sudden change of a nearby gate voltage.   

Absence of quantum phase transition in two-state quantum dot

We use continuous-time quantum Monte Carlo methods to study a model of a spinless-fermion two state quantum dot which was argued in Ref. [1] to exhibit a quantum phase transition. We find instead a smooth behavior as parameters are varied. The generalization of the model to the spinful case is also presented. [1] D. I. Golosov and Y. Gefen, {\em Phys. Rev. B} {\bf 74}, 205316 (2006).   

Kondo destruction in the Bose-Fermi Kondo model with a singular dissipative spectrum: Exact solutions and their implications

Quantum dissipation induces a critical destruction of the Kondo screening, which is of interest in the contexts of quantum critical heavy fermions and magnetic mesoscopic structures. The sub-Ohmic Bose-Fermi Kondo (BFK) model provides a setting to study such an effect. Here, we show that this many-body problem is exactly solvable when the spectrum of the dissipative bosonic bath, $J(\omega)$, is singular, such that $J (\tau)={\rm const.}$. We determine the exact results for the local spin correlation functions, which imply that the singular longitudinal fluctuations of the bosonic bath play a dominant role. We also demonstrate how the large-N limit of an SU(N) generalization of the same model fails to capture the $N=2$ physics in the cases of a singular dissipative bosonic spectrum, due to an interesting under-treatment of the longitudinal fluctuations. Our results resolve an apparent inconsistency between the previous results respectively found using numerical renormalization group and large-N treatments, providing evidence that the local quantum critical solution of the extended dynamical mean field approach to the Kondo lattice model indeed has a zero residual entropy.   

Quantum Criticality out of Equilibrium: Kondo Destruction and $V/T$ Scaling in a Magnetic Single-Electron Transistor

Non-equilibrium quantum phase transitions have so far received only limited attention despite the long-standing strong interest in classical out-of-equilibrium phase transitions. This is in part due to the fact that dynamics and statics are already intermixed at an equilibrium quantum phase transition. Nanostructured devices constitute simplified systems, both theoretically and experimentally, to study well-defined out-of-equilibrium states that give rise to unique steady-state limits. We recently showed that such a system, a magnetic single-electron transistor, can be tuned through a continuous quantum phase transition as the applied gate voltage is tuned [1,2]; the Kondo effect is critically destroyed across the quantum critical point, an effect that is also of interest in some bulk strongly correlated systems such as heavy fermions[3]. To address the non-linear electronic transport near the transition, we generalize the system to a large-N limit, where an exact quantum Boltzmann treatment becomes possible. We determine the universal scaling functions for the I-V characteristics in the linear and non-linear regime, and demonstrate a $V/T$ scaling in the quantum critical state out of equilibrium. [1] S. Kirchner et al., Proc.Natl.Acad.Sci. 102 (2005) 18824 [2] S. Kirchner, Q. Si, Physica B (2007), doi:10.1016/j.physb.2007.10.297 [3] S. Kirchner and Q. Si, Phys. Rev. Lett. in press; arXiv:0706.1783v1.   

Effects of dissipation on a quantum critical point with disorder

We study the effects of dissipation on a disordered quantum phase transition with O$(N)$ order parameter symmetry by applying a strong-disorder renormalization group to the Landau-Ginzburg-Wilson field theory of the problem. We find that Ohmic dissipation results in a non-perturbative infinite-randomness critical point with unconventional activated dynamical scaling while superohmic damping leads to conventional behavior. We discuss applications to the superconductor-metal transition in nanowires and to Hertz' theory of the itinerant antiferromagnetic transition.   

Current-Flow-Driven Nonequilibrium Paramagentic-Ferromagnetic Phase Transitions

We study a 2d itinerant electron system near a ferromagnetic-paramagnetic quantum critical point, which has been driven out of equilibrium by current flow through its bulk. The lack of Galilean invariance in physically realistic models implies that there is no co-moving frame of reference where the physics is identical to that in the absence of current. In the vicinity of the equilibrium critical point the main effect of current flow is shown to be an effective temperature, with current induced drift giving subleading corrections. The current can also destabilize a classical order, and may give rise to new kinds of ordered or quasi-ordered phases.   

Theory of a smeared quantum phase transition

We present a comprehensive strong-disorder renormalization group theory of the quantum phase transition in the dissipative random quantum Ising chain. For Ohmic dissipation, we solve the renormalization group flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.   

Rounding of a first order quantum phase transition to a quantum critical point

We give a heuristic argument for disorder rounding of a first order quantum phase transition into a continuous phase transition. From both weak and strong disorder analysis of the the $N$-color quantum Ashkin-Teller model in one spatial dimension, we find that for $N \geq 3$, the first order transition is rounded to a continuous transition and the physical picture is the same as the random transverse field Ising model for a limited parameter regime. The results are strikingly different from the corresponding classical problem in two dimensions where the fate of the renormalization group flows is a fixed point corresponding to $N$-decoupled pure Ising models.   

Criticality in Inhomogeneous magnetic systems: Applications to Quantum Ferromagnets

In standard phase transitions such as the liquid-gas transition, a homogeneous order parameter (OP) vanishes as one crosses from the ordered phase to the disordered one. An external field may preclude a homogeneous OP. This happens for a fluid in a gravitational field, where the transition becomes smeared[1] in the sense that the OP is nonzero everywhere, albeit very small in some regions of the phase diagram. A ferromagnet (FM) subject to mechanical stress is another realization of a system in an external field that has an inhomogeneous OP. We first investigate a classical Heisenberg FM, which is modeled by a $\phi^{4}$ theory with a spatially dependent mass $r(x)$. In contrast to the fluids case, we find a sharp phase transition where the envelope of the local magnetization vanishes uniformly, and mean-field critical exponents. The first order transition in quantum itinerant FMs also remains sharp and the fluctuation effects leading to a tricritical point are suppressed, and one recovers a quantum critical point with mean field exponents[2]. [1] J.V. Sengers and J.M.J. van Leeuwen, Physica A, 116, 345 (1982). [2] D. Belitz, T.R. Kirkpatrick, and R. Saha, Phys. Rev. Lett., 99, 147203(2007).   

Non-Ginzburg-Landau Type Universality in Quantum Metamagnetism Induced by Topological Change of Fermi Surface: Applications to a Weak Itinerant-Electron Ferromagnet ZrZn$_{2}$

We clarify that metamagnetic transitions show unconventional properties as quantum phase transitions if they are accompanied by changes in Fermi-surface topology. Topological change of the Fermi surface makes the phase diagram qualitatively different from that of the conventional metamagnetic transitions; the quantum critical endpoint becomes not only the terminal of the finite-temperature critical line, but also the terminal of a quantum critical line of continuous Lifshitz transitions. Around the \textit{quantum critical terminal}, power-law singularities of thermodynamic quantities are determined by the Fermi-surface topology and, therefore, are characterized \textit{neither} by the Ising symmetry breaking \textit{nor} by the Ginzburg-Landau-Wilson scheme proposed by Moriya, Hertz and Millis for the conventional quantum criticalities. We propose that such an unconventional universality indeed accounts for the metamagnetic transitions observed in ZrZn$_{2}$.