Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session U12: Strongly Correlated Electron Systems: Quantum Phase Transitions 
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Sponsoring Units: DCMP Chair: Andrew Millis, Columbia University Room: Morial Convention Center 203 
Thursday, March 13, 2008 8:00AM  8:12AM 
U12.00001: Quantum phase transition of a magnetic impurity in a dissipative environment Mengxing Cheng, Kevin Ingersent, Matthew Glossop We study the quantum phase transition (QPT) induced by dissipation in the BoseFermi 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 subOhmic bath exponents $0 < s < 1$, numerical renormalizationgroup calculations show that upon increasing the coupling to the bosonic bath from zero, there is a crossover from a conventional (spinsector) Kondo effect to a chargeKondo effect. Further increase of the bosonic coupling results in a zerotemperature 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 subOhmic spinboson model. Results for the Ohmic case $s=1$ will also be presented. [Preview Abstract] 
Thursday, March 13, 2008 8:12AM  8:24AM 
U12.00002: Quantum Criticality of the Pseudogapped Kondo Problem: Finite Temperature Scaling and Conformal Invariance Matthew T. Glossop, Stefan Kirchner, Qimiao Si The critical destruction of the Kondo effect is of interest as a potential mechanism for quantumcritical heavyfermion metals. Here, we study the pseudogapped Kondo model [1], with a conductionelectron density of states proportional to $\epsilon^r$, which provides a paradigm for understanding critical localmoment fluctuations. In general, an interacting quantum critical point (QCP), at a finite critical Kondo coupling $J_c$, separates Kondoscreened and free localmoment phases [2]. We focus on finite$T$ scaling properties in the vicinity of the QCP, obtained using a dynamical largeN 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 continuoustime quantum Monte Carlo impurity solver [3], which involves a stochastic evaluation of an expansion in the hostimpurity 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) [Preview Abstract] 
Thursday, March 13, 2008 8:24AM  8:36AM 
U12.00003: Quantumcriticality in models of an impurity coupled to fermionic and bosonic baths Kevin Ingersent, Matthew Glossop Impurity models exhibiting quantum phase transitions (QPTs) have attracted interest in connection with impurities in cuprate superconductors, heavyfermion quantum criticality, and quantumdot 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 renormalizationgroup 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 purebosonic spinboson model, with exponents that are independent of $r$. However, for sufficiently strong fermionic pseudogaps (large values of $r$), new universality classes of QPT emerge. [Preview Abstract] 
Thursday, March 13, 2008 8:36AM  8:48AM 
U12.00004: The TwoImpurity Anderson Model at Quantum Criticality David Mross, Henrik Johannesson We propose a realization of the twoimpurity Anderson model in a double quantumdot system. When charge transfer between the dots is suppressed the system exhibits a nonFermi 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 nonFermi liquid state after the system is shifted into the critical region, e.g. by a sudden change of a nearby gate voltage. [Preview Abstract] 

U12.00005: ABSTRACT WITHDRAWN 
Thursday, March 13, 2008 9:00AM  9:12AM 
U12.00006: Absence of quantum phase transition in twostate quantum dot Xin Wang, Andrew J. Millis We use continuoustime quantum Monte Carlo methods to study a model of a spinlessfermion 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). [Preview Abstract] 
Thursday, March 13, 2008 9:12AM  9:24AM 
U12.00007: Kondo destruction in the BoseFermi Kondo model with a singular dissipative spectrum: Exact solutions and their implications Jianhui Dai, C.J. Bolech, Qimiao Si 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 subOhmic BoseFermi Kondo (BFK) model provides a setting to study such an effect. Here, we show that this manybody 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 largeN 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 undertreatment of the longitudinal fluctuations. Our results resolve an apparent inconsistency between the previous results respectively found using numerical renormalization group and largeN 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. [Preview Abstract] 

U12.00008: ABSTRACT WITHDRAWN 
Thursday, March 13, 2008 9:36AM  9:48AM 
U12.00009: Quantum Criticality out of Equilibrium: Kondo Destruction and $V/T$ Scaling in a Magnetic SingleElectron Transistor Stefan Kirchner, Qimiao Si Nonequilibrium quantum phase transitions have so far received only limited attention despite the longstanding strong interest in classical outofequilibrium 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 welldefined outofequilibrium states that give rise to unique steadystate limits. We recently showed that such a system, a magnetic singleelectron 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 nonlinear electronic transport near the transition, we generalize the system to a largeN limit, where an exact quantum Boltzmann treatment becomes possible. We determine the universal scaling functions for the IV characteristics in the linear and nonlinear 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. [Preview Abstract] 
Thursday, March 13, 2008 9:48AM  10:00AM 
U12.00010: Effects of dissipation on a quantum critical point with disorder Thomas Vojta, Jose Hoyos, Chetan Kotabage We study the effects of dissipation on a disordered quantum phase transition with O$(N)$ order parameter symmetry by applying a strongdisorder renormalization group to the LandauGinzburgWilson field theory of the problem. We find that Ohmic dissipation results in a nonperturbative infiniterandomness critical point with unconventional activated dynamical scaling while superohmic damping leads to conventional behavior. We discuss applications to the superconductormetal transition in nanowires and to Hertz' theory of the itinerant antiferromagnetic transition. [Preview Abstract] 
Thursday, March 13, 2008 10:00AM  10:12AM 
U12.00011: CurrentFlowDriven Nonequilibrium ParamagenticFerromagnetic Phase Transitions Aditi Mitra, Igor Aleiner, Andrew Millis We study a 2d itinerant electron system near a ferromagneticparamagnetic 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 comoving 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 quasiordered phases. [Preview Abstract] 
Thursday, March 13, 2008 10:12AM  10:24AM 
U12.00012: Theory of a smeared quantum phase transition Jose Hoyos, Thomas Vojta We present a comprehensive strongdisorder 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 lowtemperature 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. [Preview Abstract] 
Thursday, March 13, 2008 10:24AM  10:36AM 
U12.00013: Rounding of a first order quantum phase transition to a quantum critical point Pallab Goswami, David Schwab, Sudip Chakravarty 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 AshkinTeller 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. [Preview Abstract] 
Thursday, March 13, 2008 10:36AM  10:48AM 
U12.00014: Criticality in Inhomogeneous magnetic systems: Applications to Quantum Ferromagnets R. Saha, T.R. Kirkpatrick, D. Belitz In standard phase transitions such as the liquidgas 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 meanfield 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). [Preview Abstract] 
Thursday, March 13, 2008 10:48AM  11:00AM 
U12.00015: NonGinzburgLandau Type Universality in Quantum Metamagnetism Induced by Topological Change of Fermi Surface: Applications to a Weak ItinerantElectron Ferromagnet ZrZn$_{2}$ Youhei Yamaji, Takahiro Misawa, Masatoshi Imada We clarify that metamagnetic transitions show unconventional properties as quantum phase transitions if they are accompanied by changes in Fermisurface 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 finitetemperature critical line, but also the terminal of a quantum critical line of continuous Lifshitz transitions. Around the \textit{quantum critical terminal}, powerlaw singularities of thermodynamic quantities are determined by the Fermisurface topology and, therefore, are characterized \textit{neither} by the Ising symmetry breaking \textit{nor} by the GinzburgLandauWilson 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$_{2}$. [Preview Abstract] 
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