Session Q5: Nonequilibrium and Gauge/Gravity Duality

Solution to the d=2 Hertz-Millis problem from a hairy electron star

We use holography to study the spontaneous condensation of a neutral order parameter in a (2+1)-dimensional field theory at zero-temperature and finite density, dual to the electron star background of Hartnoll and Tavanfar. An appealing feature of this field theory is the emergence of an IR Lifshitz fixed-point with a finite dynamical critical exponent $z$, which is due to the strong interaction between critical bosonic degrees of freedom and a finite density of fermions (metallic quantum criticality). We show that under some circumstances the electron star background develops a neutral scalar hair whose holographic interpretation is that the boundary field theory undergoes a quantum phase transition, with a Berezinski-Kosterlitz-Thouless character, to a phase with a neutral order parameter. Including the backreaction of the bulk neutral scalar on the background, we argue that the two phases across the quantum critical point have different $z$, a novelty that exists in certain quantum phase transitions in condensed matter systems. We also analyze the system at finite temperature and find that the phase transition becomes, as expected, second-order. Embedding the neutral scalar into a higher form, a variety of interesting phases could potentially be realized for the boundary field   

Non-Relativistic Holographic Quantum Liquids

We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we find a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system reenters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.   

Striped Superconductor and Holography

Using gauge/gravity duality, we analytically study the properties of a strongly coupled striped superconductor, with the charge density wave sourced by a modulated chemical potential. The calculation is done in the large modulation wavenumber $Q$ regime and comparing the results with numerical calculations, we find good agreement for $Q \geq 3 T_c$. In the absence of a homogeneous term in the chemical potential, we show that the critical temperature scales as a negative power of $Q$ for scaling dimensions $\Delta < \frac{3}{2}$, whereas for $\Delta > \frac{3}{2}$, there is no phase transition above a certain critical value of $Q$. The order parameter or the condensate is found to scale as a positive power of $Q$ such that the gap is proportional to $Q$. We discuss how these results change if a homogeneous term is added to the chemical potential. We also calculate the conductivity with its spatial dependence.   

Holographic noise near quantum critical points

The dynamical scaling present in equilibrium correlations near to a quantum critical point suggests the possibility of universal, out-of-equilibrium steady states. This has been demonstrated in analyses of the response of the bosonic Hubbard model to a strong electric field. The universal out-of-equilibrium behaviour is particularly apparent in the current noise; at high field, a current noise power ${\cal S}_j \propto \sqrt{E}$ was found which was interpreted as Johnson-like with an effective temperature $\propto \sqrt{E}$ [Phys. Rev. Lett. 97, 227003 (2006)]. We revisit this problem using the holographic mapping to a classical gravitational system. We recover a current noise that extends the previously known equilibrium and strongly out-of-equilibrium results with a full interpolation between the two: ${\cal S}_j \propto T_{eff}$ with $T_{eff}=(T^4+E^2/\pi^4)^{1/4}$.   

Out-of-equilibrium conductivity and current noise at quantum critical points

Quantum critical points display universal behaviour across a wide range of physical systems. These effects appear in both thermodynamics and transport. Such behaviour should also be present out-of-equilibrium where, for example, the current and current noise should follow scaling laws as a function of applied field. These expectations have been borne out in calculations for out-of-equilibrium transport at the Superfluid-Mott Insulator quantum critical point of the Bose-Hubbard model \cite{Green_2005,Green_2006}. These analyses extend the quantum Boltzmann description \cite{Damle_1997} of equilibrium transport using a trick of the 1/N expansion. Here we use an epsilon expansion to obtain similar results. This approach has the advantage of making the physical constraints of the results more transparent. We also present preliminary analysis of the evolution to the non-equilibrium steady state after the electric field is applied. \begin{thebibliography}{3} \bibitem{Green_2005}A.G. Green and S.L. Sondhi, PRL 95, 267001 (2005) \bibitem{Green_2006}A.G. Green, J.E. Moore, S.L. Sondhi and A. Vishwanath, PRL 97, 227003 (2006) \bibitem{Damle_1997}K. Damle and S. Sachdev, PRB 56, 14 (1997) \end{thebibliography}   

Wigner-Mott scaling of transport near the two-dimensional metal-insulator transition

Thermal destructions of heavy quasiparticles often dominates the transport behavior of many strongly correlated materials. It typically leads to pronounced resistivity maxima in the incoherent regime around the coherence temperature $T^{*}$, reflecting the tendency of carriers to undergo Mott localization following the demise of the Fermi liquid. This behavior is best pronounced in the vicinity of interaction-driven (Mott-like) metal-insulator transitions, where the $T^{*}$ decreases, while the resistivity maximum $\rho_{max}$ increases. Here we show that, in this regime, the entire family of resistivity curves display a characteristic scaling behavior $\rho(T)/\rho_{max}\approx F(T/T_{max}),$ while the $\rho_{max}$ and $T_{max}\sim T^{*}$ assume a powerlaw dependence on the quasi-particle effective mass $m^{*}$. Remarkably, precisely such trends are found from an appropriate scaling analysis of experimental data obtained from diluted two-dimensional electron gases in zero magnetic fields. Our analysis provides strong evidence that inelastic electron-electron scattering -- and not disorder effects -- dominates finite temperature transport in these systems, validating the Wigner-Mott picture of the two-dimensional metal-insulator transition.   

Finite-size effects in transport data from Quantum Monte Carlo simulations

We have examined the behavior of the compressibility, of the dc-conductivity, and of the Drude weight as probes of the density-driven metal-insulator transition in the Hubbard model on a square lattice. These quantities have been obtained through determinantal quantum Monte Carlo simulations at finite temperatures on lattices up to $16\times 16$ sites. While the compressibility and the dc-conductivity are known to suffer from `closed-shell' effects due to the presence of artificial gaps in the spectrum (caused by the finiteness of the lattices), we have established that the former tracks the average sign of the fermionic determinant, and that a shortcut often used to calculate the conductivity may neglect important corrections. We have also performed systematic studies of the dependence of our data with the imaginary-time interval. Our analyses also show that, by contrast, the Drude weight is not too sensitive to finite-size effects, being much more reliable as a probe to the insulating state.   

Universal transport near a continuous Mott transition in two dimensions

We discuss the universal transport signatures near a zero-temperature continuous Mott transition between a Fermi liquid and a spin liquid in 2 spatial dimensions. This transition can be described using a slave-rotor field theory, where the electron is decomposed into a fermionic spinon and charge-carrying rotor, both interacting with an emergent U(1) gauge field. The universal part of the non-zero temperature charge transport is determined by the dynamics of the charged rotors and is affected by the gauge fluctuations. Explicit predictions for the behavior of the electrical conductivity are made via the solution of a quantum kinetic equation using controlled approximations.   

Dissipation-Induced Quantum Phase Transition in a Resonant Level

We measure conductance through a resonant level coupled to a dissipative environment, which suppresses tunneling rate at low energies. Our sample consists of a single-walled carbon nanotube quantum dot contacted by resistive metal leads that serve as the dissipative environment. We study the shape of the resonant conductance peak, with the expectation that its width and height, both dependent on the tunneling rate, will be suppressed at low temperatures. However, we observe distinct regimes, including a case where the resonant tunneling conductance reaches the unitary limit, despite the presence of dissipation. We discuss the implication of these findings for a dissipation-induced quantum phase transition and extract the scaling exponents.   

Collective excitations and low temperature transport properties of bismuth

We examine the influence of collective excitations on the transport properties (resistivity and magneto-optical conductivity) for semimetals, focusing on the case of bismuth. We show, using a random-phase approximation (RPA), that the properties of the system are drastically affected by the presence of an acoustic-plasmon mode, which is a consequence of the presence of two types of carriers (electrons and holes) in this system. We find a crossover temperature $T^*$ separating two different regimes of transport. At high temperatures where $T > T^*$, the Baber scattering explains quantitatively the dc resistivity experiments, while at low temperatures where $T < T^*$, the interactions of the carriers with this collective mode lead to a $T^5$ behavior of the resistivity. We examine other consequences of the presence of this mode. In particular a two-plasmon edge feature in the magneto-optical conductivity is predicted. We compare our results with the experimental findings on bismuth. We discuss the limitations and extensions of our results beyond the RPA, and examine the case of other semimetals such as $1T-TiSe_2$.   

Photo-excitation and relaxation dynamics in junction of double-exchange systems

The photo-induced insulator-metal (I-M) transition is studied by the numerical simulation of real-time quantum dynamics of a double-exchange model. We find a characteristic multiplication of particle-hole (p-h) pairs by a p-h pair of high energy during the I-M transition. To examine the conversion from the p-h pairs into electric energy, we perform the numerical study on the junction systems combined by the double exchange models. The numerical results have been revealed including (i) the threshold behavior with respect to the intensity and energy of light, (ii) p-h pairs are well separated and pair annihilation is suppressed, (iii) enhancement of collected carrier by meta-stability of I-M transition.   

Photo excited state in spin-charge coupled correlated electron system

Recent ultrafast optical techniques open up a new frontier for research of the phase transition. Photo-induced phase is transient and highly nonequilibrium. photo-induced phenomena in correlated electron systems offer large possibility of new hidden phases which do not realize in the thermal equilibrium state, and prompt several theoretical challenges. In this talk, I will talk about recent our theoretical results for the photo-induced phase transition in correlated electron systems. We study the photo-induced spin state change in itinerant correlated electron system, motivated from the experiments in perovskite cobaltites [1]. The effective models before and after photon-pumping are derived from the two-orbital Hubbard model and are analyzed by the exact diagonalization method. When a photon is introduced in the low-spin band insulator, we found a spin-polarized bound state of photo-excited hole and the high-spin state. This bound state directly reflects the optical pump-probe spectra. These results well explain the recent femtosecond spectroscopy experiments in perovskite cobaltites We also show the unusual double-exchange interaction in photo excited state. \\[4pt] [1] Y. Kanamori, H. Matsueda and S. Ishihara, Phys. Rev. Lett. 107, 167403-1-5 (2011)   

Non-equilibrium steady state of field-driven strongly correlated electrons

We theoretically study the nature of non-equilibrium steady state of strongly correlated electrons on lattices under the influence of a static electric field. We describe the dynamics of steady state by the Floquet theory, and the electron correlation by the dynamical mean-field theory, respectively. We find that the steady-state current in a closed system is characterized by the Bloch oscillation in the metallic regime, while it vanishes in the Mott-insulating regime. Importantly, the coherent contribution to the current can be captured by measuring the quasiparticle weight in the local spectral density as in equilibrium. Based on these criteria, we draw the non-equilibrium phase diagram as a function of the strength of electric field and the on-site interaction at zero temperature. *References: [1] A. V. Joura, J. K. Freericks, and Th. Pruschke, Phys. Rev. Lett. 101, 196401 (2008); [2] N. Tsuji, T. Oka, and H. Aoki, Phys. Rev. B 78, 235124 (2008).   

Dynamical DMRG study of non-linear optical response in one-dimensional dimerized Hubbard model with nearest neighbor Coulomb interaction and alternating on-site potential

The optical response of organic compounds has been attracting much attention. The one of the reasons is the huge non-linear and ultrafast optical response [K. Yamamoto \textit{et}. \textit{al}., J. Phys. Soc. Jpn. \textbf{77}, 074709(2008)]. In order to investigate such optical properties, we carry out dynamical DMRG calculations to obtain optical responses in the 1/4-filled one-dimensional Hubbard model including the nearest neighbor Coulomb interaction and the alternating electron hopping. The charge gap [S. Nishimoto, M. Takahashi, and Y. Ohta, J. Phys. Soc. Jpn. \textbf{69}, 1594(2000)] and the bound state [H. Benthien and E. Jeckelmann, Eur. Phys. J. B \textbf{44}, 287(2005)] in this model have been discussed based on DMRG calculations. In the present study, we introduce an alternating on-site potential giving the polarization in the system into the dimerized Hubbard model, which breaks the reflection symmetry of the system. In this talk, we discuss the obtained linear and the 2nd order non-linear optical susceptibility in order to make a prediction for non-linear optical experiments in the future.   

Non-Kondo mechanism of resistivity upturn in a spin-ice Kondo lattice model

Ice rule is a configurational constraint observed in a broad range of systems in which two-state variables are defined at the vertices of a pyrochlore lattice. The constraint enforces the so-called `two-in two-out' configuration; two out of four neighboring sites within each tetrahedron are in the opposite state to the other two. Under this peculiar local constraint, the system remains disordered, whereas the ground state is characterized by macroscopic degeneracy with a hidden gauge structure. Recent experiments on pyrochlore metallic oxides have promoted interest in itinerant electrons coupled with such ice-rule type localized moments. Here we investigate how electronic and transport properties are affected by the coupling to the spin ice by applying a cellular dynamical mean-field theory to a spin-ice type Kondo lattice model. We found that a spin-ice liquid state emerges in a wide temperature range at low electron density, in which two-in two-out local correlation well develops in the absence of long-range ordering. In this spin liquid state, the resistivity shows an upturn because of an anomalous scattering of electrons by the local spin-ice type correlation. The details of this non-Kondo resistivity upturn will be discussed in relation with experiments in pyrochlore oxides.