The tetrahedron puzzle

(Yet another attempt to revive this blog. My experience from the other blog is that having a readership helps; however I don't think my interests overlap that strongly with anyone else's.)

On the arxiv this evening:

Local Quantum Criticality of an Iron-Pnictide Tetrahedron
T. Tzen Ong, Piers Coleman
arXiv:1109.4131

Abstract: Motivated by the close correlation between transition temperature ($T_c$) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground-state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.

[A little background. The pnictides/chalcogenides are of course the new iron-based superconductors; the crystal structure is such that each iron ion sits at the center of a tetrahedral cage of As-type or Se-type ions. In a plot that has now become common knowledge, a Japanese group showed [Yamada, et. al. J. Phys. Soc. Jpn 77, 083704 (2008)] that the transition temperature is highest when the tetrahedra are regular. Why should this matter? One possible line of thinking is as follows: it is either known or generally believed, from the cuprates etc., that superconducting transition temperatures are anomalously high near quantum critical points. Therefore if there were criticality associated with the perfect tetrahedral shape, you might expect criticality and hence a high transition temperature. What the Coleman paper shows is that, at least for the simplified model of a single tetrahedron in a bath, there is in fact criticality, which has to do with the degeneracy of orbitals in a perfect tetrahedron. It is a long way from proving anything directly about superconductivity but is in any case a highly interesting result.]

1/f noise and quantum criticality

One of those nice if obvious-after-the-fact results -- quantum critical correlations are preserved under the addition of 1/f noise. It's obvious after the fact because (a) 1/f noise has power law correlations in time, so it's "critical" in some sense; (b) more precisely, the 1/f noise term appears in the Keldysh action in precisely the same way as the "equilibrium" noise term -- from the FDT -- that drives the superconductor-insulator transition in a Josephson junction.

Quantum critical states and phase transitions in the presence of non-equilibrium noise
E. della Torre et al., Nature Physics doi:10.1038/nphys1754 [also arXiv:0908.0868]

"If you cannot be kind, at least have the decency to be vague"

I'm glad blogger finally got around to doing something about the comment spam. On the other hand, a small fraction of it will be missed.

I intend to revive this blog because I'm spending the semester in Santa Barbara, and would like to avoid spamming the population of Urbana with papers that I think are interesting.

On that note -- there actually are physicists called "D'Eath" and "Payne" who published a series of papers together.

Numbering equations 1a, 1b etc in TeX

This is how it's done:

One nice trick is if you want equations with lettered sublabels - 1a, 1b, etc. First you must include the amsmath package, and the enclose the relevant equations in the 'subequations' environment like this:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
...
\begin{subequations}
\begin{eqnarray}
x
&=& y^2 \\
&=& (a-b)^2 \nonumber \\
&=&
c
\end{eqnarray}
\end{subequations}
...
\end{document}

where the \nonumber command suppresses numbering of that line. You can use any number of ordinary equations or equation arrays inside the subequations environment.

Proximity-induced triplet superconductivity

A normal metal placed next to an s-wave superconductor develops superconducting correlations because of the "proximity effect" -- Cooper pairs penetrate some distance into the normal metal, for basically the same reason as the eigenstates in a finite square well leak some distance out of the well. (I think this is true; the point is that the Cooper pairs have a longish lifetime in the normal metal.) This shouldn't work for a ferromagnetic material, however, as the Cooper pairs -- being a spin-singlet -- ought to be broken and aligned with the ferromagnet if they stray into it. Efetov and coworkers made the rather surprising prediction (Bergeret et al, PRL 86, 4096 (2001)) that under certain conditions a singlet superconductor can induce a triplet proximity effect in the ferromagnet, with pair correlations (i.e., <>) that are odd in time (Bergeret et al, Rev. Mod. Phys. 77, 1321 (2005)). Norman Birge's group has a new preprint out claiming to have seen this proximity effect:

Observation of spin-triplet superconductivity in Co-based Josephson Junctions
arXiv:0912.0205
Authors: Trupti S. Khaire, Mazin A. Khasawneh, W. P. Pratt, Jr., Norman O. Birge

Abstract: We have measured a long-range supercurrent in Josephson junctions containing Co (a strong ferromagnetic material) when we insert thin layers of either PdNi or CuNi weakly-ferromagnetic alloys between the Co and the two superconducting Nb electrodes. The critical current in such junctions hardly decays for Co thicknesses in the range of 12-28 nm, whereas it decays very steeply in similar junctions without the alloy layers. The long-range supercurrent is controllable by the thickness of the alloy layer, reaching a maximum for a thickness of a few nm. These experimental observations provide strong evidence for induced spin-triplet pair correlations, which have been predicted to occur in superconducting/ferromagnetic hybrid systems in the presence of certain types of magnetic inhomogeneity.

The thermodynamic limit and the FQHE

I'm taking Tony Leggett's course on two-dimensional physics; it's the first time I've thought hard about the fractional quantum Hall effect, the quantum Hall and spin-Hall effects, fractional statistics, and related "topological" phenomena. I think I'm finally beginning to understand what's behind these effects, and it's essentially a rather subtle business with adiabaticity. Hopefully I'll straighten all of this out in due course; for now, here are two papers on the ground-state degeneracy of the FQHE:

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http://prola.aps.org/abstract/PRB/v41/i13/p9377_1
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
X.-G. Wen and Q. Niu
Phys. Rev. B 41, 9377 - 9396 (1990)

The fractional quantum Hall (FQH) states are shown to have q̃^g-fold ground-state degeneracy on a Riemann surface of genus g, where q̃ is the ground-state degeneracy in a torus topology. The ground-state degeneracies are directly related to the statistics of the quasiparticles given by θ=p̃π/q̃. The ground-state degeneracy is shown to be invariant against weak but otherwise arbitrary perturbations. Therefore the ground-state degeneracy provides a new quantum number, in addition to the Hall conductance, characterizing different phases of the FQH systems. The phases with different ground-state degeneracies are considered to have different topological orders. For a finite system of size L, the ground-state degeneracy is lifted. The energy splitting is shown to be at most of order e-L/ξ. We also show that the Ginzburg-Landau theory of the FQH states (in the low-energy limit) is a dual theory of the U(1) Chern-Simons topological theory.

http://prola.aps.org/abstract/PRL/v66/i6/p806_1
Fractional quantum Hall effect and multiple Aharonov-Bohm periods
D.J. Thouless and Y. Gefen
Phys. Rev. Lett. 66, 806 - 809 (1991)

An arrangement for obtaining Aharonov-Bohm oscillations of basic periodicity qh/e (q>1) is discussed. The relaxation towards h/e periodicity is characterized by a decay time exponential in the system size at zero temperature, and linear in this size at finite temperature.

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The Thouless-Gefen paper is particularly good, see esp. Fig. 1. [I think the following text is unintelligible without the figure but should make sense once you look at it.] The idea is to consider the FQHE in a CD-shaped geometry (called, for obscure reasons, a Corbino disk) with a fixed field B through the "substance" of the disk -- which creates the FQHE -- and a variable flux F (sorry about the notation, I really ought to install the tex widget...) threading the hole. Quantum mechanics says that the ground state energy should be periodic in the flux threading the hole, with a period of one flux quantum; Cooper pairs give you half this period because they have charge 2e, whereas a system with "fractionally charged" excitations (say q = e/3, the classic Laughlin state) gives you three times this period, which appears to contradict a basic quantum mechanical result called the Byers-Yang theorem. Ultimately this turns out to be about level crossings (Fig. 1 of Thouless-Gefen): there are three ground states that have vanishingly small matrix elements mixing them; if one increased the flux F vanishingly slowly, one would track the ground state of the system, and have 1/e-periodic behavior; if one increased the flux rapidly, one would go straight up the original curve, not notice the level crossings, and get no periodicity at all ("physically" this corresponds to continually adding quasiparticles); in practice, one goes "rapidly" as far as the second level crossing and "adiabatically" with respect to that (b'se there's a much bigger avoided-level-crossing there) so one comes back to the ground state with 3/e periodicity.

A key corollary, I think, is that fractional charge (and therefore fractional statistics) are a consequence of non-avoided and avoided level crossings when you "slowly" move a particle around another -- i.e. a consequence of the order in which you take the limit of infinite system size and the limit of moving a particle around another (or ramping up a flux) infinitely slowly. This does not mean they aren't "real," of course, since phase transitions, which are evidently real, are also ultimately a consequence of the order in which one takes limits. It appears to be true that in all known cases of fractional statistics, at least of the abelian kind (another example is Kitaev's toric code model), one has this sort of ground-state degeneracy.

Cond-mat journal club on AdS/CFT

Here's a cond-mat journal club thing on AdS/CFT and applications to cond-mat, e.g. explaining the strange metal phase. The commentary is written by cond-mat theorists incl. Abrahams who's most famous for being one of the Gang of Four.

Giant SPIDERs etc.

Some good recent stuff in PRL:

Giant Surface-Plasmon-Induced Drag Effect in Metal Nanowires
Maxim Durach,1 Anastasia Rusina,1 and Mark I. Stockman1,2,3
Phys. Rev. Lett. 103, 186801 (2009)

Here, for the first time we predict a giant surface-plasmon-induced drag-effect rectification (SPIDER), which exists under conditions of the extreme nanoplasmonic confinement. In nanowires, this giant SPIDER generates rectified THz potential differences up to 10 V and extremely strong electric fields up to ~105–106 V/cm. The giant SPIDER is an ultrafast effect whose bandwidth for nanometric wires is ~20 THz. It opens up a new field of ultraintense THz nanooptics with wide potential applications in nanotechnology and nanoscience, including microelectronics, nanoplasmonics, and biomedicine.

[sg] I haven't read this paper and I'm not sure I want to, I'm just awed by the brilliance of "giant SPIDER effect." This is obviously going to collect oodles of citations, mostly from me.

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Holstein Polarons Near Surfaces
Glen L. Goodvin, Lucian Covaci, and Mona Berciu
Phys. Rev. Lett. 103, 176402 (2009)

We study the effects of a nearby surface on the spectral weight of a Holstein polaron, using the inhomogeneous momentum average approximation which is accurate over the entire range of electron-phonon (e-ph) coupling strengths. The broken translational symmetry is taken into account exactly. We find that the e-ph coupling gives rise to a large additional surface potential, with strong retardation effects, which may bind surface states even when they are not normally expected. The surface, therefore, has a significant effect and bulk properties are recovered only very far away from it. These results demonstrate that interpretation in terms of bulk quantities of spectroscopic data sensitive only to a few surface layers is not always appropriate.

[sg] The recent work on surface polarons is pretty interesting and it's something I'd like to get into at some point. It's primarily motivated by the recent glut of exptal work on heterostructures of strongly correlated materials; the interfaces often undergo substantial electronic and/or lattice reconstruction. Naturally these not-terribly-stable surfaces are morbidly sensitive to, e.g., the electrostatic force exerted by a moving electron.
I'm also curious about whether the authors are right about the interpretation of surface-based spectroscopic data.

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Phys. Rev. Lett. 103, 177002 (2009)
Evidence for Two Time Scales in Long SNS Junctions
F. Chiodi, M. Aprili, and B. Reulet

We use microwave excitation to elucidate the dynamics of long superconductor–normal metal–superconductor Josephson junctions. By varying the excitation frequency in the range 10 MHz–40 GHz, we observe that the critical and retrapping currents, deduced from the dc voltage versus dc current characteristics of the junction, are set by two different time scales. The critical current increases when the ac frequency is larger than the inverse diffusion time in the normal metal, whereas the retrapping current is strongly modified when the excitation frequency is above the electron-phonon rate in the normal metal. Therefore the critical and retrapping currents are associated with elastic and inelastic scattering, respectively.

[sg] In the traditional Josephson junction model (i.e. tilted washboard + friction), switching happens when the washboard's wells cease to be metastable and retrapping happens when the terminal velocity of a particle going down the washboard goes to zero. Retrapping depends on friction and switching doesn't, so you have a clean separation of energy scales. In long junctions things are generally messier because switching depends on heat transfer from a locally normal area to the rest of the wire, etc.; however, this paper manages to retrieve a rather nice separation of scales.

Title: Off-diagonal correlations in a one-dimensional gas of dipolar bosons

Authors: Tommaso Roscilde, Massimo Boninsegni

We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded, in favor of quasi-solidity. For all strengths of the dipolar interaction, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay; and the momentum distribution shows sharp kinks at the wavevectors of the oscillations, $Q = \pm 2\pi n$ (where $n$ is the atom density), beyond which it is strongly suppressed. This \emph{momentum filtering} effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that one-dimensional dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.

http://arxiv.org/abs/0910.4165

Supersolid Helium and anamolous transport

Underlying Mechanism for the Giant Isochoric Compressibility of Solid 4he: Superclimb of Dislocations

authors:
S. G. Söyler,1 A. B. Kuklov,2 L. Pollet,3 N. V. Prokof'ev,1,4 and B. V. Svistunov1,4

In the experiment on superfluid transport in solid 4He [Phys. Rev. Lett. 100, 235301 (2008)], Ray and Hallock observed an anomalously large isochoric compressibility: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor “electrodes.” We propose that the effect is due to superclimb: edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by ab initio simulations of an edge dislocation in solid 4He at T=0.5 K. We argue that at low temperature the effect must be suppressed due to a crossover to the smooth dislocation.



http://link.aps.org/doi/10.1103/PhysRevLett.103.175301

QMC and Scaling

This letter addresses the case without a sign problem. I think eqn. 3 can be trivially applied to a DMC calculation. I should look at it further though.

Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions

Authors:
David Schwandt,1,2 Fabien Alet,1,2 and Sylvain Capponi1,2
1Laboratoire de Physique Théorique, Université de Toulouse, UPS, (IRSAMC), F-31062 Toulouse, France
2CNRS, LPT (IRSAMC), F-31062 Toulouse, France

Abstract:
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.

http://link.aps.org/doi/10.1103/PhysRevLett.103.170501

Gowers on Complexity Bounds

Timothy Gowers has apparently been thinking about the P = NP problem. I've enjoyed his series of posts on this so far, even if the details are often a little over my head. Here's a link to the first post; the others can be accessed by conventional means.

New preprint

I have a new preprint on the arxiv with Siddhartha Lal and Paul Goldbart. It's about N-channel Kondo physics with interacting 1D bosons (e.g. cold atoms) as the leads.

Quenches as probes of quantum phase transitions

This numerical paper has some fascinating results, and the germ of a very clever idea (I heard about this work via Andy Millis):

Dynamical phase transition in correlated fermionic lattice systems
Martin Eckstein, Marcus Kollar, Philipp Werner
http://arxiv.org/abs/0904.0976

Abstract: We use non-equilibrium dynamical mean-field theory to demonstrate the existence of a critical interaction in the real-time dynamics of the Hubbard model after an interaction quench. The critical point is characterized by fast thermalization and separates weak-coupling and strong-coupling regimes in which the relaxation is delayed due to prethermalization on intermediate timescales. This dynamical phase transition should be observable in experiments on trapped fermionic atoms.

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So what they do is quench the interaction strength and see how long it takes the system to thermalize. In general when you quench into a gapped state, thermalization can take a really long time because particles trapped on the wrong side of the gap don't have anything to decay into. (See here.) On the other hand, e.g. near a quantum phase transition, the gap is small and thermalization should be easy. So by looking at how long a system takes to approach equilibrium as you quench from a reference parameter value to some value U_f, you can essentially map out a quantum phase diagram and maybe get some information about the exponents. [I should note that this is all somewhat speculative.] What's particularly interesting about the Kollar/Eckstein case is that they didn't even know there was a phase transition there until they did their simulations.

There's some recent work on (possibly) similar ideas that I haven't read yet:

Quench dynamics as a probe of quantum criticality
Authors: R. A. Barankov
http://arxiv.org/abs/0910.0255

Abstract: Quantum critical points of many-body systems can be characterized by studying response of the ground-state wave function to the change of the external parameter, encoded in the ground-state fidelity susceptibility. This quantity characterizes the quench dynamics induced by sudden change of the parameter. In this framework, I analyze scaling relations concerning the probability of excitation and the excitation energy, with the quench amplitude of this parameter. These results are illustrated in the case of one-dimensional sine-Gordon model.

My paper in Nature Phys.

I guess I should link to my paper with Benjamin Lev and Paul Goldbart on BECs in multimode cavities now that it's finally been published.