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Tuesday, January 27th 2015

4:30 pm:

In this talk, I will briefly discuss the effective K matrix formalism of fractional quantum Hall effects base on Wen's book. I will mainly focus on the single-layered, multilayered FQH systems, and the hierarchical states.

[1] Xiao-Gang Wen, Quantum Field Theory of Many-Body Systems, (Oxford University Press, New York, 2004).

[2] Xiao-Gang Wen, Advances in Physics 44, 405 (1995).

[3] Eduardo Fradkin, Field Theories of Condensed Matter Physics, (Cambridge University Press, New York, 2013).

Tuesday, February 3rd 2015

4:30 pm:

In my presentation, I will talk about confinement effects in one-dimensional quantum systems. As a start, I will review the features of the inelastic neutron scattering data on CoNb2O6[1] realizing the predictions of Ref.[2]. After this review, I'll introduce the effective model to explain the experimental findings and present its solution as performed in Ref. [3] (and references therein). If time allows, I will mention also other approaches including e.g. TEBD [4].

[1] R. Coldea et.al. Science 327, 177 (2010)

[2] A.B. Zamolodchikov, Int. J. Mod. Phys. A 4, 4235 (1989)

[3] S.B. Rutkevich, J. Stat. Mech. (2010) P07015

[4] J.A. Kjäll, F. Pollmann, and J.E. Moore, Phys. Rev. B 83, 020407(R) (2011)

Tuesday, February 10th 2015

4:30 pm:

The volume enclosed by Fermi surface in Brillouin zone is proportional to the sum of doped electron density and the localized moment density, as required by Luttinger theorem [1]. Experiments on underdoped cuprates suggest that the Fermi pocket volume is proportional to the doping in the pseudogap region. Fractionalized Fermi liquid is proposed as one candidate to explain its violation of Luttinger theorem [2] and Fermi arc observed by ARPES. In my presentation, I will briefly review the Luttinger theorem and recent experiments on pseudogap in cuprates. An effective theory on doped U(1) spin liquid [3] will be discussed in detail. If time allows, I will also present more recent numerical calculations with quantum dimer model [4].

[1] M. Oshikawa, Phys. Rev. Lett. 84, 3370 (1999).

[2] T. Senthil, S. Sachdev, and M. Vojta, Phys. Rev. Lett. 90, 216403 (2003).

[3] Y. Qi, and S. Sachdev, Phys. Rev. B 81, 115129 (2010).

[4] M. Punk, A. Allais, and S. Sachdev, arXiv:1501.000978.

Tuesday, February 17th 2015

4:30 pm:

Tuesday, March 17th 2015

4:30 pm:

I will begin with a brief review of Mott physics in the one-band case. After having introduced the necessary terminology I introduce a general multi-band model and argue that, due to the presence of the Hund's coupling in such a model, the system can undergo a so-called orbital-selective Mott transition [1]. Subsequently, I highlight the substantial differences between the half-filled case and the non-half-filled case [2]. Finally I will discuss the possible manifestation of this transition in the iron-chalcogenides [3].

[1] L. de' Medici et al. Phys. Rev. Lett. 102, 126401 (2009).

[2] L. de' Medici, Phys. Rev. B. 83, 205112 (2011).

[3] Z. Xu et al. Phys. Rev. B. 84 052506 (2011).

Tuesday, March 31st 2015

4:30 pm:

Fractionalization is a property of both topological phases and spin liquids. Moreover, in many cases it may be the easiest characteristic to use to identify these systems in experiments. I will talk about recent work in classifying the way that symmetry acts on fractional quasiparticles [1]. I will introduce the classification scheme and discuss the measurable signatures in relation to exactly solvable examples such as Kitaev’s Toric Code model [2]. (Recent applications are [3] and [4]).

[1] “Classifying fractionalization,” Essin and Hermele, PRB 87, 104406 (2013)

[2] “Spectroscopic signatures of crystal momentum fractionalization,” Essin and Hermele, PRB 90, 121102(R) (2014)

[3] “Numerical detection of symmetry-enriched topological phases with space-group symmetry,“ Wang, Essin, Hermele, and Motrunich: PRB 91, 121103(R) (2015)

[4] “Detecting crystal symmetry fractionalization from the ground state: Application to Z2 spin liquids on the kagome lattice,“ Qi and Fu, PRB 91, 100401(R) (2015)

Tuesday, April 7th 2015

4:30 pm:

The concept of ‘Majorana fermions’, first proposed by Ettore Majorana that spin-1/2 particles could be their own antiparticles, is ubiquitous in modern physics nowadays. Majorana’s big idea was supposed to be solely relevant to high energy physics like neutrino, dark matter and supersymmetry. But now, his conjecture can not only be fulfilled in solid-state systems but also bring a promising future to the quantum information processing. In this talk, I will first introduce the historical background of Majorana fermions. Then I will bring the Majorana physics to solid-state systems by introducing two toy models that support Majorana modes. First is the Kitaev’s toy lattice model for 1D p-wave superconductor and the second is Fu-Kane model for 2D p+ip superconductor. Finally I will discussion the non-Abelian exchange statistics associated with the Majorana modes and their potential for quantum information processing.

Reference:

[1] J. Alicea, Reports on Progress in Physics, vol. 75, p. 076501, 2012.

[2] S. R. Elliott and M. Franz, Reviews of Modern Physics, vol. 87, pp. 137-163, 02/11/2015.

[3] A. Y. Kitaev, Physics-Uspekhi, vol. 44, p. 131, 2001.

[4] J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. Fisher, Nature Physics, vol. 7, pp. 412-417, 2011.

Tuesday, April 14th 2015

4:30 pm:

I will discuss the formulation of the hydrodynamic equations for liquid crystals, both in a traditional way [1,2] and using Onsager’s variational principle [3, 4]. I will then discuss a modification of these equations to account for ion impurities and describe the qualitative effect of these changes.

References:

[1] M. Kleman and O. D. Lavrentovich, Soft Matter Physics (Springer, New York, 2003).

[2] S. Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1963).

[3] M. Doi, J. Phys. Condens. Matter 23, 284118 (2011).

[4] F. M. Leslie, Contin. Mech. Thermodyn. 4, 167 (1992).

Tuesday, April 21st 2015

4:30 pm:

The coexistence of different ordered electronic states in metals has been discussed a lot. In iron pnictides, superconducting and magnetic spin density wave orders influence each other, e.g. they can support each other and lead to coexistence states [1]. This coexistence depends on the shape and area of the Fermi surface. In my presentation, I will briefly review the concepts of Fermi surface nesting and spin density waves. Then, a Ginzburg-Landau analysis in the vicinity of the crossing point of SC and SDW transitions and at T=0 will be discussed [2]. After that, I will present some numerical results and compare with the Ginzburg-Landau theory.

[1]Chubukov, Andrey V., D. V. Efremov, and Ilya Eremin. "Magnetism, superconductivity, and pairing symmetry in iron-based superconductors."Physical Review B 78.13 (2008): 134512.

[2] Vorontsov, A. B., M. G. Vavilov, and A. V. Chubukov, Physical Review B 81.17 (2010): 174538.

Tuesday, April 28th 2015

4:30 pm:

The pairing mechanism in high temperature cuprate superconductors is an interesting problem. A low energy effective theory called spin-fermion model can be applied to study cuprates, and it's argued that pairing in cuprates is mediated by spin fluctuations. The model describes low-energy fermions interacting with their own collective spin fluctuations.

For phonon mediated superconductors, vertex corrections of phonon electron interactions and momentum dependence of fermionic self energy are small and neglected, due to the small ratio of sound velocity and Fermi velocity. This leads to the well known Eliashberg equations for superconducting state. For cuprates, Eliashberg-type theory is still valid, but for different reasons with phonon mediated superconductors, in spite of strong spin fermion interactions. Many 'fingerprints' of the spin fluctuation mediated pairing mechanism has been seen in the experiments.

This is the first talk of two consecutive Journal Club talks using spin-fermion model to study cuprates. I will focus on:

1.Introduction to spin-fermion model.

2.Summary of Eliashberg theory for electron-phonon pairing.

3.Perturbation theory and Eliashberg-type equations for spin fermion model.

4.Two of the fingerprints: Comparison with ARPES and neutron scattering experiments for superconducting state.

References:

1.Ar. Abanov , Andrey V. Chubukov & J. Schmalian, Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis,

Advances in Physics,(2003) 52, 119-218

2.Andrey V. Chubukov, David Pines, Joerg Schmalian, Chapter 7 in 'The Physics of Conventional and Unconventional Superconductors' edited by K.H. Bennemann and J.B. Ketterson (Springer-Verlag) or arXiv:cond-mat/0201140

3.Ar. Abanov, A. Chubukov and J. Schmalian, Fingerprints of the spin-mediated pairing in the cuprates, J. Electron Spectroscopy, 117, 129 (2001).

Tuesday, May 5th 2015

4:30 pm:

Tuesday, May 12th 2015

4:30 pm:

In a static topological system the Chern number is equal to the number of chiral edge modes. However, in a periodically driven system there may be chiral edge modes present even in the case of trivial Chern number for all bands. In this talk I will use a toy model and Floquet theory to demonstrate this possibility, even if the Floquet operator is trivial i.e. the bulk ground state doesn't change under one period of evolution. Then I will show the derivation of a generalization to the Chern number that gives the number of edge states in a periodically driven topological system. In the end I will discuss the effects on a more realistic system with weak driving, as it may be realized in cold atom gases.

Reference:

Mark Rudner, Netanel Lindner, Erez Berg, and Michael Levin: PRX 3, 031005 (2013)

Tuesday, May 19th 2015

4:30 pm:

It is well known that spontaneous symmetry breaking can only take place in the thermodynamic limit. Yet, by general hydrodynamic and effective field theory arguments, fingerprints of this symmetry breaking are already encoded in finite volume system realizations. Here, I will discuss how to dig out these fingerprints in exact low-energy spectra of finite-size systems, a method which has been extremely successful over the last 20 years (starting e.g. with the first ‘numerical proof’ of long-range magnetic ordering in the 2D triangular antiferromagnet). The power of this method is not about system-size extrapolations (‘large enough’ system sizes are anyway quickly unreachable for many strongly correlated systems), but on the full exploitation of symmetry, which gives very stringent predictions for the structure and the exact content of the low-energy spectra. The underlying principles offer one of the most direct ways to understand the mechanism of spontaneous symmetry breaking, and as such it is a general and fundamental topic that goes beyond numerical simulations.

References:

[1] P. W. Anderson, PRB 86, 694 (1952)

[2] C. Lhuillier, cond-mat/0502464v1, chapter 2

[3] B. Bernu et al, PRL 69, 2590 (1992); PRB 50, 10048 (1994)

[4] P. Azaria et al, PRL 70, 2483 (1993)

[5] H. Neuberger and T. Ziman, PRB 39, 2608 (1989)

[6] P. Hasenfratz and F. Niedermayer, Z. Phys. B 92, 91-112 (1993)

Tuesday, September 15th 2015

4:30 pm:

In the journal club we will discuss the behavior of a N-component φ^{4}
-model in hyperbolic space based on Ref.1 I will motivate why such a study might be relevant for condensed matter physics and i will briefly sketch the derivation of the critical behavior of the model. I will follow the aforementioned reference and supplement the discussion for clarity.

1: Critical Phenomena in Hyperbolic Space, K. Mnasri, B. Jeevanesan and J. Schmalian ArXiv1507.02909

Tuesday, September 22nd 2015

4:30 pm:

I will talk about a simple, paradigmatic example of how to understand exotic spin liquids (aka non-Abelian topological phases) in terms of more simpler ones as presented in Ref.[1]. The toric code model [2] will be used as a spin-1/2 lattice model giving rise to a (relatively) simple spin liquid. Using this as a starting point, a spin-1 model is constructed from the spin-1/2 model. Borrowing also explanations from Ref.[3], we shall see that the more complex spin liquid harbors topological excitations, which correspond to those of the (doubled) Ising theory.

[1] B. Paredes PRB 86, 155122 (2012)

[2] A. Y. Kitaev, Ann. Phys. 303, 2 (2003)

[3] B. Paredes, arXiv:1402.3567

Tuesday, September 29th 2015

4:30 pm:

Recently the experimental discovery of surface Fermi arcs in TaAs were the first proof of existence of a Weyl semimetal [1]. The existence of these states in 3 spatial dimensions was theoretically proposed before, a short summary was published in a viewpoint [2]. The characteristic surface Fermi arcs appear as a projection of Weyl points in the bulk material. A Weyl point can only appear when either time reversal or spacial inversion symmetry are broken, and when there is an accidental degeneracy of two bands [3,4]. Following [4] I will show why this degeneracy is unlikely in 2 dimensions but rather generic in 3 dimensions, and how the projection of the Weyl points onto the surface yields a structure of surface Fermi arcs. However not every surface of a Weyl semimetal contains surface arcs, if two Weyl points of opposite chirality have the same projection the surface states cancel out. As example I will discuss the structure of the 24 Weyl points in the first experimentally known Weyl semimetal, TaAs.

[1] S.-Y. Xu et al, Science 349, 6248, pp.613-617 (2015)

[2] “Viewpoint: Weyl electrons kiss”, L. Balents, Physics 4, 36 (2011)

[3] H. Weng, C. Fang, Z. Fang, B.A. Bernevig and X. Dai, PRX 5, 011029 (2015)

[4] E. Witten, lectures at Princeton summer school 2015, online at https://www.youtube.com/channel/UCedUIgHkkHO-QKVhIqgkSfw

Tuesday, October 27th 2015

4:30 pm:

Tuesday, November 3rd 2015

4:30 pm:

It is well known that spontaneous broken continuous symmetry leads to the existence of a massless bosonic excitation, which is called Nambu-Goldstone bosons(NGB). Examples of NGB are pions in high energy physics, phonons and magnons(spin wave) in condensed matter physics. NGB usually interact 'weakly' with other degrees of freedom, in the sense that only its gradient couples to other particles, and so they can survive. This is the so-called Adler's principle(or Adler zero). As first discovered by Adler, forward scattering amplitude of particles off a pion vanishes quadratically as the momentum of pions goes to zero. Similarly in condensed matter physics, phonons(or magnons) have vanishing coupling with electrons as the wavevector of phonons(or magnons) goes to zero. However, Adler's principle is not always true. There is a criterion [1], saying that if the broken symmetry generator doesn't commute with translations, the coupling is non-vanishing and sometimes it results in breakdown of Fermi liquid and overdamping of NGB. The case of non-vanishing coupling is relevant to nematic fermi fluid [2].

I will talk about:

(1)Introduction: Goldstone mode in phi-4 theory and why phonons and magnons are Goldstone modes. Goldstone theorem.

(2)Warm up: phonon-electron coupling.

(3)Major part: criterion of vanishing coupling (gradient coupling) between Goldstone bosons and electrons [1].

(4)More example: magnon-electron coupling in antiferromagnets [3][4].

(5)Comments: about long range interaction and Anderson-Higgs mechanism in superconductors.(if time permits)

[1] Haruki Watanabe and Ashvin Vishwanath, Proc. Natl. Acad. Sci. 111, 16314 (2014), http://arxiv.org/abs/1404.3728

[2] Vadim Oganesyan, Steven Kivelson, and Eduardo Fradkin, Phys. Rev. B 64, 195109 (2001)

[3] John R Schrieffer, Journal of Low Temperature Physics, 1995, 99(3-4): 397-402.

[4] Andrey V. Chubukov and Dirk K. Morr, Phys. Rep. 288, 355(1997)

Tuesday, November 10th 2015

4:30 pm:

Tuesday, November 17th 2015

4:30 pm:

Tuesday, December 1st 2015

4:30 pm:

The reference is Parsa Bonderson, Caltech PhD Thesis Chapter 2 (2007)

Tuesday, December 8th 2015

4:30 pm:

Quantum phases of matter that violate time-reversal symmetry invariably develop local spin or orbital moments in the ground state, such as ferromagnets, spin density waves, electrons in loop current phases, etc. A common property is that time reversal symmetry is restored as soon as the moments melt. However, there may exist a phase of matter that violates time-reversal symmetry but has no moments, which is called the “directional scalar spin chiral order” (DSSCO) from Ref. [1]. It can be obtained by melting the spin moments in a magnetically ordered phase but retaining residual broken time-reversal symmetry.

Outline of my talk:

(1) Introduction to time-reversal symmetry and several examples

(2) Directional scalar spin chiral order(DSSCO) in 1D, 2D and 3D

(3) Experimental detection and application to the cuprates (if time allows)

Reference:

[1]:Pavan Hosur. arXiv:1510.00975

Tuesday, December 15th 2015

4:30 pm:

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