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Tuesday, January 19th 2016

4:30 pm:

Tuesday, February 2nd 2016

4:30 pm:

In this talk I will review the basic classification of topological insulators in non-interacting fermionic systems. All systems can be classified according to their behavior under the action of three discrete symmetries: time-reversal, particle-hole and sublattice symmetry. I will show how to classify a system from the behavior near a critical point. This symmetry classification relates to the presence of different topological phases, which is summarized in the periodic table of topological insulators. For this talk I will mostly follow Andreas Schnyder’s lecture slides at the Summer School in Nancy [2].

[1] S. Ryu, A. Schnyder, A. Furusaki, and A. Ludwig: “Topological insulators and superconductors: tenfold way and dimensional hierarchy”, New. J. Phys. 12, 065010 (2010)

[2] A. Schnyder: Lectures on "Topological aspects in condensed matter physics" held at the Topical School in Theoretical Physics Nancy (2014), lecture slides are on his homepage at http://www.fkf.mpg.de/556169/20_Schnyder

Tuesday, February 9th 2016

4:30 pm:

I'll discuss 1-D chain with superconductivity and show the existence of different phases for p-wave superconductivity. I'll also show the existence of Majorana bound state as well as its wave function. Also one dimensional nanowire with spin-orbit will be discussed. With the presence of Zeeman field and s-wave superconductivity, this model serves as a more realistic one for topological superconductor.

Reference: Bernevig, Taylor Hughes 'topological insulators and topological superconductors'

Tuesday, February 16th 2016

4:30 pm:

For many applications, high mobility is desirable. To achieve this goal one should eliminate all sources of scattering of carriers. In the talk i will discuss the influence of the surface roughness on the carrier mobility in an inversion layer. Namely, I will derive the relationship between the mobility and the main parameters of roughness.

Tuesday, February 23rd 2016

4:30 pm:

Landau-Ginzburg-Wilson theory is a very powerful tool to study phase transitions and critical phenomena. It takes advantage of the fact that the low energy physics is dominated by a length scale which is diverging at a critical point, namely, the correlation length of order-parameter fluctuations. So one can derive an effective theory in terms of a single order-parameter field by integrating out all the other degrees of freedom with smaller length scales. However, this theory will breakdown if there are soft (massless) modes other than order-parameter fluctuations at criticality. These extra soft modes lead to power law behaviours in various physical correlation functions even far away from the critical point. Distinct from critical scale invariance, this is called generic scale invariance (GSI). Following Ref [1], I will talk about two major mechanisms that leads to GSI. Then I will use an example to discuss how GSI influences the critical behaviour in classical systems.

[1] D. Belitz, T. R. Kirkpatrick, and T. Vojta, Rev. Mod. Phys. 77, 579 (2005).

Tuesday, March 1st 2016

4:30 pm:

The Density-matrix renormalization group is a powerful algorithm invented by Steven White in 1992, and it is nowadays the most efficient method for one-dimensional quantum many-body systems and has achieved unprecdented precision in the description of them.

I will talk about

(1) Introduction and the theory behind DMRG,

(2) DMRG algorithms,

(3) Why is DMRG successful: Entanglement entropy and DMRG,

(4) Matrix product state and DMRG(if time permits).

References

U. Schollwöck, The density-matrix renormalization group,RMP,77,259

Density-Matrix Renormalization - A New Numerical Method in Physics, Peschel, I., Wang, X., Kaulke, M., Hallberg, K.,Springer,1999

Tuesday, March 29th 2016

4:30 pm:

I will introduce a very useful method to study quantum spin systems, namely, the coherent state path integral. One can see that the Berry phase term appears naturally in the path integral. I will take the antiferromagnetic model on a bipartite lattice as an example, and discuss the phases and phase transitions in this model.

Tuesday, April 5th 2016

4:30 pm:

Spin glass is a phenomenon where spins are randomly frozen in space, while having negligible temporal fluctuations. Spin glass occurs typically in disordered systems. In this talk, I will discuss the Sherrington-Kirkpatrick (SK) model of Ising spins, the mean field phase diagram of which can be studied using the replica method. I will explain replica symmetry breaking (RSB) as a definition of spin-glass phase, and discuss the Parisi solution in full detail. I will conclude by discussing the physical implications of the Parisi solution.

Ref: Statistical Physics of Spin Glasses and Information Processing - An Introduction, Hideyoshi Nishimori

Tuesday, April 12th 2016

4:30 pm:

Abstract:

I will discuss one of the earliest examples of exactly solvable spin liquids in two spatial dimensions, introduced by G. Misguich et al back in 2002 [1] for the kagome lattice. The ground state of this model (a Rokhsar-Kiverson wavefunction) is currently believed to be adiabatically connected to the actual Z2 spin liquid ground state of the nearest-neighbor spin-1/2 Heisenberg model on the kagome, that is closely realized in herbertsmithite ZnCu3(OH)6Cl3.

[1] G. Misguich, D. Serban, and V. Pasquier, PRL 89, 137202 (2002)

Tuesday, April 19th 2016

4:30 pm:

The transverse field Ising model in one dimension is the drosophila of spin systems and their phase transitions. I'll discuss the solution presented by Pfeuty (Ann.Phys.(N.Y.) 57, 79 (1970)), also referring to the underlying works (Ann.Phys.(N.Y.) 16 , 407(1961)). The topic (including many details) may already be known to many, however, the terms, in which the mathematical approach was phrased may still be interesting.

Tuesday, April 26th 2016

4:30 pm:

Following [1], I will briefly sketch the derivation of the flow equation for the scale-dependent effective action, which generates the 1PI correlation functions. The chiral Ising and chiral Heisenberg universality class, relevant for phase transitions to CDW and SDW in two-dimensional Dirac materials, will serve as an example for the calculation of critical behavior in terms of the fRG[2]. Furthermore to establish a connection, the fRG approach will be compared to a more standard Wilsonian scheme close to the upper critical dimension of the system.

[1] arXiv:hep-ph/0611146

[2] Phys. Rev. B 89, 205403 (2014), arXiv:1402.6277

Tuesday, May 3rd 2016

4:30 pm:

I will discuss non-equilibrium dynamics of an interacting bosonic quantum field theory following a rapid change of a parameter. Such a quench protocol was realized recently in a number of cold-atom experiments and corresponds to a fast change of parameters such as magnetic field or pressure in a solid-state system. I first introduce basic features of non-equilibrium and the non-equilibrium Keldysh notation for a parameter quench in a non-interacting system, which corresponds to rapidly changing the quadratic potential of a harmonic oscillator. Then, I will discuss the effect of quartic interactions within a large-N approach. I show that if a system is tuned to close proximity of a critical point, the non-equilibrium dynamics shows universal features characterized by a new scaling exponent.

This is based on work published in

P. Gagel, PPO, J. Schmalian, Phys. Rev. Lett. 113, 220401 (2014)

P. Gagel, PPO, J. Schmalian, Phys. Rev. B 92, 115121 (2015)

Wednesday, September 28th 2016

4:30 pm:

Berezinskii-Kosterlitz-Thouless transition describes the phase transition from the quasi long range ordered phase to disordered phase of certain 2d classical systems. The physics picture of the BKT transition as a transition the bounded vortex-antivortex pair becomes unpaired will be presented first. I will show how the original theory can be mapped to interacting vortices (=2d coulomb gas) through a mathematically rigorous duality transformation. Through the RG analysis, we will understand the nature of the phase transition in terms of the interacting vortices.

Wednesday, October 5th 2016

Wednesday, October 19th 2016

4:30 pm:

I will review the basic concepts of the Renormalization Group following the review paper by Shankar. Specifically, I will define what is renormalization, the concept of a fixed point, and show a sample calculation for a complex scalar field in 4 dimensions. The goal is to build the conceptual understanding needed for more complicated systems.

References: R. Shankar, Renormalization-group approach to interacting fermions. Rev. Mod. Phys. 66, 129 (1994).

Wednesday, November 2nd 2016

4:30 pm:

Following Xiaoyu's talk on Fermi liquid and Non-Fermi liquid and Alberto's talk on renormalization group, I will talk about:

0. Introduction of phenomenological Landau Fermi liquid and review of RG for interacting fermions

1. Tomonaga-Luttinger liquid as a fixed point of RG flow for general 1d interacting fermions; spin-charge separation in the Luttinger model.

2. Why Fermi liquid is extremely robust-Landau Fermi liquid as a fixed point of RG flow for 2d and 3d interacting fermions.

3. Kohn-Luttinger effect and BCS in the language of RG(briefly).

Wednesday, November 9th 2016

4:30 pm:

I will cover M.V. Berry's classic paper:

Regular and Irregular Motion, AIP Conf. Proc. 46, 16 (1978).

I will try to cover as much of the first 90 pages :) as possible.

The subject is classical Hamiltonian chaos, the KAM theorem (which we will **not** prove), and some beautiful implications for solar system dynamics.

Wednesday, November 23rd 2016

4:30 pm:

My talk is focused on the electron transport in SrTiO3 (STO) accumulation layers which can be induced on the interface between STO and other polar dielectrics. The nonlinear dielectric response of STO here makes the distribution of electron concentration special: it has a slowly decaying long tail of electrons. When the scattering is dominated by the surface, the tail electrons have a much higher mobility compared to those close to the interface and it turns out that they dominate the total conductivity though their concentration is small. I will explain in detail how this happens together with the divergence of other quantities and compare with experimental data.

Wednesday, November 30th 2016

4:30 pm:

I will first introduce the Luttinger model, solve it using a bosonic description and obtain the spin-charge separation. Then, I will use the Luttinger model as a case study of the field theoretical bosonization. And finally, I will discuss why we can rewrite a fermionic theory in terms of boson degrees of freedom by introducing a constructive approach of bosonization.

References:

1. Altand and Simons, Condensed matter field theory

2. Fradkin, Field theories of condensed matter physics

3. Jan von Delft and Herbert Schoeller, Bosonization for beginners - refermionization for experts

Wednesday, December 14th 2016

4:30 pm:

I argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe pnictides differs qualitatively from the ordinary s+− state outside the coexistence region as it develops an additional gap component which is a mixture of intrapocket singlet (s++) and interpocket spin-triplet pairings (the t state). The coupling constant for the t channel is proportional to the SDW order and involves interactions that do not contribute to superconductivity outside of the SDW region. I argue that the s+− and t-type superconducting orders coexist at low temperatures, and the relative phase between the two is, in general, different from 0 or π, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order.

Reference: A. Hinojosa, R. M. Fernandes, and A. V. Chubukov. Phys. Rev. Lett. 113, 167001 (2014).

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