Condensed Matter

I will discuss some of the most basic questions in fermionic and bosonic transport, such as the conditions for the existence of a steady-state current, its uniqueness, the role of interactions and spin statistics, its entanglement entropy, etc. This will lead me to introduce an alternative viewpoint to conduction - the micro-canonical formalism of transport - which is ideal to study the above issues [1]. I will point out the similarities and differences with the widely used Landauer formalism, and advance a series of predictions that can be verified by loading ultra-cold atoms into artificial optical lattices.

[1] M. Di Ventra, Electrical Transport in Nanoscale Systems (Cambridge University Press, 2008).

One of the biggest challenges in physics is to develop accurate and efficient methods that can solve many currently intractable problems in correlated quantum or statistical systems. Tensor-network model/state is drawing more and more attention since it captures the feature of the area law and is absent from the sign problem. The evaluation of the expectation value of the observables can be reduced to the contraction of a tensor-network, which can be done by means of renormalization group method, and this is exactly what tensor renormalization group (TRG) method has done. In the light of comparison between numerical renormalization group (NRG) and density matrix renormalization group(DMRG), having considered the renormalization effect of the environment, second renormalization group (SRG) method has been proposed to improve the performance of TRG. Although TRG and SRG have achieved great success in 2D lattice, application to 3D is not easy. The talk will give a review of TRG and SRG, and talk about the HOTRG, i.e., TRG based on the higher-order singular value decomposition, and its SRG version, HOSRG. They can be easily applied to 3D lattice with relatively low memory and computation cost. The well-known 3D Ising model on simple cubic lattice has been tested. As far as our group know, HOSRG have achieved by far the most accurate renormalization group results for the 3D Ising model. Some analysis and possible applications will be also discussed.

I review the uses of effective field theory (EFT) techniques, originally developed in particle physics, to study gravitational dynamics. I will focus on the EFT approach to gravitational wave (GW) radiation, aka NRGR, and show how it has succeeded in producing the most accurate description of spinning binary systems to date, opening the door to a new era of precise astrophysical & cosmological measurements and tests of General Relativity via GW interferometry. I will also briefly discuss EFT applications for black hole dissipation/absorption, inflationary dynamics and  high energy gravitational scattering.