This series consists of talks in the area of Condensed Matter.
The ground state phase of spin-1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice in the maximally frustrated regime (J2 ~ 0.5J1) has been debated for decades. Here we study this model by using a recently proposed novel numerical method - the cluster update algorithm for tensor product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with the state of art exact diagonalization study, and
We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by evolving all possible results for multiple inputs, with bits represented by matrices. The action by classical probabilistic 1-bit and deterministic 2-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions.
As helium-4 is cooled below 2.17 K in undergoes a phase transition to a state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent advances in nanofabrication techniques allow for the construction of smooth pores with nanometer radii, that approach the truly one dimensional limit.
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.
We provide a brief introduction to quantum spin liquid
and review current status of theoretical and experimental progresses on this
subject. Spin liquid phases that arise in different situations are examined in
the light of both theoretical models and experimental systems.
Recent years have seen a renewed interest, both theoretically and experimentally, in the search for topological states of matter. On the theoretical side, while much progress has been achieved in providing a general classification of non-interacting topological states, the fate of these phases in the presence of strong interactions remains an open question. The purpose of this talk is to describe recent developments on this front.
The description of non-Fermi liquid metals is one of the central problems in the theory of correlated electron systems. I present a holographic theory which builds on general features of the thermal entropy density and the entanglement entropy. Remarkable connections emerge between the holographic approach, and the postulated strong-coupling behavior of the field-theoretic approach.
Although the typical physical system achieves an ordered state at low temperatures, spin liquids stay disordered even in their ground state. In addition to an increasing number of experimental candidates for spin liquids, recent numerical work from Meng, et. al and Yan, et. al. has supplied strong numerical evidence for natural Hamiltonians having spin liquid ground states. Their featureless nature, though, makes learning about these states particularly difficult. In this talk, we explore what variational ansatz can teach us about them.
The entanglement spectrum denotes the eigenvalues of the reduced density matrix of a region in the ground state of a many-body system. Given these eigenvalues, one can compute the entanglement entropy of the region, but the full spectrum contains much more information. I will review geometric methods to extract this spectrum for special subregions in lorentz and conformally invariant field theories (and any theory whose universal low energy physics is captured by such a field theory).