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Program

                                      Venue: R620, Physics Building, NTHU.

29th August
Time Title/Speaker
08:30-09:00 Registration
09:00-10:15 Lectures: Background of correlated physics
Prof. Yi-Ping Huang
Abstract:
We will start with a brief motivation about why studying correlated systems and an overview of the summer school.
10:15-10:45 Coffee break: Morning break
10:45-12:00 Lectures: General introduction of tensor representation Matrix product states and Matrix product operators.
Prof. Chia-Min Chung
Abstract:
Matrix product state is an excellent approximation for a many-body state in low dimensions. I will start from the basic tensor language, and introduce the matrix product state and its important properties. I will then show how we can use the density matrix renormalization group (DMRG) algorithm to obtain the ground state of a low-dimensional system.
12:00-14:00 Lunch
14:00-15:15 Lectures: Detecting topological order from tensor network method
Prof. Ching-Yu Huang
Abstract:
Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. In our talk, we will introduce how to use the tensor network to detect the topological order phase.
15:15-15:45 Coffee break: Afternoon break
15:45-17:00 Hands on tutorial: DMRG
Prof. Chia-Min Chung
17:00-19:45 Hands on tutorial: Discussion and Extention
 
30th August
Time Title/Speaker
08:30-09:00 Registration
09:00-10:15 Lectures: Renormalization of the Tensor Network for Classical Models
Prof. Pochung Chen
Abstract:
We start from the partition functions of the classical models and discuss the general method to express them as a tensor networks. We also demonstrate how to express the expectation values as tensor networks. We then introduce the idea of renormalization. In particular, we discuss two standard methods: (1) tensor renormalization group (TRG) method and (2) higher order tensor renormalization group (HOTRG) method, which can be used to coarse-grain the tensor networks. On the other hand, we review the basic idea of the transfer matrix and the finite-size scaling analysis. Incorporating the renormalization of the tensor network, we demonstrate how to obtain the correlation length and estimate the critical temperature as well as the critical exponents.
10:15-10:45 Coffee break: Morning break
10:45-12:00 Lectures: A textbook implementation of the real-space renormalization group.
Prof. Naoki Kawashima
Abstract:
When introducing the idea of renormalization group in lectures in statistical mechanics, probably the most intuitively apealing example is the real-space renormalization mapping. The basic program there is that (1) we define an approximate mapping from the original problem into the 
renormalized problem, (2) by regarding this mapping as a super operator that maps an operator to another operator, (3) linearize the super operator at its fixed point, and (4) obtain its eigenvalues, which are bacially the scaling dimensions. However, until quite recently I have never been able to offer to my students any practical implementation of this program that yields accurate and, more importantly, systematically improvable results. In this lecture, we consider how we can use the tensor-network language to obtain a systematically improvable method for the real-space renormalization group that can actually produce good estimates (at least better than the most textbook examples of the real-space RG).

Xinliang Lyu, RuQing G. Xu and Naoki Kawashima, PRR 3, 023048 (2021)
 
12:00-14:00 Lunch
14:00-15:15 Lectures: Projected Entangled Pair States, topological order, and topological spin liquids.
Prof. Norbert Schuch
Abstract: In my talk, I will discuss how two-dimensional tensor networks - Projected Entangled Pair States (PEPS) - can be used to model topologically ordered systems, and in particular topological spin liquids, and to analyze the properties of their ground space as well as of their excitations.
15:15-15:45 Coffee break: Afternoon break
15:45-17:00 Hands on tutorial: TRG for classical Ising model

17:00-19:45 Hands on tutorial: Discussion and Extention

31st August
Time Title/Speaker
08:30-09:00 Registration
09:00-10:15 Lectures: Simulation of dynamics using tensor networks methods.
Prof. Ying-Jer Kao
Abstract:
In this talk, I will give basic introduction on how to use tensor networks to simulate quantum many-body systems. In particular I will introduce the concept of the two base methods:  time-evolution block-decimation (TEBD) and time-dependent variational principle (TDVP). We will also discuss the application and extensions of these methods.
 
10:15-10:45 Coffee break: Morning break
10:45-12:00
Lectures: Annealing Dynamics of the Two-Dimensional Fully Frustrated Ising Model.
Mr Kai-Hsin Wu
Abstract:
We study the dynamical scaling properties of the two-dimensional fully frustrated Ising model by simulated annealing. The model has a highly degenerate, critical ground state with well-known equilibrium properties. To study its out-of-equilibrium behavior, we develop an annealing protocol that is convenient for accessing a generalized Kibble-Zurek mechanism in the case of an exponentially divergent correlation length in the limit of the temperature T
Tc = 0. We find excellent agreement with the scaling forms derived, including a dependence on the initial temperature that is not present in the conventional Kibble-Zurek mechanism.
12:00-14:00 Lunch
14:00-15:15 Lectures: Matrix Product Operators and Higher Moments.
Prof. Ian McCulloch
Abstract:
I will give an overview of matrix product operator and transfer matrix techniques for calculating correlation functions and order parameters, including examples of how to calculate cumulants of an order parameter and using this to probe quantum critical points, including dynamical quantum
criticality.
15:15-15:45 Coffee break: Afternoon break
15:45-17:00 Hands on tutorial: Dynamics using tensor networks methods.

17:00-19:45 Hands on tutorial: Discussion and Extention