Add tutorial on symmetric tensors

lectures/2-TensorNetworks/Symmetries.md

@@ -406,19 +406,18 @@ coefficients for $SU(2)$ have been computed analytically, and for low-dimensiona
 have been tabulated for example
 [here](https://pdg.lbl.gov/2018/reviews/rpp2018-rev-clebsch-gordan-coefs.pdf).
 
+(symmetric_tensors)=
 ## Symmetric Tensors
 
 In physics we are often dealing with tensors that transform according to the tensor product
 representation of a given group $G$. A symmetric tensor can then be understood as a tensor
 that transforms trivially under the action of $G$, or more concretely under the tensor
 product representation $X\otimes\bar Y\otimes\bar Z$:
 
-
-```
- - X_g - T - Y_g - =  - T -    for all g.
-         |              |
-        Z_g
-         |
+```{figure} ../_static/SymmetricTensors/symmtens.svg
+:scale: 12%
+:name: symmtens
+:align: center
 ```
 
 This has strong implications for the structure of the tensor $T$. Notice that we didn't

lectures/2-TensorNetworks/TensorNetworkStates.md

@@ -13,7 +13,7 @@ kernelspec:
 (tensor_network_states)=
 # Tensor Network States
 
-After our introduction on [quantum many body systems](many_body_intro) and
+After our introduction on [quantum many body systems](many_body) and
 [tensor networks](tensor_networks), we move on to considering how tensor networks can
 characterize many-body systems. We start with a constructive approach to approximating an
 arbitrary quantum state by a *tensor network state*. We then qualify in what settings such a

lectures/3-MatrixProductStates/InfiniteMPS.md

@@ -155,7 +155,7 @@ contraction
 :align: center
 ```
 
-(imps_corr)=
+(imps_correlation)=
 ### Correlation Functions
 
 Correlation functions are computed similarly. Let us look at

lectures/3-MatrixProductStates/MatrixProductStates.md

@@ -95,7 +95,7 @@ a state
 
 ```{image} /_static/FiniteMPS/peps.svg
 :scale: 12%
-:name: pfmps
+:name: peps
 :align: center
 ```
 

lectures/4-Algorithms/FixedpointAlgorithms.md

@@ -26,7 +26,7 @@ over a restricted class of states $D$. For simplicity, we will assume the Hamilt
 which can encode interactions of arbitrary range as discussed in the previous section. In this formulation, approximating the ground state of $H$ is equivalent to finding the MPS fixed point the MPO Hamiltonian corresponding to the eigenvalue $\Lambda$ with the smallest real part,
 ```{image} /_static/FixedpointAlgorithms/fixedpoint.svg
 :scale: 12%
-:name: mpoHam
+:name: fixedpoint
 :align: center
 ```
 

lectures/4-Algorithms/TimeEvolutionAlgorithms.md

@@ -12,7 +12,7 @@ kernelspec:
 % put the references in 
 % test the code
 
-
+(time_evolution)=
 # Time Evolution
 
 In this segment of the tutorial, we delve into some time evolution techniques for MPS. In particular we will focus on the [TDVP](TDVP_header) and [Time Evolution MPO](TMPO_header) methods. Another method (i)[TEBD](tebd) has already been explained in an earlier section. Following this we briefly explain how [imaginary time evolution](Imag_header) can be used to find ground states and how [thermal density matrices](FinTemp_header) can be simulated using MPS.

lectures/5-Tutorials/FiniteEntanglementScaling.md

@@ -0,0 +1,17 @@
+---
+jupytext:
+  formats: md:myst
+  text_representation:
+    extension: .md
+    format_name: myst
+kernelspec:
+  display_name: Julia
+  language: julia
+  name: julia-1.9
+---
+
+# Finite Entanglement Scaling
+
+Tutorial on finite entanglement scaling with uniform MPS, using [MPSKit.jl](https://github.com/maartenvd/MPSKit.jl).
+
+*Coming soon*.