Add Tree Tensor Networks

[liwt31]

Related to #149

Status of the code

• It is ready to be merged into the master branch after review
• The code is tested for production-level study of spin-boson model and quantum charge transport model. See the new examples for details.
• The framework is flexible and extensive, meaning it is unlikely further development will dramatically change the architecture
• I can still improve the document, and optimize performance for some functions.

Functionalities

• Define arbitrary tree topology using TreeNodeBasis and BasisTree. In each site/node, there could be no basis set (by BasisDummy) or more than one basis sets.
• Auto Tree Tensor Network Operator (TTNO) construction with the same interface as MPO
• Routine TTNS/TTNO manipulation: applying TTNO on TTNS, calculating expectations, TTNS compression, adding TTNS, etc.
• QN support is the same as MPS
• 2-site ground state optimization
• 1-site and 2-site TDVP-PS, TDVP-VMF (unoptimized), P&C-RK4
• Imaginary thermal propagation with proper computational scaling (i.e. Mpdm)
• GPU acceleration

A guide to the code

The functionalities are implemented in the tn module. The original MPS/MPO implementation/interface largely remain unchanged.

• node.py and treebase.py provide basic utilities to build a tree where each node is associated with one or more physical dof.
• On top of that tree.py provides definitions for TTNS and TTNO. The environment tensors are also stored in a tree format, in TTNEnviron
• hop_expr.py contains functions to build opt_einsum expression as the effective Hamiltonian operator. The implementation of the whole tn module relies heavily on opt_einsum.
• gs.py implements 2-site optimization, which relies on hop_expr.py
• time_evolution.py contains time evolution algorithms, which also relies on hop_expr.py. In the mps.py implementation the time evolution takes a lot of lines, so I decided to move them to a new file in TTNS implementation.
• symbolic_mpo.py for auto construction of MPO
• utils_eph.py now only has a function to construct the maximum entangled state. The current implementation of TTNS/TTNO is completely model agnostic and I hope it will stay so. Anything related to a specific model will be put in a separate file as another abstraction layer between actual applications.

[codecov]

Codecov Report

Attention: Patch coverage is 89.27987% with 262 lines in your changes are missing coverage. Please review.

Project coverage is 85.87%. Comparing base (2044db8) to head (883546a).

Files	Patch %	Lines
renormalizer/lib/davidson/logger.py	55.28%	55 Missing ⚠️
renormalizer/lib/davidson/davidson.py	69.18%	53 Missing ⚠️
renormalizer/tn/treebase.py	76.88%	43 Missing ⚠️
renormalizer/sbm/lib.py	53.48%	40 Missing ⚠️
renormalizer/tn/tree.py	96.41%	27 Missing ⚠️
renormalizer/tn/gs.py	70.78%	26 Missing ⚠️
renormalizer/mps/mps.py	92.95%	5 Missing ⚠️
renormalizer/tn/hop_expr.py	95.91%	4 Missing ⚠️
renormalizer/model/basis.py	84.21%	3 Missing ⚠️
renormalizer/tn/node.py	96.62%	3 Missing ⚠️
... and 3 more

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #166      +/-   ##
==========================================
+ Coverage   84.86%   85.87%   +1.01%     
==========================================
  Files         105      117      +12     
  Lines       10232    12342    +2110     
==========================================
+ Hits         8683    10599    +1916     
- Misses       1549     1743     +194     

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