code_XY_clock

A research project implementing HOTRG (Higher-Order Tensor Renormalization Group) simulations using the Cytnx library.

1. Environment Requirements

• Operating System: Linux or Windows Subsystem for Linux 2 (WSL2).

• WSL2 Installation Guide:
  Official Microsoft WSL2 Instruction

2. Anaconda Installation

You can download the installer from the Anaconda Archive.

Or use the following command line:

curl -O https://repo.anaconda.com/archive/Anaconda3-2025.12-2-Linux-x86_64.sh

Install Anaconda:

bash ~/Anaconda3-2025.12-2-Linux-x86_64.sh

3. Cytnx Installation

Create a dedicated Conda environment build Cytnx from source.

3.1 Create Conda Environment

conda config --add channels conda-forge
conda create --name cytnx python=3.9 _openmp_mutex=*=*_llvm
conda activate cytnx
conda upgrade --all

3.2 Install Build Dependencies

conda install cmake make boost libboost git compilers numpy openblas pybind11 beartype boost-cpp arpack

3.3 Clone and Build

git clone https://github.com/cytnx-dev/cytnx.git
cd cytnx
mkdir build
cd build

Configure (Replace /home/chansh/cytnx_install with your desired path):

cmake .. -DCMAKE_INSTALL_PREFIX=/home/chansh/cytnx_install

Compile and install:

make -j$(nproc)
make install

4. Usage Configuration

Path Setup
To use the compiled library in Python, add the installation path manually.

Quick Start (In-script)
Add the following snippet at the beginning of your Python files (make sure this path is correctly modified in all_fn.py):

import sys

# Update this path to where you installed Cytnx
sys.path.insert(0, "/home/chansh/cytnx_install")

import cytnx as cy
print(cy.__version__)

5. Code implement

Parameters

model_name
Defines the physical model

• 2D XY model,

model_name = "2D_M={}_XY"

Replace {} with the Fourier cutoff value $M$.

• 2D clock model:

model_name = "2D_q={}_clock"

Replace {} with the q-value.

---

symm
Boolean. Whether to preserve the symmetric block structure of tensors.

---

dcut
The bond-dimension cutoff used in HOTRG.

---

Lmax
Upper limit of system size $L$.

---

unit_size
Controls the initial size of the system before applying HOTRG.
The elementary tensor $T^{(1,1)}$ is first exactly contracted into system size unit_size * unit_size.
For example, when unit_size=3, we produces an effective tensor $T^{(3,3)}$ representing a $3\times 3$ lattice.

     ┏━┷━┓ ┏━┷━┓ ┏━┷━┓
    ─┨ T ┠─┨ T ┠─┨ T ┠─
     ┗━┯━┛ ┗━┯━┛ ┗━┯━┛
     ┏━┷━┓ ┏━┷━┓ ┏━┷━┓          ┏━━━┷━━━┓    
    ─┨ T ┠─┨ T ┠─┨ T ┠─   =    ─┨ T_3x3 ┠─
     ┗━┯━┛ ┗━┯━┛ ┗━┯━┛          ┗━━━┯━━━┛
     ┏━┷━┓ ┏━┷━┓ ┏━┷━┓
    ─┨ T ┠─┨ T ┠─┨ T ┠─
     ┗━┯━┛ ┗━┯━┛ ┗━┯━┛

After N steps HOTRG, the system size becomes $L = 3 \times 2^N $.

---

iteration
The label of temperature list Ts_tot.

---

iT
Index of temperature T within temperature list Ts_tot.

---

iL
Index of size L within size list Ls_tot.

---

n
Stacking number used to constructed transfer matrix TM $^{(L, nL)}$.
The transfer matrix is built by tracing all vertical bonds using n copies of $T$ tensor.

Example: Transfer matrix (PBC) with n=3

          ┌───┐
        ┏━┷━┓ │
    1───┨ T ┠─│──101
        ┗━┯━┛ │                ┏━━╳━┓
        ┏━┷━┓ │              1─┨    ┠─101    
    2───┨ T ┠─│──102    =    2─┨ TM ┠─102
        ┗━┯━┛ │              3─┨    ┠─103
        ┏━┷━┓ │                ┗━━━━┛
    3───┨ T ┠─│──103
        ┗━┯━┛ │
          └───┘

---

num_collect
Maximum number of eigenvalues to compute.

---

hermitian
Boolean. Whether to perform Hermitian diagonalization.

---