---
library_name: transformers
tags: []
---

<!-- Provide a quick summary of what the model is/does. -->
Foundation Neural-Network Quantum State trained on the Ising in transverse field model on a chain with \\(L=100\\) sites. 
The system is described by the following Hamiltonian (with periodic boundary conditions):

$$
    \hat{H} = -J\sum_{i=1}^N \hat{S}_i^z \hat{S}_{i+1}^z - h \sum_{i=1}^N \hat{S}_i^x \ ,
$$

where \\(\hat{S}_i^x\\) and \\(\hat{S}_i^z\\) are spin- \\(1/2\\) operators on site \\(i\\).


The model has been trained on \\(R=6000\\) different values of the field \\(h\\) equispaced in the interval \\(h \in [0.8, 1.2]\\),
using a total batch size of \\(M=12000\\) samples.

The computation has been distributed over 4 A100-64GB GPUs for few hours. 


## How to Get Started with the Model

Use the code below to get started with the model. In particular, we sample the model for a fixed value of the external field \\(h\\) using NetKet.

```python
from functools import partial
import numpy as np

import jax
import jax.numpy as jnp
import netket as nk

import flax
from flax.training import checkpoints

flax.config.update('flax_use_orbax_checkpointing', False)

lattice = nk.graph.Hypercube(length=100, n_dim=1, pbc=True)

revision = "main"
h = 1.0 #* fix the value of the external field

assert h >= 0.8 and h <= 1.2 #* the model has been trained on this interval

from transformers import FlaxAutoModel
wf = FlaxAutoModel.from_pretrained("nqs-models/ising_fnqs", trust_remote_code=True)
N_params = nk.jax.tree_size(wf.params)
print('Number of parameters = ', N_params, flush=True)

hilbert = nk.hilbert.Spin(s=1/2, N=lattice.n_nodes)
hamiltonian = nk.operator.IsingJax(hilbert=hilbert, graph=lattice, h=h, J=-1.0)

action = nk.sampler.rules.LocalRule()
sampler = nk.sampler.MetropolisSampler(hilbert=hilbert, 
                                       rule=action, 
                                       n_chains=12000, 
                                       n_sweeps=lattice.n_nodes)

key = jax.random.PRNGKey(0)
key, subkey = jax.random.split(key, 2)
vstate = nk.vqs.MCState(sampler=sampler, 
                        apply_fun=partial(wf.__call__, coups=h), 
                        sampler_seed=subkey,
                        n_samples=12000, 
                        n_discard_per_chain=0,
                        variables=wf.params,
                        chunk_size=12000)

# start from thermalized configurations
from huggingface_hub import hf_hub_download
path = hf_hub_download(repo_id="nqs-models/ising_fnqs", filename="spins", revision=revision)
samples = checkpoints.restore_checkpoint(path, prefix="spins", target=None)
samples = jnp.array(samples, dtype='int8')
vstate.sampler_state = vstate.sampler_state.replace(σ = samples)

import time
# Sample the model
for _ in range(10):
    start = time.time()
    E = vstate.expect(hamiltonian)
    vstate.sample()

    print("Mean: ", E.mean.real / lattice.n_nodes, "\t time=", time.time()-start)

```

The time per sweep is 3.5s, evaluated on a single A100-40GB GPU.

### Extract hidden representation

The hidden representation associated to the input batch of configurations can be extracted as:

```python
wf = FlaxAutoModel.from_pretrained("nqs-models/ising_fnqs", trust_remote_code=True, return_z=True)

z = wf(wf.params, samples, h)
```

#### Training Hyperparameters

Number of layers: 6  
Embedding dimension: 72   
Hidden dimension: 144  
Number of heads: 12  
Patch size: 4

Total number of parameters: 198288 


## Model Card Contact

Riccardo Rende (rrende@sissa.it)  
Luciano Loris Viteritti (luciano.viteritti@epfl.ch)