hmftpy: Hierarchical mean-field theory implemented in Python

Implements hierarchical mean-field theory, a cluster mean-field theory that systematically preserves and breaks symmetries of the Hamiltonian to understand the phase diagrams of strongly-correlated models.

This package relies on QuSpin, an exact-diagonalization package. To install QuSpin, make sure you have the conda package manager installed and then use command conda install -c weinbe58 quspin

Usage

For example usage, see the Jupyter notebook demo.ipynb.

Input/output dictionary formats

Functions in this package use the following formats for input and output dictionaries:

cluster = {'L': # of sites in cluster,
             'inner': {
                'nearest': [[intra-cluster nearest neighbors of site i]
                            for i in cluster],
                'n_nearest': [[intra-cluster next-nearest neighbors of site i]
                              for i in cluster],
                'n_n_nearest': [[intra-cluster next-next-nearest neighbors of site i]
                                for i in cluster]}
             'outer': {
                'nearest': [[inter-cluster nearest neighbors of site i]
                            for i in cluster],
                'n_nearest': [[inter-cluster next-nearest neighbors of site i]
                              for i in cluster],
                'n_n_nearest': [[inter-cluster next-next-nearest neighbors of site i]
                                for i in cluster]}
             }

interactions = {'local': {'z': -2},
                'nearest': {'xx': 1, 'yy': 1},
                'n_nearest': {'xy': 1, 'yx': -1},
                'n_n_nearest': {'yx': -1, 'yx', -1}}

mean_fields = {'x': [List of <sigma_i^x> for i in cluster],
               'y': [List of <sigma_i^y> for i in cluster],
               'z': [List of <sigma_i^z> for i in cluster]}

coeffs = {'inner': {local': {'z': 1-D NUMPY ARRAY OF LENGTH L},
                    'nearest': {'xx': 2-D NUMPY ARRAY OF LENGTH L, 'yy': ...},
                    'n_nearest': {'xy': ..., 'yx': ...},
                    'n_n_nearest': {'yx': ..., 'yx', ...}}
          'outer': {local': {'z': ...},
                    'nearest': {'xx': ..., 'yy': ...},
                    'n_nearest': {'xy': ..., 'yx': ...},
                    'n_n_nearest': {'yx': ..., 'yx', ...}}}