From cf866adf267aa21c11b7d160ebe00d76be9e7698 Mon Sep 17 00:00:00 2001
From: Antonio Manesco <am@antoniomanesco.org>
Date: Tue, 19 Dec 2023 18:43:05 +0100
Subject: [PATCH] implement multidimensional hermitian Hamiltonians
---
codes/utils.py | 28 ++++++++++++++++++++++++----
1 file changed, 24 insertions(+), 4 deletions(-)
diff --git a/codes/utils.py b/codes/utils.py
index 47ac550..bb3e915 100644
--- a/codes/utils.py
+++ b/codes/utils.py
@@ -188,7 +188,7 @@ def model2hk(tb_model):
return bloch_ham
-def kgrid_hamiltonian(nk, hk, dim, return_ks=False):
+def kgrid_hamiltonian(nk, hk, dim, return_ks=False, hermitian=True):
"""
Evaluates Hamiltonian on a k-point grid.
@@ -220,9 +220,10 @@ def kgrid_hamiltonian(nk, hk, dim, return_ks=False):
for k in product(*k_pts):
ham.append(hk(k))
ham = np.array(ham)
- assert np.allclose(
- ham, np.transpose(ham, (0, 2, 1)).conj()
- ), "Tight-binding provided is non-Hermitian. Not supported yet"
+ if hermitian:
+ assert np.allclose(
+ ham, np.transpose(ham, (0, 2, 1)).conj()
+ ), "Tight-binding provided is non-Hermitian. Not supported yet"
shape = (*[nk] * dim, ham.shape[-1], ham.shape[-1])
if return_ks:
return ham.reshape(*shape), ks
@@ -358,3 +359,22 @@ def calc_gap(vals, E_F):
emax = np.max(vals[vals <= E_F])
emin = np.min(vals[vals > E_F])
return np.abs(emin - emax)
+
+def flat_to_matrix(flat, shape):
+ matrix = np.zeros(shape, dtype=complex)
+ matrix[..., *np.triu_indices(shape[-1])] = flat.reshape(*shape[:-2], -1)
+ indices = np.arange(shape[-1])
+ diagonal = matrix[..., indices, indices]
+ matrix += np.moveaxis(matrix, -1, -2).conj()
+ matrix[..., indices, indices] -= diagonal
+ return matrix
+
+
+def matrix_to_flat(matrix):
+ return matrix[..., *np.triu_indices(matrix.shape[-1])].flatten()
+
+def real_to_complex(z): # real vector of length 2n -> complex of length n
+ return z[:len(z)//2] + 1j * z[len(z)//2:]
+
+def complex_to_real(z): # complex vector of length n -> real of length 2n
+ return np.concatenate((np.real(z), np.imag(z)))
\ No newline at end of file
--
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