From 09e9038a8cc4d52dc40886df671e49669f235a88 Mon Sep 17 00:00:00 2001
From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com>
Date: Thu, 5 Mar 2026 19:25:21 +0000
Subject: [PATCH 1/2] Initial plan


From f29607e73c8d1afc15846a353a97e770265fd9af Mon Sep 17 00:00:00 2001
From: "copilot-swe-agent[bot]" <198982749+Copilot@users.noreply.github.com>
Date: Thu, 5 Mar 2026 19:31:18 +0000
Subject: [PATCH 2/2] Add chemical potential parameter mu to Hubbard model

Co-authored-by: hzhangxyz <11623447+hzhangxyz@users.noreply.github.com>
---
 qmp/models/hubbard.py | 22 +++++++++++++++-------
 1 file changed, 15 insertions(+), 7 deletions(-)

diff --git a/qmp/models/hubbard.py b/qmp/models/hubbard.py
index ecc4773..4669423 100644
--- a/qmp/models/hubbard.py
+++ b/qmp/models/hubbard.py
@@ -28,8 +28,11 @@ class ModelConfig:
     t: float = 1
     # The coefficient of U
     u: float = 0
+    # The chemical potential mu
+    mu: float = 0
 
-    # The electron number, left empty for half-filling
+    # The electron number, left empty for half-filling.
+    # Note: if a network without particle number conservation is used, this parameter will be ignored.
     electron_number: int | None = None
 
     # The ref energy of the model
@@ -65,11 +68,6 @@ def _index(i: int, j: int, o: int) -> int:
         hamiltonian_dict: dict[tuple[tuple[int, int], ...], complex] = {}
         for i in range(args.m):
             for j in range(args.n):
-                # On-site interaction
-                hamiltonian_dict[
-                    (_index(i, j, 0), 1), (_index(i, j, 0), 0), (_index(i, j, 1), 1), (_index(i, j, 1), 0)
-                ] = args.u
-
                 # Nearest neighbor hopping
                 if i != 0:
                     hamiltonian_dict[(_index(i, j, 0), 1), (_index(i - 1, j, 0), 0)] = -args.t
@@ -82,6 +80,15 @@ def _index(i: int, j: int, o: int) -> int:
                     hamiltonian_dict[(_index(i, j, 1), 1), (_index(i, j - 1, 1), 0)] = -args.t
                     hamiltonian_dict[(_index(i, j - 1, 1), 1), (_index(i, j, 1), 0)] = -args.t
 
+                # On-site interaction
+                hamiltonian_dict[
+                    (_index(i, j, 0), 1), (_index(i, j, 0), 0), (_index(i, j, 1), 1), (_index(i, j, 1), 0)
+                ] = args.u
+
+                # Chemical potential
+                hamiltonian_dict[(_index(i, j, 0), 1), (_index(i, j, 0), 0)] = -args.mu
+                hamiltonian_dict[(_index(i, j, 1), 1), (_index(i, j, 1), 0)] = -args.mu
+
         return hamiltonian_dict
 
     def __init__(self, args: ModelConfig):
@@ -90,11 +97,12 @@ def __init__(self, args: ModelConfig):
         self.n: int = args.n
         self.electron_number: int = args.electron_number
         logging.info(
-            "Constructing Hubbard model: width = %d, height = %d, t = %.4f, U = %.4f, N = %d, ref_energy = %.4f",
+            "Constructing Hubbard model: width = %d, height = %d, t = %.4f, U = %.4f, mu = %.4f, N = %d, ref_energy = %.4f",
             self.m,
             self.n,
             args.t,
             args.u,
+            args.mu,
             args.electron_number,
             args.ref_energy,
         )