diff --git a/python/taichi/lang/impl.py b/python/taichi/lang/impl.py
index 18bf2bbbb..e3d010be0 100644
--- a/python/taichi/lang/impl.py
+++ b/python/taichi/lang/impl.py
@@ -442,15 +442,6 @@ def field(dtype, shape=None, offset=None, needs_grad=False):
 
     assert (offset is not None and shape is None
             ) == False, f'The shape cannot be None when offset is being set'
-    '''
-    if get_runtime().materialized:
-        raise RuntimeError(
-            "No new variables can be declared after materialization, i.e. kernel invocations "
-            "or Python-scope field accesses. I.e., data layouts must be specified before "
-            "any computation. Try appending ti.init() or ti.reset() "
-            "right after 'import taichi as ti' if you are using Jupyter notebook or Blender."
-        )
-    '''
 
     del _taichi_skip_traceback
 
diff --git a/taichi/codegen/codegen_llvm.cpp b/taichi/codegen/codegen_llvm.cpp
index 7b6c6e5b6..59d4b9335 100644
--- a/taichi/codegen/codegen_llvm.cpp
+++ b/taichi/codegen/codegen_llvm.cpp
@@ -1251,12 +1251,19 @@ llvm::Value *CodeGenLLVM::call(SNode *snode,
 }
 
 void CodeGenLLVM::visit(GetRootStmt *stmt) {
-  llvm_val[stmt] = builder->CreateBitCast(
-      get_root(),
-      llvm::PointerType::get(
-          StructCompilerLLVM::get_llvm_node_type(
-              module.get(), prog->get_snode_root(SNodeTree::kFirstID)),
-          0));
+  if (stmt->root() == nullptr)
+    llvm_val[stmt] = builder->CreateBitCast(
+        get_root(SNodeTree::kFirstID),
+        llvm::PointerType::get(
+            StructCompilerLLVM::get_llvm_node_type(
+                module.get(), prog->get_snode_root(SNodeTree::kFirstID)),
+            0));
+  else
+    llvm_val[stmt] = builder->CreateBitCast(
+        get_root(stmt->root()->get_snode_tree_id()),
+        llvm::PointerType::get(
+            StructCompilerLLVM::get_llvm_node_type(module.get(), stmt->root()),
+            0));
 }
 
 void CodeGenLLVM::visit(BitExtractStmt *stmt) {
@@ -2011,8 +2018,9 @@ llvm::Type *CodeGenLLVM::get_xlogue_function_type() {
                                  get_xlogue_argument_types(), false);
 }
 
-llvm::Value *CodeGenLLVM::get_root() {
-  return create_call("LLVMRuntime_get_root", {get_runtime()});
+llvm::Value *CodeGenLLVM::get_root(int snode_tree_id) {
+  return create_call("LLVMRuntime_get_roots",
+                     {get_runtime(), tlctx->get_constant(snode_tree_id)});
 }
 
 llvm::Value *CodeGenLLVM::get_runtime() {
diff --git a/taichi/codegen/codegen_llvm.h b/taichi/codegen/codegen_llvm.h
index e95cd366c..255f677bc 100644
--- a/taichi/codegen/codegen_llvm.h
+++ b/taichi/codegen/codegen_llvm.h
@@ -101,7 +101,7 @@ class CodeGenLLVM : public IRVisitor, public LLVMModuleBuilder {
 
   llvm::Type *get_xlogue_function_type();
 
-  llvm::Value *get_root();
+  llvm::Value *get_root(int snode_tree_id);
 
   llvm::Value *get_runtime();
 
diff --git a/taichi/inc/constants.h b/taichi/inc/constants.h
index 7241da5da..66a4eb227 100644
--- a/taichi/inc/constants.h
+++ b/taichi/inc/constants.h
@@ -5,6 +5,7 @@
 constexpr int taichi_max_num_indices = 8;
 constexpr int taichi_max_num_args = 8;
 constexpr int taichi_max_num_snodes = 1024;
+constexpr int taichi_max_num_snode_trees = 32;
 constexpr int taichi_max_gpu_block_dim = 1024;
 constexpr std::size_t taichi_global_tmp_buffer_size = 1024 * 1024;
 constexpr int taichi_max_num_mem_requests = 1024 * 64;
diff --git a/taichi/ir/snode.cpp b/taichi/ir/snode.cpp
index b875b74bd..2bdf25156 100644
--- a/taichi/ir/snode.cpp
+++ b/taichi/ir/snode.cpp
@@ -200,4 +200,12 @@ SNode *SNode::get_grad() const {
   return grad_info->grad_snode();
 }
 
+void SNode::set_snode_tree_id(int id) {
+  snode_tree_id_ = id;
+}
+
+int SNode::get_snode_tree_id() {
+  return snode_tree_id_;
+}
+
 TLANG_NAMESPACE_END
diff --git a/taichi/ir/snode.h b/taichi/ir/snode.h
index 5b002a454..5740e0d27 100644
--- a/taichi/ir/snode.h
+++ b/taichi/ir/snode.h
@@ -293,6 +293,15 @@ class SNode {
   void begin_shared_exp_placement();
 
   void end_shared_exp_placement();
+
+  // SNodeTree part
+
+  void set_snode_tree_id(int id);
+
+  int get_snode_tree_id();
+
+ private:
+  int snode_tree_id_{0};
 };
 
 }  // namespace lang
diff --git a/taichi/ir/statements.h b/taichi/ir/statements.h
index 209e88ac5..408d28e0d 100644
--- a/taichi/ir/statements.h
+++ b/taichi/ir/statements.h
@@ -912,7 +912,12 @@ class BitExtractStmt : public Stmt {
  */
 class GetRootStmt : public Stmt {
  public:
-  GetRootStmt() {
+  GetRootStmt(SNode *root = nullptr) : root_(root) {
+    if (this->root_ != nullptr) {
+      while (this->root_->parent) {
+        this->root_ = this->root_->parent;
+      }
+    }
     TI_STMT_REG_FIELDS;
   }
 
@@ -920,8 +925,15 @@ class GetRootStmt : public Stmt {
     return false;
   }
 
-  TI_STMT_DEF_FIELDS(ret_type);
+  TI_STMT_DEF_FIELDS(ret_type, root_);
   TI_DEFINE_ACCEPT_AND_CLONE
+
+  SNode *root() {
+    return root_;
+  }
+
+ private:
+  SNode *root_;
 };
 
 /**
diff --git a/taichi/program/program.cpp b/taichi/program/program.cpp
index 47c719a24..5a02c1dd0 100644
--- a/taichi/program/program.cpp
+++ b/taichi/program/program.cpp
@@ -402,7 +402,7 @@ void Program::initialize_llvm_runtime_snodes(const SNodeTree *tree,
   TI_TRACE("Allocating data structure of size {} bytes", scomp->root_size);
   runtime_jit->call<void *, std::size_t, int, int>(
       "runtime_initialize_snodes", llvm_runtime, scomp->root_size, root_id,
-      (int)snodes.size());
+      (int)snodes.size(), tree->id());
   for (int i = 0; i < (int)snodes.size(); i++) {
     if (is_gc_able(snodes[i]->type)) {
       std::size_t node_size;
@@ -430,6 +430,7 @@ void Program::initialize_llvm_runtime_snodes(const SNodeTree *tree,
 int Program::add_snode_tree(std::unique_ptr<SNode> root) {
   const int id = snode_trees_.size();
   auto tree = std::make_unique<SNodeTree>(id, std::move(root));
+  tree->root()->set_snode_tree_id(id);
   materialize_snode_tree(tree.get());
   snode_trees_.push_back(std::move(tree));
   return id;
@@ -655,7 +656,9 @@ void Program::visualize_layout(const std::string &fn) {
       emit("]");
     };
 
-    visit(get_snode_root(SNodeTree::kFirstID));
+    for (auto &a : snode_trees_) {
+      visit(a->root());
+    }
 
     auto tail = R"(
 \end{tikzpicture}
@@ -891,7 +894,9 @@ void Program::print_memory_profiler_info() {
     }
   };
 
-  visit(get_snode_root(SNodeTree::kFirstID), /*depth=*/0);
+  for (auto &a : snode_trees_) {
+    visit(a->root(), /*depth=*/0);
+  }
 
   auto total_requested_memory = runtime_query<std::size_t>(
       "LLVMRuntime_get_total_requested_memory", llvm_runtime);
diff --git a/taichi/runtime/llvm/runtime.cpp b/taichi/runtime/llvm/runtime.cpp
index 13df86bf8..43cb5a1ef 100644
--- a/taichi/runtime/llvm/runtime.cpp
+++ b/taichi/runtime/llvm/runtime.cpp
@@ -525,8 +525,10 @@ struct LLVMRuntime {
   host_printf_type host_printf;
   host_vsnprintf_type host_vsnprintf;
   Ptr program;
-  Ptr root;
-  size_t root_mem_size;
+
+  Ptr roots[taichi_max_num_snode_trees];
+  size_t root_mem_sizes[taichi_max_num_snode_trees];
+
   Ptr thread_pool;
   parallel_for_type parallel_for;
   ListManager *element_lists[taichi_max_num_snodes];
@@ -573,8 +575,8 @@ struct LLVMRuntime {
 // TODO: are these necessary?
 STRUCT_FIELD_ARRAY(LLVMRuntime, element_lists);
 STRUCT_FIELD_ARRAY(LLVMRuntime, node_allocators);
-STRUCT_FIELD(LLVMRuntime, root);
-STRUCT_FIELD(LLVMRuntime, root_mem_size);
+STRUCT_FIELD_ARRAY(LLVMRuntime, roots);
+STRUCT_FIELD_ARRAY(LLVMRuntime, root_mem_sizes);
 STRUCT_FIELD(LLVMRuntime, temporaries);
 STRUCT_FIELD(LLVMRuntime, assert_failed);
 STRUCT_FIELD(LLVMRuntime, host_printf);
@@ -890,14 +892,15 @@ void runtime_initialize(
 
 void runtime_initialize_snodes(LLVMRuntime *runtime,
                                std::size_t root_size,
-                               int root_id,
-                               int num_snodes) {
+                               const int root_id,
+                               const int num_snodes,
+                               const int snode_tree_id) {
   // For Metal runtime, we have to make sure that both the beginning address
   // and the size of the root buffer memory are aligned to page size.
-  runtime->root_mem_size =
+  runtime->root_mem_sizes[snode_tree_id] =
       taichi::iroundup((size_t)root_size, taichi_page_size);
-  runtime->root =
-      runtime->allocate_aligned(runtime->root_mem_size, taichi_page_size);
+  runtime->roots[snode_tree_id] = runtime->allocate_aligned(
+      runtime->root_mem_sizes[snode_tree_id], taichi_page_size);
   // runtime->request_allocate_aligned ready to use
   // initialize the root node element list
   for (int i = root_id; i < root_id + num_snodes; i++) {
@@ -908,7 +911,7 @@ void runtime_initialize_snodes(LLVMRuntime *runtime,
   Element elem;
   elem.loop_bounds[0] = 0;
   elem.loop_bounds[1] = 1;
-  elem.element = runtime->root;
+  elem.element = runtime->roots[snode_tree_id];
   for (int i = 0; i < taichi_max_num_indices; i++) {
     elem.pcoord.val[i] = 0;
   }
@@ -1743,9 +1746,10 @@ i32 wasm_materialize(Context *context) {
       (RandState *)((size_t)context->runtime + sizeof(LLVMRuntime));
   // set random seed to (1, 0, 0, 0)
   context->runtime->rand_states[0].x = 1;
-  context->runtime->root =
+  // TODO: remove hard coding on root id 0(SNodeTree::kFirstID)
+  context->runtime->roots[0] =
       (Ptr)((size_t)context->runtime->rand_states + sizeof(RandState));
-  return (i32)(size_t)context->runtime->root;
+  return (i32)(size_t)context->runtime->roots[0];
 }
 }
 
diff --git a/taichi/transforms/ir_printer.cpp b/taichi/transforms/ir_printer.cpp
index cd1895b74..6c68cd3e8 100644
--- a/taichi/transforms/ir_printer.cpp
+++ b/taichi/transforms/ir_printer.cpp
@@ -466,7 +466,12 @@ class IRPrinter : public IRVisitor {
   }
 
   void visit(GetRootStmt *stmt) override {
-    print("{}{} = get root", stmt->type_hint(), stmt->name());
+    if (stmt->root() == nullptr)
+      print("{}{} = get root nullptr", stmt->type_hint(), stmt->name());
+    else
+      print("{}{} = get root [{}][{}]", stmt->type_hint(), stmt->name(),
+            stmt->root()->get_node_type_name_hinted(),
+            stmt->root()->type_name());
   }
 
   void visit(SNodeLookupStmt *stmt) override {
diff --git a/taichi/transforms/scalar_pointer_lowerer.cpp b/taichi/transforms/scalar_pointer_lowerer.cpp
index b52b29e10..9a922452e 100644
--- a/taichi/transforms/scalar_pointer_lowerer.cpp
+++ b/taichi/transforms/scalar_pointer_lowerer.cpp
@@ -46,7 +46,10 @@ void ScalarPointerLowerer::run() {
     }
   }
 
-  Stmt *last = lowered_->push_back<GetRootStmt>();
+  if (path_length_ == 0)
+    return;
+
+  Stmt *last = lowered_->push_back<GetRootStmt>(snodes_[0]);
   for (int i = 0; i < path_length_; i++) {
     auto *snode = snodes_[i];
     // TODO: Explain this condition
diff --git a/tests/python/test_fields_builder.py b/tests/python/test_fields_builder.py
index 927ad7b56..f315b4692 100644
--- a/tests/python/test_fields_builder.py
+++ b/tests/python/test_fields_builder.py
@@ -28,48 +28,57 @@ def func():
 
 
 @ti.test(arch=[ti.cpu, ti.cuda])
-def test_fields_builder1():
+def test_fields_builder_dense():
     n = 5
-    x = ti.field(ti.f32, [n])
+
+    fb1 = ti.FieldsBuilder()
+    x = ti.field(ti.f32)
+    fb1.dense(ti.i, n).place(x)
+    fb1.finalize()
 
     @ti.kernel
     def func1():
         for i in range(n):
-            x[i] = i * 2
+            x[i] = i * 3
 
     func1()
     for i in range(n):
-        assert x[i] == i * 2
+        assert x[i] == i * 3
 
-    fb = ti.FieldsBuilder()
+    fb2 = ti.FieldsBuilder()
     y = ti.field(ti.f32)
-    fb.dense(ti.i, n).place(y)
-    fb.finalize()
+    fb2.dense(ti.i, n).place(y)
+    z = ti.field(ti.f32)
+    fb2.dense(ti.i, n).place(z)
+    fb2.finalize()
 
     @ti.kernel
     def func2():
         for i in range(n):
-            y[i] = i // 2
+            x[i] = i * 2
+        for i in range(n):
+            y[i] = i + 5
+        for i in range(n):
+            z[i] = i + 10
 
     func2()
     for i in range(n):
-        assert y[i] == i // 2
+        assert x[i] == i * 2
+        assert y[i] == i + 5
+        assert z[i] == i + 10
 
     func1()
     for i in range(n):
-        assert x[i] == i * 2
+        assert x[i] == i * 3
 
 
 @ti.test(arch=[ti.cpu, ti.cuda])
-def test_fields_builder2():
-    # TODO: x, y share the same memory location
-    pass
-    '''
+def test_fields_builder_pointer():
     n = 5
 
     fb1 = ti.FieldsBuilder()
     x = ti.field(ti.f32)
-    fb1.dense(ti.i, n).place(x)
+    fb1.pointer(ti.i, n).place(x)
     fb1.finalize()
 
     @ti.kernel
@@ -83,7 +92,9 @@ def func1():
 
     fb2 = ti.FieldsBuilder()
     y = ti.field(ti.f32)
-    fb2.dense(ti.i, n).place(y)
+    fb2.pointer(ti.i, n).place(y)
+    z = ti.field(ti.f32)
+    fb2.pointer(ti.i, n).place(z)
     fb2.finalize()
 
     @ti.kernel
@@ -92,9 +103,15 @@ def func2():
             x[i] = i * 2
         for i in range(n):
             y[i] = i + 5
+        for i in range(n):
+            z[i] = i + 10
 
     func2()
     for i in range(n):
         assert x[i] == i * 2
         assert y[i] == i + 5
-    '''
+        assert z[i] == i + 10
+
+    func1()
+    for i in range(n):
+        assert x[i] == i * 3
diff --git a/tests/python/test_runtime.py b/tests/python/test_runtime.py
index abaaf9601..624e184aa 100644
--- a/tests/python/test_runtime.py
+++ b/tests/python/test_runtime.py
@@ -131,52 +131,6 @@ def test_init_bad_arg():
         ti.init(_test_mode=True, debug=True, foo_bar=233)
 
 
-@ti.test(arch=ti.cpu)
-def test_materialization_after_kernel():
-    pass
-    '''
-    x = ti.field(ti.f32, (3, 4))
-
-    @ti.kernel
-    def func():
-        print(x[2, 3])
-
-    func()
-
-    with pytest.raises(RuntimeError, match='declared after'):
-        y = ti.field(ti.f32, (2, 3))
-    # ERROR: No new variable should be declared after kernel invocation!
-    '''
-
-
-@ti.test(arch=ti.cpu)
-def test_materialization_after_access():
-    pass
-    '''
-    x = ti.field(ti.f32, (3, 4))
-
-    print(x[2, 3])
-
-    with pytest.raises(RuntimeError, match='declared after'):
-        y = ti.field(ti.f32, (2, 3))
-    # ERROR: No new variable should be declared after Python-scope field access!
-    '''
-
-
-@ti.test(arch=ti.cpu)
-def test_materialization_after_get_shape():
-    pass
-    '''
-    x = ti.field(ti.f32, (3, 4))
-
-    print(x.shape)
-
-    with pytest.raises(RuntimeError, match='declared after'):
-        y = ti.field(ti.f32, (2, 3))
-    # ERROR: No new variable should be declared after Python-scope field access!
-    '''
-
-
 @ti.test(arch=ti.cpu)
 def test_materialize_callback():
     x = ti.field(ti.f32, (3, 4))