If we compile this code and look at the generated bytecode we can examine that exactly
  public static void main(java.lang.String[]) throws java.io.IOException;
Code:
   0: new           #19                 // class java/lang/StringBuilder
   3: dup
   4: invokespecial #21                 // Method java/lang/StringBuilder."<init>":()V
   7: astore_1
   8: new           #22                 // class java/lang/String
  11: dup
  12: invokespecial #24                 // Method java/lang/String."<init>":()V
  15: astore_2
  16: iconst_0
  17: istore_3
  18: goto          47
  21: new           #19                 // class java/lang/StringBuilder
  24: dup
  25: ldc           #25                 // String
  27: invokespecial #27                 // Method java/lang/StringBuilder."<init>":(Ljava/lang/String;)V
  30: iload_3
  31: invokevirtual #30                 // Method java/lang/StringBuilder.append:(I)Ljava/lang/StringBuilder;
  34: invokevirtual #34                 // Method java/lang/StringBuilder.toString:()Ljava/lang/String;
  37: astore_2
  38: aload_1
  39: aload_2
  40: invokevirtual #38                 // Method java/lang/StringBuilder.append:(Ljava/lang/String;)Ljava/lang/StringBuilder;
  43: pop
  44: iinc          3, 1
  47: iload_3
  48: sipush        1000
  51: if_icmplt     21
  54: return
The instructions we care about are from 21 to 40. In 21, there is a second StringBuilder created, we will come back to that later.
In 25 We see, that there is a ldc, which means that a literal is pushed to the stack, in this case it is the literal String " ".
Then the real magic happens. The constructor of the second StringBuilder is called, which takes the literal from the stack as argument. Then the int i is loaded from the local variable array with iload_3, after that the append method of the second StringBuilder is called to append that i to it, and then the toString is called. With astore_2 and aload_1 the return value of the toString call is stored, and the first StringBuilder is loaded, and after that the String is loaded again. And finally the append method of the first StringBuilder is called to add that new String to the StringBuilder.
So it turns out, that ther is a new StringBuilder created in every loop, because everytime you use " " + i a StringBuilder has to be created to concatenate the String and int. Additionally a new String will be created by the toString method of the intermediate StringBuilder, so there will be a total of 2000 Objects there.
A better version would look like this:
for (int i = 0; i < 1000; i++) {
        sb.append(' ');
        sb.append(i);
    }
That will create the following bytecode:
  public static void main(java.lang.String[]) throws java.io.IOException;
Code:
   0: new           #19                 // class java/lang/StringBuilder
   3: dup
   4: invokespecial #21                 // Method java/lang/StringBuilder."<init>":()V
   7: astore_1
   8: new           #22                 // class java/lang/String
  11: dup
  12: invokespecial #24                 // Method java/lang/String."<init>":()V
  15: astore_2
  16: iconst_0
  17: istore_3
  18: goto          37
  21: aload_1
  22: bipush        32
  24: invokevirtual #25                 // Method java/lang/StringBuilder.append:(C)Ljava/lang/StringBuilder;
  27: pop
  28: aload_1
  29: iload_3
  30: invokevirtual #29                 // Method java/lang/StringBuilder.append:(I)Ljava/lang/StringBuilder;
  33: pop
  34: iinc          3, 1
  37: iload_3
  38: sipush        1000
  41: if_icmplt     21
  44: return
We can see, that there now is only one StringBuilder, which gets its append method called twice, so no memory is allocated here and this should be better.