The sacral and lumbar multifidus.
The multifidus are small muscles that work on the back of the spine. Viewed from behind they create an upward pointing chevron pattern at the back of the spine originating at the transverse processes or mamillary processes of lower vertebrae and inserting at the spinous processes of upper vertebrae.
(Note that I may be incorrect in the use of the word origin and insertion. I'm assuming a bottom to top reference with the lower point of attachment for spinal muscles labelled as the origin and the upper point of attachment the insertion.)
The multifidus span two to four vertebral levels joining adjacent vertebrae or vertebrae separated by one or two other vertebrae. In the sacral and lumbar region these muscles also originate in part from the front facing surface of the spinal erector aponeurosis.
In the sacral region the multifidus originate in the sacral groove, the region at the back of the sacrum between the sacral middle crest and the sacral articular crests. They also originate from the posterior sacroiliac ligaments and the medial (inward facing) surface of the posterior superior iliac spine.
(The sacral articular crests represent the fused articular processes of the sacral vertebrae.)
The Long Posterior Sacroiliac Ligament attaches from the PSIS or Posterior Superior Iliac spine to sacrum at about the level of the third sacral vertebrae. This ligament, when tension is added to it, tends to nutate the sacrum, or resist counter nutation.
The multifidus probably attach to the front surface of this ligament, as opposed to the rear surface. The muscle probably fills the gap between the back of the sacrum, the inner surfaces of the rear of the ilium and the front surfaces of the aforementioned ligament. When the multifidus are activated, they may add tension to the Posterior Sacroiliac Ligaments helping to create nutation (or resist counternutation.)
In the lumbar region the multifidus originate from the mamillary processes of the lumbar vertebrae. The multifidus then insert on the spinous process of a vertebrae above with shorter (and deeper) fascicles attaching close to the root of the spinous process at or near the lamina, and longer (more superficial) fibers attaching closer to the tip of the spinous process.
(Mamillary processes are located on the back (non-articulating) surface of the upper articular processes. )
In the thoracic region the multifidus are positioned superficially to the rotators. Here they originate from transverse processes and insert on spinous process.
In the cervical region they arise from the articular processes of the lower four vertebrae.
When considering the function of the Multifidus it helps to understand the position that the body is in when they activate. It also helps to understand some of the other muscles that act on the lumbar spine including the Transverse Abdominis, Quadratus Lumborum and Psoas Major muscle.
Of these the middle layer of the Thoracolumbar Fascia (MLF) is perhaps most relevant. The MLF attaches the transverse abdominis to the transverse processes of the lumbar spine. It also connects to the twelfth (lowermost) rib and the top of the iliac crest. Most noteworthy is that it passes between the quadratus lumborum and the spinal erectors. It not only passes behind the quadratus lumborum but is partially made up of fibers from the outer fascial covering of that muscle.
The quadratus lumborum attaches from the iliac crest to the transverse processes of the upper four lumbar vertebrae and the lowermost rib.
Tension from the transverse abdominis pulling inwards, may help to pull forwards on the center of the quadratus lumborum, adding tension to it. This tension may help to stabilize the lumbar spine when the torso is upright.
The psoas major muscle also has fibers (fascicles) that attach to the fronts of the transverse processes of the lumbar vertebrae. The fibers from this muscle also pull downwards, but also forwards, towards the front of the pelvis.
Assuming the psoas to be active, say while standing with legs and hips straight, the psoas could create a forwards and downwards pull on the lumbar transverse processes. The multifidus then have a stable foundation from which to create a downward pull on the rear of the vertebrae above, helping to keep the spine upright.
If the hips are bend forwards, say in a partial squat or chair pose, then the psoas may be too slack to effectively create a forward and downward pull on the fronts of the transverse processes. The quadratus lumborum could then be activated to do that job instead. To aid quadratus lumborum activation, the transverse abdominus could be activated to help pull out any slack in the QL making it easier for that muscle to activate. It then provides a downwards pull on the transverse processes of the lumbar vertebrae giving the multifidus a stable foundation from which to pull down on the reach of the vertebrae above helping to keep the spine upright.
Assuming an upright position with knees slightly bent, it is possible to find a position where the back of the lumbar spine is flat. Tilting the pelvis rearwards so that the tailbone drops, it's possible to find a position where the back of the lumbar spine feels comfortably open. In this position it is possibly the lumbar multifidus that are activating.
In this instance instead of driving a backward bending action of the lumbar vertebral joints they are acting to stabilize the spine while it is straight, helping to prevent it from curving forwards any further.
(I generally define forward bending as bending around something in front of the part of the body that is bending forwards. This terminology can be a bit confusing when talking about bending the lumbar spine forwards since the middle portion of the lumbar spine actually moves rearwards. )
In preventing the lumbar spine from further bending forwards what are the lumbar multifidus working against? The weight of the ribcage and head.
Both of these are supported at the rear by the lumbar spine and cervical spine respectively. With the lumbar spine flattened the weight of the ribcage and head tends to pull both structures down increasing the forward bend of the spine. The multifidus can activate to work against this weight helping to maintain a flat lumbar spine.
In a standing single leg lift to the front (flexing one hip with the knee bent or straight) it may be helpful to give the psoas a firm foundation and room to contract. Standing with weight on one leg (so that the hip of the un-weighted leg can be flexed), the standing knee can be slightly bent so that the pelvis has room to tilt backwards. This then allows the back of the lumbar spine to flatten so that the multifidus can then activate. The un-weighted leg can then be flexed and I would suggest that the higher the knee is lifted the more the lumbar spine can be flattened to give the psoas room to contract.
With the lumbar spine reasonably flat (or straight) the articular process of the vertebral joints may actually have some slack giving the lumbar vertebrae more room so that they can twist relative to each other.
In general lumbar rotation is limited because of the orientation of these articular processes. The multifidus and psoas together may be the main muscles able to twist the lumbar vertebrae relative to each other working on opposite quarters of the spine.
Twisting to the right the multifidus on the right side may activate along with the left side psoas.
That being said it may be desirable to work on lumbar twisting with the lumbar spine straight but also with it extended (bend backwards) and all points in-between.