Hi Lisbeth - Sorry to hear that your arborvitae are encroaching on your garden. The root systems of arborvitae are generally shallow depending on the variety and they may spread to the drip line edges of the branches. A large arborvitae variety major roots can reach ~18-24 inches deep. A root barrier, like a trench, can limit but not stop root growth altogether. It just takes longer for the roots to grow around them. The good news however is that the roots that do make it around a barrier tend to be smaller for longer. For an established large variety arborvitae, you would want to consider installing the barrier as deep as 24-30” if possible and at a distance from the trunk equal to twice the distance from the trunk to edge of the leaves. The further you can place the barrier from the arborvitae the less likely you will disturb the roots. You could try a raised bed but be aware that the roots of your arborvitae are always seeking moisture and nutrients. A raised bed provides them both. So, at some point you might want/need to add a physical barrier to block root penetration to the raised bed!