LTspice not giving correct output
As pointed out, you need an AC supply (like output of a step down transformer that has no middle common terminal). For a lot less complexity, the circuit below also works. It may supply a bit less current than a full wave rectifier, but this is not a problem with op amps. Also, electrolytic caps are cheap. Remember that you need voltage regulators (e.g. LM317 and LM337) to reduce the ripple further. LM317 requires about 2V headroom at low currents.





If you're looking to get opamp dual supply, from a single ended DC, you need a rail splitter. This needs to have ability to both source and sink current at the midpoint (Virtual Ground).

Something like this will split a regulated DC into halves (eg 10V to ±5V, or 12V to ±6V). Note that the BJT sinking the +ve is bigger (TO92), as that current is usually higher. (I'd probably also change the 3904 to a 2222 just to be safe.)



Here's another that splits an arbitrary higher ripple DC and then has a +5V regulator. The tracked -ve is done with the left over opamp. Q2 is only a regulator for the -ve, so does not need to be beefy. But Q1 sinks the +ve rail so may need some heatsinking if it's passing a lot of current, and the input DC is much more than 14V (78L05 requires 2V headroom).



And finally, this is an extremely quick and very dirty solution. The LM358 can source upto 40mA but can sink only 20mA (so your load on the +ve rail is severely limited).



Here are some additional links to rail splitters https://tangentsoft.net/elec/vgrounds.html
https://www.maximintegrated.com/en/app-notes/index.mvp/id/4344
https://www.tubecad.com/2018/02/blog0412.htm
(That last page has circuits similar to what you have posted)