Do we get any AC pwm module to drive 750Watt heater,5 Amp for Arduino?
Use a relay to simply turn on and off, else use some kind of MOSFET switch
Sounds like you need a 1000w wall dimmer that you can control with an arduino.
I can think of only two solutions:
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use one of the Home Automation dimmers, but of course you will need their hub etc. Probably too much to just control a heater.
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use a rotary wall dimmer with the control connected to a hobby servo. Bit of a kluge but conceptually will work.
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Reconsider the need for PWM as it is normally understood. What I mean is to get a solid state relay and PWM it at a really slow rate. Say at a 60 second rate. Heaters have a long thermal constant and you might find the heat output to feel near constant.
Virtually all heating & cooling systems simply cycle on & off and this works because temperature can't change instantly.
...It's not easy to use PWM with AC because MOSFETS & transistors are "polarized" so you'd have to use two transistors or MOSFETS and you need positive & negative power supplies to control them, etc.
[u]TRIACs[/u] are bi-directional so most AC solid state relays and dimmers are built-around TRIACs. But, the only way to turn-off a TRIAC is to cut the current so regular PWM won't work.
[u]How Dimmers Work[/u]. You have to synchronize the switching with the AC zero-crossings which means you need an electrically isolated (transformer or optically isolated) low-voltage AC signal onto the microcontroller.
Plus, the time-lag actually makes the "dimming" trickier to control in a feedback-loop...