no LTE access in Canada for iphone 5 purchased in Hong Kong?

Hi all,

I have purchased an iPhone 5 (unlocked) from a phone carrier in Hong Kong. According to the link http://www.apple.com/iphone/LTE/ it appears to be A1429 GSM model.

I brought the phone back to Canada, Toronto, and could not obtain LTE access in any part of the location since then. My phone carrier in Canada is with Rogers which does support LTE for a wide range of areas.

Please advise on whether it is possible to obtain LTE access on my phone. I didn't anticipate this potential problem from the beginning because as a reasonable buyer I expected that if I were to purchase an unlocked phone and there is LTE service in one country, the same would also take place when I'm in another country and with another phone carrier that supports LTE.

Thanks!