If a tenant breaks a1 year lease, can you sue her for the remainder of the lease?

Assuming the tenant was not justified in terminating the lease (e.g. you did not yourself violate some material term of  the lease; the premises was habitable; you provided all the premises and services/amenities to which she was entitled; etc.), then you could sue her for the remaining months of rent due under the lease. You are obligated to begin immediately making good faith efforts to re-rent the premises; and if you can do so, before what would have been the end of the lease term had the tenant not breached  it, you have to "credit" her for new rental. For example: say there are 7 months left on the lease. You start a lawsuit. Before the suit goes to trial, you re-rent the premises at the same (or greater rent) after 5 months of trying, which means that you haven't actually lost anything for  the last 2 months of the first tenant's rental--you could therefore recover 5 months rent from her. The law requires you to make this good faith effort to re-rent, in order to "mitigate" your damges. (If you rent the premises for less than she was paying, you would apply the rent you do receive versus what the tenant would have  owed you for those months.)