What is the relationship like between Thomas and Ann Putnam in The Crucible?

I would say that the relationship between Ann and Thomas
Putnam is not a very good one.  I think that they feel that their relationship is fine,
but in their association, Miller is making a fundamental point about how relationships
are not able to progress if the people in them are not willing to progress from an
emotional standpoint.  Both Thomas and Ann are fundamentally unhappy people because they
are filled with so much in terms of resentment of
others.

Thomas Putnam is driven by the desire to be wealthy
and to own more land.  It is something that has taken root in him and represents an end
that is never satisfied.  We see this in Act I when Proctor and Corey enter and Putnam
engages in a heated discussion about land rights and lumber.  In Act III, Corey accuses
Putnam of taking advantage of those who are accused in the attempts to consolidate his
own wealth and increase his land ownership.  At a historical moment when the land
charter of Salem had been revoked, Putnam's desire for more land and greater economic
wealth knows no real limits.  It is for this reason that he is shown to be a very
unhappy or at least unlikeable person.

Ann Putnam is not
much better.  Her resentment stems from the fact that so many of her children have died
at such young ages.  Ann cannot fully accept this reality or the idea that somehow, she
has experienced death more than others.  This resentment takes its greatest form in her
hatred and envy of Sarah Good, who has experienced bounty in childbirth and rearing. 
Ann is someone who is shown to be searching for someone, anyone, to blame for her
condition of her children's death.  To a great extent, her support of Sarah Good's
prosecution as a witch is fed by this need to blame.

Both
Thomas and Ann never experience moments alone in the play where their relationship is
examined.  However, it becomes fairly clear that both of them together do not help ease
the pain and bitterness of the other.  If anything, Miller seems to be suggesting that
their own conditions of anger, misapplied hatred, and envy of others corrupt or taint
their ability to interact properly with society. It would only make sense that this
would taint or corrupt their interactions with one another, as
well.