The tenant cannot unilaterally deduct from the rent.
You are correct that under California law, all leases have the implied covenant of "quiet enjoyment". (California Civil Code, § 1927). The landlord (and management company) has the duty to preserve the quiet enjoyment of all tenants. (Davis v. Gomez (1989) 207 Cal.App.3d 1401, 1404.)
If you as a tenant unilaterally deduct from the rent, the landlord has the right to take your security deposit for the unpaid rent, and bring a lawsuit to recover the rent due for the remaining duration of the lease.
The concept of a “constructive eviction” exists under the rubric of a breach of the covenant of quiet enjoyment that is implied in every rental agreement. (Stoiber v Honeychuck (1980) 101 Cal.App.3d 903, 925–926.)
Substantial interference is required to establish a breach of quiet enjoyment. An interference by the landlord "by which the tenant is deprived of the beneficial enjoyment of the premises amounts to a constructive eviction if the tenant so elects and surrenders possession, and the tenant will not be liable for rentals for the portion of the term following his eviction." (Kulawitz v. Pacific Paper Co. (1944) 25 Cal.2d 664, 670.)
Minor inconveniences and annoyances are not actionable breaches of the implied covenant of quiet enjoyment. To be actionable, the landlord's act or omission must substantially interfere with a tenant's right to use and enjoy the premises for the purposes contemplated by the tenancy. (Petroleum Collections Inc. v. Swords (1975) 48 Cal.App.3d 841, 846.)
Given your situation, it might be helpful for you to have a dialogue with your landlord to see how the landlord is willing to compromise with you.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult with your own attorney.