Recently, reconfigurable intelligent surface (RIS) technology has provided new opportunities to rescale the performance metric and boost network coverage for sixth-generation (6G) wireless communications. In RIS-assisted wireless communication systems, traditional analog beamforming requires a huge number of phase shifters, which increases exponential and computational complexity. In order to accomplish computationally efficient hybrid beamforming for 6G communications, we therefore propose a branchwise phase shifters (BPS) architecture of analog beamforming in this paper. To establish the best baseband configuration for wireless 6G communications, we first consider an RIS element and a transmitter antenna branchwise millimeter wideband (B-MW) channel model. Following that, we design a BPS-based analog beamforming architecture using a power splitting technique, which splits the transmit power associated with each RF chain and allows each RF chain to utilize two PS branches. The B-MW channel can easily provide a low-dimensional hybrid beamforming solution with the BPS architecture, which allows easy rescaling of the beamforming gain, thus enhancing the achievable rate. We then present an iterative algorithm with zero-forcing to tackle a joint optimization problem of RIS-assisted hybrid beamforming. Lastly, the beam coverage and achievable rate of the proposed BPS architecture are verified by the simulation results, which outperform the traditional single, double, and combined phase-shifter architecture.