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The intricate interplay between frustration and spin chirality has thepotential to give rise to unprecedented phases in frustrated quantum magnets.We examine the ground state phase diagram of the spin-1/2 square latticeJ1-J2-Jx model by employing critical level crossings and ground state fidelitysusceptibility (FS) using exact diagonalization (ED) with full latticesymmetries. Our analysis reveals the evolution of highly symmetric energylevels as a function of J2 at fixed Jx. During a magnetic to non-magnetic phasetransition, the precise identification of the phase boundary is achievedthrough critical level crossings between the gapless excitation of a magneticphase and the quasi-degenerate ground state of a non-magnet phase. Conversely,a direct transition between two non-magnetic phases is characterized by a FSpeak accompanied by an avoided ground state level crossing, serving as adistinctive signal. Within a substantial range of Jx, we identify ananticipated chiral spin liquid (CSL) state and an adjacent nematic spin liquid(NSL) phase with a degeneracy of two on a cylinder. These two phases aredemarcated by a nearly vertical boundary line at J2 = 0.65. This critical lineterminates at the lower boundary of a magnetic ordered chiral spin solid (CSS)phase. We validate the topological nature of the CSL using the modular S matrixof the minimum entangled states (MES) on a torus, along with the entanglementspectra (ES) of even and odd sectors on a cylinder, employing anSU(2)-symmetric density matrix renormalization group (DMRG) method.Furthermore, we delve into a comprehensive discussion on the nature of the NSL,exploring aspects such as ground state degeneracy, the local bond energylandscape, and the singlet and triplet gaps on various tori. These analysisprovide substantial evidence supporting the nematic nature of the NSL.

Ground state phase diagram and the exotic phases in the spin-1/2 square lattice J1-J2-Jx model