The Quantum pyrochlore $S=\frac{1}{2}$ Heisenberg antiferromagnet at finite and zero temperature*

We use cutting-edge computational methods to investigate the pyrochlore $S=1/2$ antiferromagnet at finite and zero temperature.

By a systematic numerical high temperature expansion we gain insights into thermodynamic properties in the thermodynamic limit. Within the limit of convergence of our method ($T\approx 0.25J$) we establish a pronounced maximum in the specific heat at $T=0.57J$.

At zero temperature, we apply large scale $SU (2)$ DMRG to finite size clusters with up to 128 sites. Besides a precise determination of the ground state energy, $E_0 / N_{\text{sites}} = −0.49J$, our most striking finding is a robust spontaneous inversion symmetry breaking. This suggests a scenario in which a finite-temperature spin liquid regime gives way to an ordered state which breaks inversion symmetry spontaneously.

In a magnetic field, the pyrochlore antiferromagnet exhibits a nontrivial magnetization process which can host exotic magnetic phases. We find a particularly robust incompressible state reflected by a magnetization plateau at $\frac{1}{2}$ saturation. This state spontaneously breaks a different lattice symmetry compared to the zero field case: oppositely polarized spins on alternating kagome and triangular planes discard C_3 rotations.