Symmetry Breaking in Quantum Systems

Carmine Ortix, Jorrit Rijnbeek, Jeroen van den Brink

The theory of spontaneous symmetry breaking---one of the cornerstones of modern condensed-matter physics---underlies the connection between a classically ordered object in the thermodynamic limit and its microscopic quantum-mechanical constituents. However, a large, but not infinitely large, system requires a finite symmetry-breaking perturbation to stabilize a symmetry-broken state over the exact quantum-mechanical ground state, respecting the symmetry. Here, we use the example of a particular antiferromagnetic model system to show that no matter how slowly such a symmetry-breaking perturbation is driven, the adiabatic limit can never be reached. Dynamically induced collective excitations---``quantum defects''---preempt the symmetry-breaking phenomenon and trigger the appearance of a symmetric nonequilibrium state that recursively collapses into the classical equilibrium state, breaking the symmetry at punctured times. The presence of this state allows ``quantum-classical'' transitions to be investigated and controlled in mesoscopic devices by externally supplying a proper dynamical symmetry-breaking perturbation.

Franco Strocchi

Luke W. Bertels, Harper R. Grimsley, Sophia E. Economou +2 more

The accurate treatment of molecular systems exhibiting strong electronic correlations has long been a target of quantum simulation. Strong correlation often results in symmetry-breaking of the mean-field reference, leading to Löwdin's “symmetry dilemma”[1] whereby accuracy in the energy can be increased by breaking intrinsic symmetries of the system. We explore the impact of symmetry breaking on the performance of ADAPT-VQE using two strongly correlated systems where increasing correlation leads to spontaneous symmetry breaking of the mean-field solutions. We analyze the role that symmetry breaking in the reference states and orbital mappings of the fermionic Hamiltonians have on the performance of ADAPT-VQE. We observe that breaking symmetry has a deleterious effect on ADAPT-VQE by increasing the length of the ansatz necessary for energy convergence and exacerbating the problem of “gradient troughs”.

R. Jackiw

Ding Gu, Zijian Wang, Zhong Wang

The authors systematically unravel here the physical consequences of spontaneous symmetry breaking in open quantum systems. They elucidate three scenarios: weak symmetry breaking, which leads to time-crystalline order; strong-to-weak symmetry breaking, which universally generates a gapless Goldstone mode for charge diffusion; and the complete breaking of strong symmetry, characterized by two Goldstone modes that govern order-parameter fluctuations and conserved-charge diffusion, respectively. This work establishes a theoretical framework for characterizing symmetry breaking in open quantum matter.

Anthony Brinton Wolbarst