Search for symmetry breaking phases in strongly correlated systems

Bing Ye

Zeyu Liu, Langxuan Chen, Yuke Zhang +2 more

Symmetry breaking in quantum many-body systems is pivotal for understanding phase transitions, yet its extension to mixed states remains underexplored. The authors introduce the Wightman correlator as a diagnostic tool, demonstrating its equivalence to the fidelity correlator in identifying strong-to-weak symmetry breaking, with implications for analyzing complex quantum phases.

Xiaotian Zhang

Alex Zunger, Jia-Xin Xiong, John P. Perdew

Material scientists and condensed matter physicists have long been divided on the issue of choosing the conceptual framework for explaining why open-shell transition-metal oxides tend to be insulators, whereas otherwise successful theories such as DFT often predict them to be (false) metals. Strong correlation becomes the recommended medicine. We point out that strong correlation can be mitigated by allowing DFT to lower the energy by breaking structural, magnetic or dipolar symmetries. Such local motifs are observed experimentally by local probes beyond the 'average structure' determined by X-Ray diffraction. Observed broken symmetries can arise from slow fluctuations that persist over the observation time or longer. The surprising fact is that when symmetry breaking motifs are used as input to electronic structure calculations, false metals are converted into real insulators without the recommended medicine of strong correlation. Consistently, DFT calculations that show energy lowering symmetry breaking correct most cases where DFT, even with advanced exchange-correlation functionals, previously missed the correct metal vs insulator designation. Total energy calculations distinguish systems that support energy-lowering symmetry breaking from those that do not. This approach distinguishes between paramagnetic insulating and metallic phases and shows mass enhancement in Mott metals. The reason is that symmetry breaking removes many of the degeneracies that exist in a symmetry-unbroken system, reducing significantly the need for strong correlation. If one chooses to ignore symmetry breaking, the persistent degeneracies often call for strong correlation treatment. Thus, symmetry breaking transforms strong to normal correlation and false metals to true insulators. This view sheds light on the historic controversy between Mott and Slater that still reverberates today.

Ning G. Sun, Pengfei Zhang, Lei Feng

Symmetry breaking plays a central role in classifying the phases of quantum many-body systems. Recent developments have highlighted a novel symmetry-breaking pattern, in which the strong symmetry of a density matrix spontaneously breaks to the weak symmetry. This strong-to-weak symmetry breaking is typically detected using multireplica correlation functions, such as the Rényi-2 correlator. In this Letter, we propose a practical protocol for detecting strong-to-weak symmetry breaking in experiments using the randomized measurement toolbox. Our scheme involves collecting the results of random Pauli measurements for (i) the original quantum state and (ii) the quantum state after evolution with the charged operators. Based on the measurement results, with a large number of samples, we can obtain an unbiased estimate of the Rényi-2 correlator. With a small sample size, we can still provide an alternative approach to estimate the phase boundary to a decent accuracy. We perform numerical simulations of Ising chains with all-to-all decoherence as an exemplary demonstration. Our result opens the opportunity for the experimental studies of the novel quantum phases in mixed quantum states.