Breaking symmetry

Detlef Dürr, Stefan Teufel

Cheng-Ju Lin, Liujun Zou

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

Maximilian Prüfer

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”.

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.