Theoretical Physics Seminar

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Strongly symmetric interactions, i.e. those that preserve a system's symmetry, however, can enforce non-trivial quantum entanglement patterns. We provide three examples of this phenomenon.

First, we show that for a unital quantum channel that is ‘strongly symmetric’ with a global on-site non-Abelian symmetry, the unique steady state in certain symmetry sectors can be highly entangled. We show that the entanglement of formation and distillation in the such states are exactly computable and equal for any bipartition. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. SU(2)), their bipartite entanglement of formation scales logarithmically ∼ log N with the number of qudits N. [1]

Second, we show that such highly entangled steady states can also arise in models with unconventional symmetries such as the Temperley Lieb algebra, which exhibits quantum Hilbert space fragmentation. These states exhibit a surprising entanglement structure: the logarithmic negativity for equal-size bipartitions scales with the volume of the system, while the entanglement of formation, squashed entanglement, entanglement cost, and distillable entanglement exhibit subextensive scaling. [2]

Third, we study strongly symmetric Gibbs states, or the canonical ensemble, at finite temperatures for generic local Hamiltonians with global on-site symmetries. Unlike the usual Gibbs state, we prove that the canonical ensemble remains entangled at all finite temperatures even for Abelian symmetries, and has no sudden death of entanglement. [3]

[1] "Symmetry enforced entanglement in maximally mixed states" - Amin Moharramipour, Leonardo A. Lessa, Chong Wang, Timothy H. Hsieh, SS (PRX Quantum 5, 040336).

[2] "Entanglement cost hierarchies in quantum fragmented mixed states" - SS, Yahui Li, Pablo Sala. (ArXiv:2506.04637).

[3] "Symmetry enforce​s entanglement at high temperatures" - Amirreza Negari, Leonardo A. Lessa, SS. (2508.20166)