Degeneracy patterns in quantum mechanics stem from the system symmetries. In particular, the broken-symmetry phase in the well-known Lipkin-Meshkov-Glick (LMG) model is composed of doubly-degenerate states of different parity. In this work, we show that such doublets can exist even if parity is not conserved. For this purpose, our starting point is an anharmonic LMG Hamiltonian with a second-order ground-state quantum phase transition (GSQPT) and a rich spectrum, with two different excited-state quantum phase transitions. The inclusion in the Hamiltonian of a term inducing a first-order GSQPT breaks the parity symmetry but conserving the exponential degeneracy in the energy doublets. We demonstrate that this phenomenon can be traced back to the existence of a $\mathbb{Z}_2$ symmetry (reflection symmetry) in the system's classical limit phase space that leads to an anti-unitary $\mathbb{Z}_2$ symmetry in the quantum system.
Recently, a generalized Landau paradigm has been proposed, in which a broad class of"unconventional"phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such"topological"or"deconfined"tr...
We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called $S^1$-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such $S^1$-family...
The fate of average symmetry-protected topological (ASPT) states based on the one-dimensional cluster state is investigated by using the Choi mapping, namely, the doubled Hilbert-space formalism. By introducing two effective spins, $\tau$ and $\eta$, on each doubled rung, we obtain a transparent representation of the A...
In condensed matter physics, symmetry profoundly governs the fundamentals of topological matter. The emergence of new topological phase is typically linked to the enrichment of symmetries. Different parity-time symmetry relations (PT)2 = ± 1 distinguish between spinless and spinful physical systems. In spinless systems...
Xiao Xiang, Feng Gao, Cheng-Tai Hu et al.· npj Acoustics· 0 citations
Completeness is widely recognized in quantum information as an important property of a family of monotones, because it ensures that no information relevant to state conversion is lost. We show that completeness is also physically important in many-body systems: an incomplete measure of symmetry breaking can miss essent...
We investigate the basic symmetry rule for the particle permutation in superconducting (SC) pairing states by examining the numerical solution of the linearized Eliashberg equation for Sr$_2$RuO$_4$. We find that the general multi-band, frequency-dependent SC gap function does not simply transform to itself up to the m...
Chang-Youn Moon· 0 citations
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