The phenomenon of quantum many-body scars has received widespread attention both in theoretical and experimental physics in recent years due to its unique physical properties. In this paper, based on the su(2) algebraic relations, we propose a general method for constructing scar models by combining simple modules. This allows us to investigate many-body scar phenomena in high-spin systems. We numerically verify the thermalization and nonintegrability of this model and demonstrate the dynamical properties of the scar states. We also provide a theoretical analysis of the properties of these scar states. For spin-1 case, we find that our 1D chain model reduces to the famous PXP model [C. J. Turner et al., Phys. Rev. B 98, 155134 (2018)] under special parameter conditions. In addition, due to the continuous tunability of the parameters, our model also enables us to investigate the transitions of quantum many-body scar phenomena from nonintegrable to integrable system.
Abstract We study the one-dimensional Fermi gas subject to dissipative reactions. The dynamics is governed by the quantum master equation, where the Hamiltonian describes coherent motion of the particles, while dissipation accounts for irreversible reactions. For lattice one-dimensional fermionic systems, emergent critical behavior has been found in the dynamics in the reaction-limited regime of weak dissipation. Here, we address the question whether such features are present also in a gas in continuum space. We do this in the weakly dissipative regime by applying the time-dependent generalized Gibbs ensemble method. We show that for two body 2 A → ∅ and three 3 A → ∅ body annihilation, as well as for coagulation A + A → A , the density features an asymptotic algebraic decay in time akin to the lattice problem. In all the cases, we find that upon increasing the temperature of the initial state the density decay accelerates, but the asymptotic algebraic decay exponents are not affected. We eventually consider the competition between branching A → A + A and the decay processes A → ∅ and 2 A → ∅ . We find a second-order absorbing-state phase transition in the mean-field directed percolation universality class. This analysis shows that emergent behavior observed in lattice quantum reaction-diffusion systems is present also in continuum space, where it may be probed using ultra-cold atomic physics.
In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented. It includes the Smorodinsky-Winternitz potentials I-II (the Holt potential), the Fokas-Lagerstrom model, the 3-body Calogero and Wolfes (equivalently,
G2 rational, or
I6) models, and the Tremblay-Turbiner-Winternitz (TTW) system with integer index
k. It is shown that all of them are exactly-solvable, thus, confirming the Montreal conjecture (2001); they admit algebraic forms for the Hamiltonian and both integrals (all three can be written as differential operators with polynomial coefficients without a constant term), they have polynomial eigenfunctions with the invariants of the discrete symmetry group of invariance taken as variables, they have hidden (Lie) algebraic structure
g(k) with various
k, and they possess a (finite order) polynomial algebras of integrals. Each model is characterized by infinitely-many finite-dimensional invariant subspaces, which form the infinite flag. Each subspace coincides with the finite-dimensional representation space of the algebra
g(k) for a certain
k. In all presented cases the algebra of integrals is a 4-generated
(H,I1,I2,I12≡[I1,I2]) infinite-dimensional algebra of ordered monomials of degrees 2,3,4,5, which is a subalgebra of the universal enveloping algebra of the hidden algebra.