Application of a Two-Step Coupled Cluster Method to the Lipkin-Meshkov-Glick Model

Peter Babinec

Li-Jun Tian, Min-Min Ti, Xiang-Dong Zhai

We study the non-Markovianity of the single qubit system coupled with an isotropic Lipkin–Meshkov–Glick (LMG) model by an effective method proposed by Breuer et al . (Breuer H P and Piilo J 2009 Europhys. Lett. 85 5004). It is discovered that the non-Markovianity is concerned with the quantum phase transitions (QPTs). In the open system, we present that the strong coupling inside the bath and the strong interaction between the system and bath can enhance the degree of non-Markovianity. Moreover, the non-Markovianity is stronger and more sensitive for the bath in the symmetric phase than the symmetry broken phase.

G. Schalow, M. Yamamura

N. I. Robinson, R. F. Bishop, J. Arponen

Earlier papers in this series have shown how the extended coupled-cluster method (ECCM) provides a widely applicable biorthogonal formulation of quantum many-body and quantum field theory. Rules for calculating matrix elements of arbitrary operators have been formulated, and an exact description of the excited states has been given in terms of a generalized random-phase approximation for the many-body, quasilocal c-number (classical), ECCM cluster amplitudes which completely and exactly parametrize the system. The present paper introduces a variational functional in order to treat the excited states differently within the ECCM framework, so as to allow extra flexibility in the choice of approximation schemes. The method is tested on the SU(2) quasispin model of Lipkin, Meshkov, and Glick [Nucl. Phys. 62, 188 (1965); 62, 199 (1965)], which contains the spontaneous breakdown of parity, and which models a shape transition in finite atomic nuclei. The method very well describes both the ground and excited states of the model Hamiltonian over a broad range of coupling parameters on both sides of the critical value corresponding to the transition.

Janice D. Prie, Jay D. Mancini, Yuan Zhou +1 more

Isaac Hobday, P. D. Stevenson, James Benstead

Quantum computing can potentially provide advantages for specific computational tasks. The simulation of fermionic systems is one such task that lends itself well to quantum computation, with applications in nuclear physics and electronic systems. Here we present work in which we use a variance minimisation method to find the full spectrum of energy eigenvalues of the Lipkin-Meshkov-Glick model; an exactly-solvable nuclear shell model-type system. We perform these calculations using both quantum simulators and real quantum hardware accessed via IBM cloud-based quantum computers. Using these IBM quantum computers we are able to obtain all eigenvalues for the cases of three and seven fermions (nucleons) in the Lipkin-Meshkov-Glick model.