Phase transition in a fermion model

R. Citro

Hou-Ji Shao, Yu‐Xuan Wang, De-Zhi Zhu +9 more

Tao Yang, Bangming Wang, Peng Song +2 more

Quantum phase transitions in quantum magnets constitute an important field that has attracted great interests. Although a variety of analytic and numerical methods have been introduced in this direction, faithful fermionic descriptions are still desired because they can transform the spin models to a form tractable by conventional many-body techniques, yielding more transparent physical pictures. We generalize the Chern-Simons fermionization approach and apply it to the XXZ quantum magnets. After fermionzation, the Ising interaction of the XXZ spin model leads to a fermion-fermion interaction. We show that the additional fermion-fermion interaction generates an interesting phase transition between two fermionic ordered states, i.e., the Chern-Simons superconductor and the Chern-Simons exciton insulator. We also demonstrate that this transition in the fermionic language essentially describes the quantum phase transition between the planar and out-of-plane N\'eel orders in the spin picture. The fermionic mean-field theory further leads to a nonlinear $\ensuremath{\sigma}$ model that describes the quantum phase transition, which is further supported by our density matrix renormalization group calculations in the original spin model. Our work introduces a fermionic interpretation of quantum phase transitions and advances the existing knowledge of quantum magnets.

Виктор Павлович Маслов

Paweł Jakubczyk

Samuel Warren, LeeAnn M. Sager-Smith, David A. Mazziotti

Quantum states of a novel Bose-Einstein condensate, in which both fermion-pair and exciton condensations are simultaneously present, have recently been realized theoretically in a model Hamiltonian system. Here we identify quantum phase transitions in that model between fermion-pair and exciton condensations based on a geometric analysis of the convex set of ground-state two-particle reduced density matrices (2-RDMs). The 2-RDM set provides a finite representation of the infinite parameter space of Hamiltonians that readily reveals a fermion-pair condensate phase and two distinct exciton condensate phases, as well as the emergence of first- and second-order phase transitions as the particle number of the system is increased. The set, furthermore, shows that the fermion-exciton condensate (FEC) lies along the second-order phase transition between the exciton and fermion-pair condensate phases. The detailed information about the exciton and fermion-pair phases, the forces behind these phases, as well as their associated transitions provides additional insight into the formation of the FEC condensate, which we anticipate will prove useful in its experimental realization.