Daisuke Yoshioka | Searcharxiv

arXiv2004

Spontaneous Symmetry Breakings in $Z_2$ Gauge Theories for Doped Quantum Dimer and Eight-Vertex Models

Behavior of doped fermions in $Z_2$ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the $Z_2$ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically-ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped-fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.

cond-mat.str-el↗

arXiv2004

Néel-Dimer Transition in Antiferromagnetic Heisenberg Model and Deconfinement of Spinons at the Critical Point

Quantum phase transition from the Néel to the dimer states in an antiferromagnetic(AF) Heisenberg model on square lattice is studied. We introduce a control parameter $α$ for the exchange coupling which connects the Néel ($α=0$) and the dimer ($α=1$) states. We employ the $CP^1$ (the Schwinger boson) representation of the $s={1\over 2}$ spin operator and integrate out the half of the $CP^1$ variables at odd sites and we obtain a $CP^1$ nonlinear $σ$ model. The effective coupling constant is a function of $α$ and at $α=0$ the $CP^1$ model is in the ordered phase which corresponds to the Néel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of $α_C$ as $α$ increases. In the Néel state, the dynamical composite U(1) gauge field in the $CP^1$ model is in a Higgs phase and low-energy excitations are gapless spin wave. In the dimer phase, a confinement phase of the gauge theory is realized and low-energy excitations are $s=1$ magnons. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in 3 spatial dimensions, is realized and $s={1\over 2}$ spinons appear as low-energy excitations.

cond-mat.str-el↗