Torus spectroscopy of the Gross-Neveu-Yukawa quantum field theory: Free Dirac versus chiral Ising fixed point

Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions

“…We leave the study of the effects of quantum fluctuations at this transition for future work. For 𝑁 = 2 on both lattices, we find the generalized antiferromagnet to be stable up to the large 𝐽/𝑡 limit, in agreement with previous works [52][53][54][55][56][57][58][59][60]. For this small value of 𝑁, there is therefore no transition towards dimerized order.…”

“…On the level of mean-field theory, this transition is, independently of the value of 𝑁, continuous. The presence of the generalized Néel antiferromagnet at intermediate to strong coupling and small 𝑁 is expected from the previous calculations for 𝑁 = 3 on the honeycomb lattice [32] and 𝑁 = 2 on both lattices [52][53][54][55][56][57][58][59][60]. For general 𝑁, the spontaneous symmetry breaking of this antiferromagnetic state is "maximal" in the sense that the eigenvalues of 𝜙 𝑎𝑏 𝐿 𝑎𝑏 come in 𝑁/2 identical pairs ± φ, where • corresponds to the floor function.…”

“…In the SO(2) model, the two Majorana modes can be combined into a single complex fermion 𝑓 𝑖 = (𝑐 1 𝑖 + i𝑐 2 𝑖 )/2. In this representation, the SO(2) Majorana-Hubbard Hamiltonian describes a model of spinless complex fermions subject to nearest-neighbor repulsion [32], which has been intensely studied previously on both the honeycomb and 𝜋-flux lattices [52][53][54][55][56][57][58][59][60]. The mapping can be understood as a consequence of the fact that SO(2) has only a single generator 𝐿 12 = 𝜎 𝑦 , the antisymmetric 2 × 2 Pauli matrix, leading to a density-density form of the interaction.…”

Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class

“…This would imply that M is robust to weak interactions V V c , based on the assumption that v F in our model is also renormalized in a similar manner to those in the Hubbard model. On the other hand, another theoretical study proposed that v F increases by the interaction V < V c in the t-V model 57 . Based on this result, we suppose that the increase of v F tends to enhance M but at the same time the magnetic catalysis generating fermion mass does to suppress it, and as a result of this cancellation, M remains almost unchanged for small V .…”

“…In D = 1+1 dimensions, the Casimir amplitude is written as Φ(0) ∼ cv with a boundary condition dependent coefficient, where v is the speed of light (velocity of excitations) and c is the central charge of the underlying conformal field theory [72][73][74] . Generalizations to higher dimensional systems have been first discussed for a cylinderical spacetime geometry 72 and also recently examined in torus and infinite systems 57,75,76 . It was proposed that the Casimir amplitude in a (2 + 1)-dimensional torus system is decomposed as Φtorus (0) = C torus v, where C torus contains some universal information of the underlying field theory.…”