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An electronic nematic phase can be classified by a spontaneously broken discrete rotational symmetry of a host lattice. In a square lattice, there are two distinct nematic phases. The parallel nematic phase breaks $x$ and $y$ symmetry, while the diagonal nematic phase breaks the diagonal $(x+y)$ and anti-diagonal $(x-y)$ symmetry. We investigate the interplay between the parallel and diagonal nematic orders using mean field theory. We found that the nematic phases compete with each other, while they coexist in a finite window of parameter space. The quantum critical point between the diagonal nematic and isotropic phases exists, and its location in a phase diagram depends on the topology of the Fermi surface. We discuss the implication of our results in the context of neutron scattering and Raman spectroscopy measurements on La$_{2-x}$Sr$_x$CuO$_4$.
We establish the qualitative behavior of the incommensurability $epsilon$, optimal domain wall filling $ u$ and chemical potential $mu$ for increasing doping by a systematic slave-boson study of an array of vertical stripes separated by up to $d=11$
We study the layered $J_1$-$J_2$ classical Heisenberg model on the square lattice using a self-consistent bond theory. We derive the phase diagram for fixed $J_1$ as a function of temperature $T$, $J_2$ and interplane coupling $J_z$. Broad regions of
The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ ulesssim 1/6$, experi
Systems with strong electron-phonon couplings typically exhibit various forms of charge order, while strong electron-electron interactions lead to magnetism. We use determinant quantum Monte Carlo (DQMC) calculations to solve a model on a square latt
The classification and lattice model construction of symmetry protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed point wave function construction of fermio