Related papers: Fermionic Lieb-Schultz-Mattis Theorems and Weak Sy…
Symmetry-Protected Topological (SPT) phases are gapped phases of quantum matter protected by global symmetries that cannot be adiabatically deformed to a trivial phase without breaking symmetry. In this work, we show that, for several SPT…
We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G,…
We investigate the properties of Lindblad equations on $d$-dimensional lattices supporting a unique steady-state configuration. We consider the case of a time evolution weakly symmetric under the action of a finite group $G$, which is also…
We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and…
We review the current status of the long-term programme of numerical investigation of $Sp(2N)$ gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for…
We consider renormalizable Standard-Model extensions that violate Lorentz symmetry at high energies, but preserve CPT, and do not contain elementary scalar fields. A Nambu--Jona-Lasinio mechanism gives masses to fermions and gauge bosons,…
We investigate a family of lattice models with manifest N=2 supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special…
We consider a two dimensional model of non-interacting chains of spinless fermions weakly coupled via a small inter-chain hopping and a repulsive inter-chain interaction. The phase diagram of this model has a surprising feature: an abrupt…
Symmetry protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For non-interacting fermion systems with time…
Numerous efforts have been devoted to reveal exotic semimetallic phases with topologically non-trivial bulk and/or surface states in materials with strong spin-orbit coupling. In particular, semimetals with nodal line Fermi surface (FS)…
Recent experiments on triangular lattice organic Mott insulators have found evidence for a 2D spin liquid in proximity to the metal-insulator transition. A Gutzwiller wavefunction study of the triangular lattice Heisenberg model with…
We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and $2\pi$-flux topological semimetal in different parameter ranges. We show that the band…
The Lieb-Shultz-Mattis theorem is extended to Heisenberg chains with long-range interactions. We prove that the half-integer spin chain has no gap, if it possesses unique ground state and the exchange decays faster than the inverse-square…
Motivated by ongoing interest in the universal behaviour of the Hubbard model of spinning electrons on honeycomb and $\pi$-flux lattices at the semi-metal -- Mott insulator phase transition, we formulate the \threeD~chiral Heisenberg model,…
Using the 2D Jordan-Wigner transformation we reformulate the square-lattice s=1/2 XY (XZ) model in terms of noninteracting spinless fermions and examine the ground-state and thermodynamic properties of this spin system. We consider the…
Nonlinear $\sigma$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the…
Using field-theoretic techniques, we study the $SU(3)$ analogue of anti-ferromagnetic Heisenberg spin model on the triangular lattice putting the $p$-box symmetric representation on each site. Taking the large-$p$ limit, we show that the…
We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites, N -> \infty. For spin systems, these are product states, a fact that follows directly from the quantum…
Quantum fluctuations of the N\'eel state of the square lattice antiferromagnet are usually described by a $\mathbb{CP}^1$ theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory…
We study various Mott insulating phases of interacting spin-3/2 fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two…