Related papers: Hamiltonian models of lattice fermions solvable by…
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,…
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in…
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The…
Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make…
We present a novel graph-theoretic approach to simplifying generic many-body Hamiltonians. Our primary result introduces a recursive twin-collapse algorithm, leveraging the identification and elimination of symmetric vertex pairs (twins),…
We report the study of phases and transitions of SU(N) Hofstadter-Hubbard model subject to commensurate magnetic field on the triangular lattice. At filling one fermion per site, for the number of fermion flavors 2 <= N <= 8, we identify…
A spin-$\frac{1}{2}$ Kitaev sublattice interacting with a subsystem of spinless fermions is studied on a honeycomb lattice when the fermion band is half filled. The model Hamiltonian describes a topological Kondo lattice with the Kitaev…
Recent research shows that the partition function for a class of models involving fermions can be written as a statistical mechanics of clusters with positive definite weights. This new representation of the model allows one to construct…
We investigate the ground state phase diagram of an extended Hubbard model with $\pi$-flux hopping term at half-filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of…
In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. With this formulation of the Kondo lattice, we study a spin chain coupled to two-dimensional Dirac conduction electrons. The spin…
The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used…
For Majorana-Wilson lattice fermions in two dimensions we derive a dimer representation. This is equivalent to Gattringer's loop representation, but is made exact here on the torus. A subsequent dual mapping leads to yet another…
Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from…
We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with…
We study the critical behavior of the three-dimensional (3D) Gross-Neveu (GN) model with $N_f$ Dirac fermionic flavors and quartic interactions, at the chiral ${\mathbb Z}_2$ transition in the massless ${\mathbb Z}_2$-symmetric limit. For…
A two-dimensional spin-up ideal Fermi gas interacting attractively with a spin-down impurity in the continuum undergoes, at zero temperature, a first-order phase transition from a polaron to a dimeron state. Here we study a similar system…
We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two…
The extended Hubbard model (EHM) describes fermions on a lattice coupled through on-site, $U$, and first-neighbor, $V$, interactions. In the context of high-$T_c$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel,…
We construct a family of rotationally invariant, local, S=1/2 Klein Hamiltonians on various lattices that exhibit ground state manifolds spanned by nearest-neighbor valence bond states. We show that with selected perturbations such models…
The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the…