Related papers: A magnetic model with a possible Chern-Simons phas…
We introduce topological phases of matter defined by skyrmions in the ground state spin -- or pseudospin -- expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are…
We study the effect of a Chern-Simons term on the electrically charged and spinning solitons of several $U(1)$ gauged models in $2+1$ dimensions. These are vortices of complex scalar field theories, both with and without symmetry breaking…
The notion of {\em entanglement entropy} in quantum mechanical systems is an important quantity, which measures how much a physical state is entangled in a composite system. Mathematically, it measures how much the state vector is not…
The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a group-theoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory…
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as…
A Chern--Simons system in $2+1$ dimensions invariant under local Lorentz rotations, $SU(2)$ gauge transformations, and local $\mathcal{N}=2$ supersymmetry transformations is proposed. The field content is that of $(2+1)$-gravity plus an…
We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional $J_1 - J_2$ Heisenberg model. The ground states of this model are exactly obtained at a first order quantum phase transition between two regions…
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection,…
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting…
We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square…
Spin ice is a frustrated magnetic system that at low temperatures exhibits a Coulomb phase, a classical spin liquid with topological order and deconfined excitations. This work establishes the presence of a Coulomb phase with coexisting…
In three dimensional (3D) momentum space of solid crystal, a topological phase boundary separating the Chern insulating layers from normal insulating layers may exist, where the gap must be closed, resulting in a "Chern semi-metal" state…
We study the Hamiltonian describing two anyons moving in a plane in presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schr\"{o}dinger operator. We also discuss the…
In the quantum Hall regime, the longitudinal resistivity $\rho_{xx}$ plotted as a density--magnetic-field ($n_{2D}-B$) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands…
Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this…
In this article it is studied, at variational level, a mathematical setup given by the Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensions within the framework of dimensional reduced Ue(1)xUg(1) extended electromagnetism with…
We study the thermodynamics of degenerate electron and charged vector boson gases in very intense magnetic fields. In degenerate conditions of the electron gas, the pressure transverse to the magnetic field $B$ may vanish, leading to a…
We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian…
In a quantizing magnetic field, the chiral two-dimensional electron gas in Landau level $N=0$ of bilayer graphene goes through a series of phase transitions at integer filling factors $\nu \in \left[ -3,3\right] $ when the strength of an…
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. This paper is the first in a series where we…