Related papers: The Non Linear Sigma Model and Spin Ladders
We construct a two-dimensional (2D) lattice model that is argued to realize a gapped chiral spin liquid with (Ising) non-Abelian topological order. The building blocks are spin-1/2 two-leg ladders with $SU(2)$-symmetric spin-spin…
We investigate the topological physics and the nonlinearity-induced trap phenomenon in a coupled system of pendulums. It is described by the dimerized sine-Gordon model, which is a combination of the sine-Gordon model and the…
In the present paper, we propose a mean field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean field level that ladders with even number legs open a energy gap in…
We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta-parameters in the lagrangian. They arise as invariant angle associated…
The higher-order corner modes for quantum anomalous Hall insulators in $C_3$ symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice…
We present preliminary numerical results from a lattice study of the two-dimensional O(3) non-linear sigma model. In the continuum this model possesses N=2 supersymmetry. The lattice formulation we use retains an exact (twisted)…
We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the…
We introduce a strategy to write down lattice models of spin rotational symmetric Hamiltonians with arbitrary spin-$S$ that are Marshall positive and can be simulated efficiently using world line Monte Carlo methods. As an application of…
We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A…
Supplementing the Heisenberg model with a Hubbard-commuting kinetic of electrons adds to its spectrum without interference. One consequence is the precise incorporation of canonical linear spin wave theory within the time-dependent…
Both the Haldane spin-$1$ chain and dimerized chains of spin-$1/2$ exhibit topologically protected edge states that are robust against specific perturbations. Recently, such spin chains have been specifically assembled on surfaces and we…
A model with a half boson degree of freedom per lattice site in one dimension is developed. The boson is protected from developing a gap by translation symmetry: while the left movers are at zero quasi-momentum, the associated right movers…
A field theory describing the low-energy, long-wavelength sector of an incommensurate, spiral magnetic phase is derived from a spin-fermion model that is commonly used as a microscopic model for high-temperature superconductors. After…
Infinite projected entangled pair states simulations of the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and 3-sublattice…
We write down a local $CP_1$ model involving two gauge fields, which is exactly equivalent to the O(3) $\sigma$ model with the Hopf term. We impose the $CP_1$ constraint by using the gaussian representation of the delta function. For the…
Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear…
In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been found before with standard discretizations and lattice spacings. Here the situation is analyzed further employing additional data for the step scaling function of…
We show that, in addition to SO(4), the Hubbard model at half filling on a bipartite lattice has a group of discrete symmetries and transformations. A unique Hubbard-Stratonovich decomposition of the interaction term, incorporating both…
Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor, next-nearest-neighbor and…
By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of $SU(M)$ Haldane-Shastry (HS) spin…