Related papers: Fermionic observables in the transverse Ising chai…
We study the ground-state entanglement of two halves of a critical transverse Ising chain, separated by an interface defect. From the relation to a two-dimensional Ising model with a defect line we obtain an exact expression for the…
We study numerically the critical region and the disordered phase of the random transverse-field Ising chain. By using a mapping of Lieb, Schultz and Mattis to non-interacting fermions, we can obtain a numerically exact solution for rather…
This chapter is devoted to a discussion of quantum phase transitions in regularly alternating spin-1/2 Ising chain in a transverse field. After recalling some generally-known topics of the classical (temperature-driven) phase transition…
Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which…
We define an index for invertible phases of two-dimensional fermionic and bosonic quantum spin systems without any additional symmetry. Conjecturally, it provides a microscopic definition of an invariant related to the chiral central charge…
We consider the general $\mathbb{Z}_2$-symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and $\mathbb{Z}_n$-symmetric BBS $\tau^{(2)}$-model…
We study Nielsen complexity and Fubini-Study complexity for a class of exactly solvable one dimensional spin systems. Our examples include the transverse XY spin chain and its natural extensions, the quantum compass model with and without…
In this paper, we study the control theoretic properties of a couple of interacting spin 1's driven by an electro-magnetic field. In particular, we assume that it is possible to observe the expectation value of the total magnetization and…
The conjecture that the states of the fermionic quasi-particles in minimal conformal field theories are eigenstates of the integrals of motion to certain eigenvalues is checked and shown to be correct only for the Ising model.
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the…
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical…
We built a model where all spins are in interaction with each other via an antiferromagnetic Ising Hamiltonian. The geometry of such a model is a tetrahedron placed on a hypersphere in spaces of dimensions enclosed between 1 and 9. Due to…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Generalizations of oscillator and Coulomb models are discussed via introduction of holomorphic coordinates. Complex Euclidean analogue of the Smorodinsky-Winternitz system is introduced and studied. Complex projective analogue of…
We review the approach of generalized permutator to produce a class of integrable quantum Hamiltonians, as well as the technique of Sutherland species (SS) to map a subclass of it into solvable spinless fermions models. In particular, we…
The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types: homogeneous, periodically modulated and random.…
We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. These spin chains are defined with Gamma matrices and can be exactly solved by mapping to $n$ species of itinerant Majorana…