Related papers: Prime Suspects in a Quantum Ladder
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
The idea of confinement states that in certain systems constituent particles can be discerned only indirectly being bound by an interaction whose strength increases with increasing particle separation. Though the most famous example is the…
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent $\alpha$. Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we…
Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an integer $N$, the test tries to find an…
We study spin-1/2 Heisenberg XXX antiferromagnet. The spectrum of the Hamiltonian was found by Hans Bethe in 1931. We study the probability of formation of ferromagnetic string in the antiferromagnetic ground state, which we call emptiness…
We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin $j=1$. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have…
We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…
The paper presents a computational study of the ground-state properties of a quantum nanomagnet possessing the shape of a finite two-legged ladder composed of 12 spins $S=1/2$. The system is described with isotropic quantum Heisenberg model…
We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…
We give criteria for oriented links to be periodic of prime order using the quantum $\mathrm{SL}(N)$-invariant. The criteria are based upon an observation on the linking number between a periodic knot and its axis of the rotation.
The implementation of a spin qubit in a quantum ring occupied by one or a few electrons is proposed. Quantum bit involves the Zeeman sublevels of the highest occupied orbital. Such a qubit can be initialized, addressed, manipulated, read…
A uniformly coupled double quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission…
We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two…
Strongly correlated quantum many-body systems at low dimension exhibit a wealth of phenomena, ranging from features of geometric frustration to signatures of symmetry-protected topological order. In suitable descriptions of such systems, it…
Motivated by the ability of triangular spin ladders to implement quantum information processing, we propose a type of such systems whose Hamiltonian includes the XX Heisenberg interaction on the rungs and DzyaloshinskiiMoriya (DM) coupling…
A large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete set of integrals of motion is constructed…
We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules…
A variational approach for constructing an effective particle description of the low-energy physics of one-dimensional quantum spin chains is presented. Based on the matrix product state formalism, we compute the one- and two-particle…