The quantum inverse scattering method is a means of finding exact solutions two-dimensional models in field theory and statistical physics (such as the sine-Gordon equation or non-linear Schrödinger equation). These are subject much attention amongst physicists mathematicians. present work an introduction to this important exciting area. It consists four parts. first deals with Bethe ansatz calculation physical quantities. authors then tackle before applying it second half book correlation...

The book contain detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well. Main Models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon Thiring models. Heisenberg Antiferromagnet Hubbard It is explained in detail, how to calculate correlation functions.

Using results on the scaling of energies with size system and principles conformal quantum field theory, we calculate asymptotics correlation functions for one-dimensional Hubbard model in repulsive regime presence an external magnetic field. The critical exponents are given terms a dressed charge matrix that is defined set integral equations obtained from Bethe-Ansatz solution model. An interpretation this thermodynamical coefficients given, several limiting cases considered.

We consider critical models in one dimension. study the ground state thermodynamic limit (infinite lattice). are interested an entropy of a subsystem. calculate part from space interval (0,x). At zero temperature it describes entanglement this with rest state. obtain explicit formula for subsystem at any temperature. our reproduces logarithmic formula, discovered by Vidal, Latorre, Rico, and Kitaev spin chains. prove means conformal field theory second law thermodynamics. Our is universal....

The quantum nonlinear Schrödinger equation (one dimensional Bose gas) is considered. Classification of representations Yangians with highest weight vector permits us to represent correlation function as a determinant Fredholm integral operator. This operator can be treated the Gelfand-Levitan for some new differential equation. These equations are written down in paper. They generalize fifth Painlève transcendent, which describe equal time, zero temperature an impenetrable gas. drive...

We consider the ground state of XY model on an infinite chain at zero temperature. Following Bennett, Bernstein, Popescu, and Schumacher we use entropy a sub-system as measure entanglement. Vidal, Latorre, Rico Kitaev conjectured that von Neumann large block neighboring spins approaches constant size increases. evaluated this limiting function anisotropy transverse magnetic field. used methods based integrable Fredholm operators Riemann-Hilbert problem. The is singular phase transitions.

We present a new model describing strongly correlated electrons on general d-dimensional lattice. It is an extended Hubbard and it contains the t-J as special case. The naturally describes local electron pairs, which can move coherently at arbitrary momentum. By using \ensuremath{\eta}-pairing mechanism we construct eigenstates of Hamiltonian with off-diagonal long-range order. In attractive case exact ground state superconducting in any number dimensions. On one-dimensional lattice, exactly...

We construct the enveloping fundamental spin model of t-J Hamiltonian using quantum-inverse-scattering method (QISM), and present all three possible algebraic Bethe Ansa$iuml---tze. Two solutions have been previously obtained in framework coordinate-space Ansatz by Sutherland Schlottmann Lai, whereas third solution is new. The formulation terms QISM enables us to derive explicit expressions for higher conservation laws.

We present a general method for the calculation of correlation functions in repulsive one-dimensional Hubbard model at less than half-filling magnetic field h. describe dependence critical exponents that drive their long-distance asymptotics on Coulomb coupling, density, and This can be described terms set coupled Bethe-Ansatz integral equations. It simplifies significantly strong-coupling limit, where we give explicit formulas field. In particular, find small functional h algebraic or...

The partition function of a six-vertex model with domain wall boundary conditions is considered on the finite lattice. authors show that satisfies recursive relation. They solve recursion relation by determinant formula. This gives representation for function. use Quantum Inverse Scattering Method (QISM).

The production of jets should allow testing the real-time response QCD vacuum disturbed by propagation high-momentum color charges. Addressing this problem theoretically requires a real-time, nonperturbative method. It is well known that Schwinger model [QED in (1+1) dimensions] shares many common properties with QCD, including confinement, chiral symmetry breaking, and existence fermion condensate. As step developing such an approach, we report here on fully quantum simulations massive...

Abstract Grover's algorithm solves the unstructured search problem. can find target state with certainty only if searching one out of four. Designing deterministic avoid any repetition algorithm, especially when is a subroutine in other algorithms. be phase oracle or diffusion operator delicately designed. The precision phases could A near‐deterministic quantum without design proposed. has same and operators as algorithm. One additional component rescaled operator. It acts partially on...

We address the question of dependence bulk free energy on boundary conditions for six-vertex model. Here we compare periodic and domain wall conditions. Using a determinant representation partition function with conditions, derive Toda differential equations solve them asymptotically in order to extract energy. find that it is different bears no simple relation The model closely related algebraic combinatorics (alternating sign matrices). This implies new results weighted counting large-size...