Boundary correlation function of fixed-to-free bcc operators in square-lattice Ising model

We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using $2\times2$ block Toeplitz determinants. We show that these can be transformed into a scalar Toeplitz determinant when the size of the matrix is even. To know the asymptotic behavior of the correlation function at large distance we calculate the asymptotic behavior of this scalar Toeplitz determinant using the Szeg\"o's theorem and the Fisher-Hartwig theorem. At the critical temperature we confirm the power-law behavior of the correlation function predicted by conformal field theory

Spin Chains as Perfect Quantum State Mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the text, one new reference. Accepted by Phys. Rev. A (Rapid Communications

Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases

The real-space renormalization group (RG) treatment of random transverse-field Ising spin chains by Fisher ({\it Phys. Rev. B{\bf 51}, 6411 (1995)}) has been extended into the strongly ordered and strongly disordered Griffiths phases and asymptotically exact results are obtained. In the non-critical region the asymmetry of the renormalization of the couplings and the transverse fields is related to a non-linear quantum control parameter, $\Delta$, which is a natural measure of the distance from the quantum critical point. $\Delta$, which is found to stay invariant along the RG trajectories and has been expressed by the initial disorder distributions, stands in the singularity exponents of different physical quantities (magnetization, susceptibility, specific heat, etc), which are exactly calculated. In this way we have observed a weak-universality scenario: the Griffiths-McCoy singularities does not depend on the form of the disorder, provided the non-linear quantum control parameter has the same value. The exact scaling function of the magnetization with a small applied magnetic field is calculated and the critical point magnetization singularity is determined in a simple, direct way.Comment: 11 page

Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain

We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the non-linear susceptibility, higher excitations and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the average energy-density autocorrelations decay with another exponent as [G^e]_av(t)~t^{-2-1/z}.Comment: 8 pages RevTeX, 8 eps-figures include

Painlev\'e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point

We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field $h_c$ (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra.Comment: 10 pages, LaTeX2

Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder

The Random Transverse Field Ising Chain is the simplest disordered model presenting a quantum phase transition at T=0. We compare analytically its finite-size scaling properties in two different ensembles for the disorder (i) the canonical ensemble, where the disorder variables are independent (ii) the microcanonical ensemble, where there exists a global constraint on the disorder variables. The observables under study are the surface magnetization, the correlation of the two surface magnetizations, the gap and the end-to-end spin-spin correlation $C(L)$ for a chain of length $L$. At criticality, each observable decays typically as $e^{- w \sqrt{L}}$ in both ensembles, but the probability distributions of the rescaled variable $w$ are different in the two ensembles, in particular in their asymptotic behaviors. As a consequence, the dependence in $L$ of averaged observables differ in the two ensembles. For instance, the correlation $C(L)$ decays algebraically as 1/L in the canonical ensemble, but sub-exponentially as $e^{-c L^{1/3}}$ in the microcanonical ensemble. Off criticality, probability distributions of rescaled variables are governed by the critical exponent $\nu=2$ in both ensembles, but the following observables are governed by the exponent $\tilde \nu=1$ in the microcanonical ensemble, instead of the exponent $\nu=2$ in the canonical ensemble (a) in the disordered phase : the averaged surface magnetization, the averaged correlation of the two surface magnetizations and the averaged end-to-end spin-spin correlation (b) in the ordered phase : the averaged gap. In conclusion, the measure of the rare events that dominate various averaged observables can be very sensitive to the microcanonical constraint.Comment: 24 page

Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition.Comment: 4 pages RevTeX, 3 eps-figures include

Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include

Dynamic Scaling in Diluted Systems Phase Transitions: Deactivation trough Thermal Dilution

Activated scaling is confirmed to hold in transverse field induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold but well bellow and above it including the Griffiths-McCoy phase. A novel deactivation phenomena in the Griffiths-McCoy phase is observed using a thermal (in contrast to random) dilution of the system.Comment: 4 pages, 4 figures, RevTe

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657