Field-induced nonmagnetic impurities interaction in the quantum Ising chain

We study static vacancies on a ferromagnetic spin-1/2 chain described by the transverse Ising model with second neighbor interactions at zero temperature. Using exact diagonalization techniques and applying a finite-size scaling approach, it is found that a strong magnetic field induces an effective potential of interaction between two vacancies that is attractive.     

Enhancement of next-nearest-neighbouring entanglement in quantum Ising spin chain

Using the method of the Jordan--Wigner transformation for solving different spin--spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.     

Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field Γ. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.     

High temperature limit of the order parameter correlation functions in the quantum Ising model

In this paper we use the exact results for the anisotropic two-dimensional Ising model obtained by Bugrii and Lisovyy [A.I. Bugrii, O.O. Lisovyy, Theor. Math. Phys. 140 (2004) 987] to derive the expressions for dynamical correlation functions for the quantum Ising model in one dimension at high temperatures.     

Order parameter to characterize valence-bond-solid states in quantum spin chains

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method.     

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is $\text{1}\text{2}\text{Σ}{}_{\mathrm{l}}\text{{σ}{}_{\mathrm{l}}{}^{\mathrm{x}}\text{σ}{}_{\mathrm{l+1}}{}^{\mathrm{x}}\text{?σ}{}_{\mathrm{l}}{}^{\mathrm{z}}\text{}}$. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n. The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.     

Anomalous dynamics in the Ising chain

We analyze a 1D Ising system with anomalous distributions of nearest neighbor interactions and show that the single-spin-flip dynamics exhibit breakdown of dynamic scaling. The results are obtained by a real-space numerical method applied to the exact equations of motion and they may be explained by domain wall motion arguments reformulated in terms of extreme value statistics.     

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n ₀ (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n ₀ increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n ₀<10, while quantum fluctuations in the phase are significant when n ₀<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n ₀ using the method of functional integration. Zh. éksp. Teor. Fiz. 113, 261–277 (January 1998)     

Conformal invariance and the critical behavior of the tripletXY quantum chain

We introduce and study the critical properties of the tripletXY quantum chain. This system is described in terms of three-spin interactions and is the generalization of the standardXY quantum chain. We show that this model, with periodic boundaries, has a local gauge invariance and can be described by the composition of two triplet Ising models, with general toroidal boundary conditions. From this composition the phase diagram as well the conformai anomaly and critical exponents are determined by exploring their relations with the mass gap amplitudes predicted by conformai invariance.     

Exact universal amplitude ratios for two-dimensional Ising models and a quantum spin chain

Let f(N) and xi(-1)(N) represent, respectively, the free energy per spin and the inverse spin-spin correlation length of the critical Ising model on a N x infinity lattice, with f(N)-->f(infinity) as N-->infinity. We obtain analytic expressions for a(k) and b(k) in the expansions N( f(N)-f(infinity)) = SUM (k = 1)(infinity)a(k)/N(2k-1) and xi(-1)(N) = SUM (k = 1)(infinity)b(k)/N(2k-1) for square, honeycomb, and plane-triangular lattices, and find that b(k)/a(k) = (2(2k)-1)/(2(2k-1)-1) for all of these lattices, i.e., the amplitude ratio b(k)/a(k) is universal. We also obtain similar results for a critical quantum spin chain and find that such results could be understood from a perturbated conformal field theory.     

Quantum quench in the transverse-field Ising chain

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.     

Order parameter criticality of the d = 3 random-field Ising antiferromagnet Fe0.85Zn0.15F2

The critical exponent beta=0.16+/-0.02 for the random-field Ising model order parameter is determined using extinction-free magnetic x-ray scattering for Fe0.85Zn0.15F2 in magnetic fields of 10 and 11 T. The observed value is consistent with other experimental random-field critical exponents, but disagrees sharply with Monte Carlo and exact ground state calculations on finite-sized systems.