Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice

Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combined effect most visibly appears in the elementary excitation spectra. In contrast to the ground state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The threshold value of frustration that signals a transition from a classical ferrimagnetic state to a spiral state, decreases with dimerization, showing that dimerization further helps in the phase transition. The correlation length and sublattice magnetization decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic. The linear spin wave theory shows that in the case of a square lattice, dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition. It also shows that the transition to spiral state is inhibited in a square lattice beyond a certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

Intrinsic double-peak structure of the specific heat in low-dimensional quantum ferrimagnets

Motivated by recent magnetic measurements on A3Cu3(PO4)4 (A=Ca,Sr) and Cu(3-Clpy)2(N3)2 (3-Clpy=3-Chloropyridine), both of which behave like one-dimensional ferrimagnets, we extensively investigate the ferrimagnetic specific heat with particular emphasis on its double-peak structure. Developing a modified spin-wave theory, we reveal that ferromagnetic and antiferromagnetic dual features of ferrimagnets may potentially induce an extra low-temperature peak as well as a Schottky-type peak at mid temperatures in the specific heat.Comment: 5 pages, 6 figures embedded, Phys. Rev. B 65, 214418 (2002

Parametrization of the feedback Hamiltonian realizing a pure steady state

Feedback control is expected to considerably protect quantum states against decoherence caused by interaction between the system and environment. Especially, Markovian feedback scheme developed by Wiseman can modify the properties of decoherence and eventually recover the purity of the steadystate of the corresponding master equation. This paper provides a condition for which the modified master equation has a pure steady state. By applying this condition to a two-qubit system, we obtain a complete parametrization of the feedback Hamiltonian such that the steady state becomes a maximally entangled state.Comment: 4 page

Relevant gluonic energy scale of spontaneous chiral symmetry breaking from lattice QCD

We analyze which momentum component of the gluon field induces spontaneous chiral symmetry breaking in lattice QCD. After removing the high-momentum or low-momentum component of the gluon field, we calculate the chiral condensate and observe the roles of these momentum components. The chiral condensate is found to be drastically reduced by removing the zero-momentum gluon. The reduction is about 40% of the total in our calculation condition. The nonzero-momentum infrared gluon also has a sizable contribution to the chiral condensate. From the Banks-Casher relation, this result reflects the nontrivial relation between the infrared gluon and the zero-mode quark

Certifying isolated singular points and their multiplicity structure

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear instead of the quadratic increase of previous methods. The second construction gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root. We present a system of equations in the original variables plus a relatively small number of new vari-ables. We show that the roots of this new system include the original singular root but now with multiplicity one, and the new variables uniquely determine the multiplicity structure. Both constructions are "exact", meaning that they permit one to treat all conjugate roots simultaneously and can be used in certification procedures for singular roots and their multiplicity structure with respect to an exact rational polynomial system

Majorana-Like Modes of Light in a One-Dimensional Array of Nonlinear Cavities

The search for Majorana fermions in p-wave paired fermionic systems has recently moved to the forefront of condensed-matter research. Here we propose an alternative route and show theoretically that Majorana-like modes can be realized and probed in a driven-dissipative system of strongly correlated photons consisting of a chain of tunnel-coupled cavities, where p-wave pairing effectively arises from the interplay between strong on-site interactions and two-photon parametric driving. The nonlocal nature of these exotic modes could be demonstrated through cross-correlation measurements carried out at the ends of the chain---revealing a strong photon bunching signature---and their non-Abelian properties could be simulated through tunnel-braid operations.Comment: 5 pages, 2 figures; with Supplemental Material (12 pages

Ground State Property of an Alternating Spin Ladder Involving Two Kinds of Inter-Chain Interactions

The ground state property of the alternating spin ladder is studied in the case that the system involves an antiferromagnetic intra-chain interaction as well as two kinds of inter-chain interactions; one is between spins of the same magnitude and the other is between spins with different magnitudes. The calculation has been carried out by the exact diagonalization method. As a consequence of the competition among interactions, the system is revealed to show an interesting variety of phases in the ground state property. Its phase diagram is exhibited in the parameter space of the system. We find that, however small the total amount of the inter-chain interactions is, the ferrimagnetic ground state becomes unstable in a certain region. In this case, which of the ferrimagnetic and the singlet ground state to appear is determined only by the ratio between the inter-chain interactions regardless of their total amount. The nature of two phases appearing in the singlet region of the phase diagram and the type of the phase transition between them are also discussed. The results are ensured by comparing with those of obtained in other models which are contained in our model as special limiting cases.Comment: 12 pages, 9 PostScript figure

Simulating lattice gauge theories on a quantum computer

We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.Comment: 15 pages, 4 figures, 3 table