Gapless Condition Research Articles

Exact solution of a cluster model with next-nearest-neighbor interaction

Abstract A 1D cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a transformation obtained automatically from its interactions, which is an algebraic generalization of the Jordan–Wigner transformation. The gapless condition is expressed as a condition on the roots of a cubic equation, and the phase diagram is obtained exactly. We find that the distribution of roots for this algebraic equation determines the existence of long-range order, and we again obtain the ground-state phase diagram. We also derive the central charges of the corresponding conformal field theory. Finally, we note that our results are universally valid for an infinite number of solvable spin chains whose interactions obey the same algebraic relations.

Investigation of springback during electromagnetic-assisted bending of aluminium alloy sheet

Electromagnetic-assisted forming (EMAF) combining quasi-static stamping and electromagnetic forming (EMF) is a potential method for controlling the springback of aluminium alloy materials. In this study, to further promote the application of EMAF in the high-precision forming of aluminium alloy sheet parts, the springback during electromagnetic-assisted bending of aluminium alloy sheet was investigated using a custom-designed U-shaped bending tool with the optimised curved spiral coils. Two types of conditions to control springback were designed: gapless and gap conditions, and the springback under these conditions was studied both experimentally and using numerical simulations. In addition, the effects of the discharge parameters on springback were analysed. Finally, the mechanism for controlling springback under different forming conditions was revealed. The results showed that the efficiency of springback control was significantly higher under gap conditions compared with gapless condition. With increasing gap, the springback angle decreased, but negative springback easily occurred when using excessively wide gaps. As the discharge voltage or number of discharges increased, the tangential stress of the fillet area decreased, thereby reducing the springback angle. Stress oscillations under the gapless condition reduced the tangential stress of the fillet area to a certain extent, while inertial motions under gap conditions greatly reduced the tangential stress, which were the essential mechanism for the observed springback reduction.

The ω-SQUIPT as a tool to phase-engineer Josephson topological materials.

Multi-terminal superconducting Josephson junctions based on the proximity effect offer the opportunity to tailor non-trivial quantum states in nanoscale weak links. These structures can realize exotic topologies in several dimensions, for example, artificial topological superconductors that are able to support Majorana bound states, and pave the way to emerging quantum technologies and future quantum information schemes. Here we report the realization of a three-terminal Josephson interferometer based on a proximized nanosized weak link. Our tunnelling spectroscopy measurements reveal transitions between gapped (that is, insulating) and gapless (conducting) states that are controlled by the phase configuration of the three superconducting leads connected to the junction. We demonstrate the topological nature of these transitions: a gapless state necessarily occurs between two gapped states of different topological indices, in much the same way that the interface between two insulators of different topologies is necessarily conducting. The topological numbers that characterize such gapped states are given by superconducting phase windings over the two loops that form the Josephson interferometer. As these gapped states cannot be transformed to one another continuously without passing through a gapless condition, they are topologically protected. The same behaviour is found for all of the points of the weak link, confirming that this topology is a non-local property. Our observation of the gapless state is pivotal for enabling phase engineering of different and more sophisticated artificial topological materials.

Topological phase transitions driven by real next-nearest-neighbor hopping in cold fermi gases

The strength t′ of the next-nearest-neighbor (NNN) hopping in most realized square optical lattices is much smaller than that of the nearest-neighbor hopping, and is usually seen as zero. Recently, both experimental and theoretical works have shown that the magnitude of the NNN hopping can be tuned in a wide range by shaking the optical lattice. In this paper, we study the effect of the real NNN term on topological phase transitions of the cold fermi gases in a two-dimensional square anisotropic optical lattice. We investigate the gapless condition of the system and the topological phase symbolized by the TKNN number. For the real NNN hopping, there exists a critical point tc′ as a function of μ, when 0<t′<tc′, there are only non-Abelian topological phases which are indicted by an odd TKNN number, and when t′>tc′ , the Abelian topological phase appears and the zone of the phase will be widened with the increase of t′. By numerically diagonalizing the Hamiltonian in the real space, the corresponding edge states for different topological phase and Majorana zero modes are discussed.

Monotone Triangles and 312 Pattern Avoidance

We demonstrate a natural bijection between a subclass of alternating sign matrices (ASMs) defined by a condition on the corresponding monotone triangle which we call the gapless condition and a subclass of totally symmetric self-complementary plane partitions defined by a similar condition on the corresponding fundamental domains or Magog triangles. We prove that, when restricted to permutations, this class of ASMs reduces to 312-avoiding permutations. This leads us to generalize pattern avoidance on permutations to a family of words associated to ASMs, which we call Gog words. We translate the gapless condition on monotone triangles into a pattern avoidance-like condition on Gog words associated. We estimate the number of gapless monotone triangles using a bijection with $p$-branchings.

Phase diagram of the [formula omitted]– [formula omitted]-1–1 spin chain by the nonlinear σ model

We examine a periodic mixed spin chain with spin magnitudes 1 2 and 1 which are arrayed as 1 2 – 1 2 -1–1. The three independent parameters are ratios of the four exchange couplings. We determine phase boundaries in the parameter space by using the gapless condition which was previously derived by mapping a general inhomogeneous spin chain to the nonlinear σ model. We find two gapless boundaries separating three disordered phases. The features of the phases are explained in terms of singlet clusters.

Phase diagrams of mixed-spin chains with period 4 using the nonlinearσmodel

We study mixed quantum spin chains consisting of two kinds of spins with magnitudes, s_a and s_b. The spins are arrayed as s_a-s_a-s_b-s_b in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear $\sigma$ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear $\sigma$ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of s_a and s_b. We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.

NonlinearσModel for Inhomogeneous Spin Chains

We derive a nonlinear $\ensuremath{\sigma}$ model (NLSM) that represents antiferromagnetic Heisenberg spin chains with inhomogeneous spin magnitudes and inhomogeneous nearest-neighbor exchange constants arrayed in finite periods. The only restriction is that the average spin magnitude on a sublattice is the same as that on another sublattice. The NLSM yields the gapless condition in terms of the spin magnitudes and exchange constants. We apply this condition to several cases, including systems with impurities. The result shows that the spin gap persists, despite impurities, in many cases.

Time dependent theory of gapless d-wave superconductors: Application to the flux flow

Time-dependent equations for a d-wave superconductor are derived for temperatures close to Tcunder the gapless condition τΔ(T) « 1. They differ from the usual time-dependent Ginzburg–Landau (TDGL) theory by an additional term which describes a diffusive relaxation of nonequilibrium excitations. These equations are applied to the problem of flux flow. The longitudinal conductivity is found to differ considerably from the Bardeen and Stephen model; the implication of this result for resistive measurements of the upper critical field is discussed. The Hall conductivity, however, coincides with the usual TDGL expression.

Density of States and Hopping Conductivity in Nearly Metallic Polyacetylene

Abstract Nearly metallic polyacetylene doped to the level, y, of -0.01 to 0.05 acceptors or donors per carbon has a high, “nearly metallic” conductivity yet susceptibility very much less than the metallic value. We present here the results of an extensive study of the transport properties of this regime coordinated with magnetic, optical and structural experiments, using ClO4 − and l3 − doped (CH)x. We conclude that for all samples studied, the charge conduction is via three dimensional variable range hopping among states near the Fermi level, cF. The variation of the density of states, N(ϵ), near ϵF, is measured using susceptibility, and shown to determine the detailed transport behavior. Our results are in agreement with the transition to an incommensurate Peierls semiconductor for higher doping levels, with disorder leading to a gapless condition.